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Introduction           Model          AAT             Experiments and Results   Conclusions




               Efficient Sharing of Conflicting Opinions with
                         Minimal Communication
                      in Large Decentralised Teams

               Oleksandr Pryymak, Alex Rogers and Nicholas R. Jennings

                                 University of Southampton
                               {op08r,acr,nrj}@ecs.soton.ac.uk


                                      July 20, 2011



                                                                                      0 / 19
Introduction   Model       AAT         Experiments and Results   Conclusions



Disaster response and large decentralised teams
                       2010, Haiti earthquake – Citizen and public
                       news reporting, plotted on an online map
                       (Ushahidi).




                                                                       1 / 19
Introduction   Model       AAT         Experiments and Results   Conclusions



Disaster response and large decentralised teams
                       2010, Haiti earthquake – Citizen and public
                       news reporting, plotted on an online map
                       (Ushahidi).
                       2010, Chile earthquake – Twitter is one of
                       the speediest, albeit not the most accurate,
                       sources of real-time information (France24).




                                                                       1 / 19
Introduction   Model       AAT         Experiments and Results   Conclusions



Disaster response and large decentralised teams
                       2010, Haiti earthquake – Citizen and public
                       news reporting, plotted on an online map
                       (Ushahidi).
                       2010, Chile earthquake – Twitter is one of
                       the speediest, albeit not the most accurate,
                       sources of real-time information (France24).
                           Large teams of individuals




                                                                       1 / 19
Introduction   Model       AAT         Experiments and Results   Conclusions



Disaster response and large decentralised teams
                       2010, Haiti earthquake – Citizen and public
                       news reporting, plotted on an online map
                       (Ushahidi).
                       2010, Chile earthquake – Twitter is one of
                       the speediest, albeit not the most accurate,
                       sources of real-time information (France24).
                           Large teams of individuals
                           Decentralised




                                                                       1 / 19
Introduction   Model       AAT         Experiments and Results   Conclusions



Disaster response and large decentralised teams
                       2010, Haiti earthquake – Citizen and public
                       news reporting, plotted on an online map
                       (Ushahidi).
                       2010, Chile earthquake – Twitter is one of
                       the speediest, albeit not the most accurate,
                       sources of real-time information (France24).
                           Large teams of individuals
                           Decentralised
                           Not every individual can make an
                           observation




                                                                       1 / 19
Introduction   Model       AAT         Experiments and Results   Conclusions



Disaster response and large decentralised teams
                       2010, Haiti earthquake – Citizen and public
                       news reporting, plotted on an online map
                       (Ushahidi).
                       2010, Chile earthquake – Twitter is one of
                       the speediest, albeit not the most accurate,
                       sources of real-time information (France24).
                           Large teams of individuals
                           Decentralised
                           Not every individual can make an
                           observation
                           Observations are uncertain and conflicting




                                                                       1 / 19
Introduction   Model       AAT         Experiments and Results   Conclusions



Disaster response and large decentralised teams
                       2010, Haiti earthquake – Citizen and public
                       news reporting, plotted on an online map
                       (Ushahidi).
                       2010, Chile earthquake – Twitter is one of
                       the speediest, albeit not the most accurate,
                       sources of real-time information (France24).
                           Large teams of individuals
                           Decentralised
                           Not every individual can make an
                           observation
                           Observations are uncertain and conflicting
                           Individuals share opinions without
                           supporting information

                                                                       1 / 19
Introduction      Model       AAT         Experiments and Results   Conclusions



Disaster response and large decentralised teams
                          2010, Haiti earthquake – Citizen and public
                          news reporting, plotted on an online map
                          (Ushahidi).
                          2010, Chile earthquake – Twitter is one of
                          the speediest, albeit not the most accurate,
                          sources of real-time information (France24).
                              Large teams of individuals
                              Decentralised
                              Not every individual can make an
                              observation
                              Observations are uncertain and conflicting
                              Individuals share opinions without
                              supporting information
       How opinions are shared and how to improve their accuracy?
                                                                          1 / 19
Introduction   Model   AAT      Experiments and Results   Conclusions



How opinions are shared – Can we trust what we share?




                                                                2 / 19
Introduction           Model        AAT          Experiments and Results   Conclusions



How opinions are shared – Can we trust what we share?




               Opinions are shared in cascades (avalanches)

                                                                                 2 / 19
Introduction           Model        AAT          Experiments and Results   Conclusions



How opinions are shared – Can we trust what we share?
                                             Can we trust what we share?




               Opinions are shared in cascades (avalanches)

                                                                                 2 / 19
Introduction           Model        AAT          Experiments and Results       Conclusions



How opinions are shared – Can we trust what we share?
                                             Can we trust what we share?
                                             Chile’10 : yes / no (Mendoza et al.
                                             2010)




               Opinions are shared in cascades (avalanches)

                                                                                     2 / 19
Introduction           Model        AAT          Experiments and Results       Conclusions



How opinions are shared – Can we trust what we share?
                                             Can we trust what we share?
                                             Chile’10 : yes / no (Mendoza et al.
                                             2010)
                                                  Santiago airport is closed
                                                  Fire at the University of
                                                  Conceptcion
                                                  Looting in Conceptcion




               Opinions are shared in cascades (avalanches)

                                                                                     2 / 19
Introduction           Model        AAT          Experiments and Results       Conclusions



How opinions are shared – Can we trust what we share?
                                             Can we trust what we share?
                                             Chile’10 : yes / no (Mendoza et al.
                                             2010)
                                                  Santiago airport is closed
                                                  Fire at the University of
                                                  Conceptcion
                                                  Looting in Conceptcion
                                                  Looting in Santiago
                                                  Tsunami warning
                                                  Active volcano




               Opinions are shared in cascades (avalanches)

                                                                                     2 / 19
Introduction           Model        AAT          Experiments and Results       Conclusions



How opinions are shared – Can we trust what we share?
                                             Can we trust what we share?
                                             Chile’10 : yes / no (Mendoza et al.
                                             2010)
                                                  Santiago airport is closed
                                                  Fire at the University of
                                                  Conceptcion
                                                  Looting in Conceptcion
                                                  Looting in Santiago
                                                  Tsunami warning
                                                  Active volcano




               Opinions are shared in cascades (avalanches)
               Even in cooperative settings opinions might be incorrect
                                                                                     2 / 19
Introduction          Model          AAT           Experiments and Results   Conclusions



Problem of Forming a Correct Opinion
               How do agents make a decision which opinion is correct?
                   based on own priors, observations
                   based on information from others




                                                                                   3 / 19
Introduction          Model           AAT            Experiments and Results   Conclusions



Problem of Forming a Correct Opinion
               How do agents make a decision which opinion is correct?
                   based on own priors, observations
                   based on information from others
                        by analysing communicated information
                        reaching agreements interactivity with others




                                                                                     3 / 19
Introduction           Model           AAT             Experiments and Results   Conclusions



Problem of Forming a Correct Opinion
               How do agents make a decision which opinion is correct?
                    based on own priors, observations
                    based on information from others
                         by analysing communicated information
                         reaching agreements interactivity with others

       The Problem
                                        However, if:
               agents’ processing abilities are limited
               communication is strictly limited to opinion sharing




                                                                                       3 / 19
Introduction           Model           AAT             Experiments and Results   Conclusions



Problem of Forming a Correct Opinion
               How do agents make a decision which opinion is correct?
                    based on own priors, observations
                    based on information from others
                         by analysing communicated information
                         reaching agreements interactivity with others

       The Problem
                                        However, if:
               agents’ processing abilities are limited
               communication is strictly limited to opinion sharing

       The Solution
       Agents have to exploit properties of opinion sharing dynamics, and
       filter out incorrect opinions in the sharing process


                                                                                       3 / 19
Introduction           Model           AAT             Experiments and Results   Conclusions



Problem of Forming a Correct Opinion
               How do agents make a decision which opinion is correct?
                    based on own priors, observations
                    based on information from others
                         by analysing communicated information
                         reaching agreements interactivity with others

       The Problem
                                        However, if:
               agents’ processing abilities are limited
               communication is strictly limited to opinion sharing

       The Solution
       Agents have to exploit properties of opinion sharing dynamics, and
       filter out incorrect opinions in the sharing process

       How to find such settings by independent actions of the agents?
                                                                                       3 / 19
Introduction           Model        AAT         Experiments and Results   Conclusions



Outline




       Remaining sections:
          1    Model of opinion sharing
          2    Existing message-passing algorithm
          3    Our algorithm based on independent actions
          4    Evaluation




                                                                                4 / 19
Introduction   Model   AAT   Experiments and Results   Conclusions



Model – an Agent




                                         Agent




                                                             5 / 19
Introduction   Model          AAT   Experiments and Results   Conclusions



Model – an Agent

                   Will it rain                Subject of
                   tonight?                    interest




                                                Agent




                                                                    5 / 19
Introduction        Model          AAT       Experiments and Results   Conclusions



Model – an Agent

                        Will it rain                    Subject of
                        tonight?                        interest

               No     Don't know       Yes              Opinion

                                                         Agent




                                                                             5 / 19
Introduction        Model          AAT       Experiments and Results   Conclusions



Model – an Agent

                        Will it rain                    Subject of
                        tonight?                        interest

               No     Don't know       Yes              Opinion

                                                         Agent




                                                                             5 / 19
Introduction            Model           AAT          Experiments and Results   Conclusions



Model – an Agent

                            Will it rain                        Subject of
                            tonight?                            interest

                   No     Don't know       Yes                  Opinion

                                                                 Agent


                                                                 Belief
               0                Prior            1




                                                                                     5 / 19
Introduction            Model           AAT          Experiments and Results    Conclusions



Model – an Agent

                            Will it rain                        Subject of
                            tonight?                            interest

                   No     Don't know       Yes                  Opinion

                                                                 Agent


                                                                 Belief
               0                Prior            1
                                                                Updated with:
                                Own observations
                                                                sensors




                                                                                      5 / 19
Introduction            Model           AAT          Experiments and Results    Conclusions



Model – an Agent

                            Will it rain                        Subject of
                            tonight?                            interest

                   No     Don't know       Yes                  Opinion

                                                                 Agent


                                                                 Belief
               0                Prior            1
                                                                Updated with:
                                Own observations
                                                                sensors




                                                                                      5 / 19
Introduction            Model                 AAT              Experiments and Results    Conclusions



Model – an Agent

                            Will it rain                                  Subject of
                            tonight?                                      interest

                   No     Don't know            Yes                       Opinion

                                                                           Agent


                                                                           Belief
               0                 Prior                1
                                                                          Updated with:
                                 Own observations
                                                                          sensors
                                Opinions' of others                       network


                                             ...
                                Yes      ?          No    No              neighbours


                                                                                                5 / 19
Introduction            Model                 AAT              Experiments and Results    Conclusions



Model – an Agent

                            Will it rain                                  Subject of
                            tonight?                                      interest

                   No     Don't know            Yes                       Opinion

                                                                           Agent


                                                                           Belief
               0                 Prior                1
                                                                          Updated with:
                                 Own observations
                                                                          sensors
                                Opinions' of others                       network


                                             ...
                                Yes      ?          No    No              neighbours


                                                                                                5 / 19
Introduction            Model                 AAT              Experiments and Results    Conclusions



Model – an Agent

                            Will it rain                                  Subject of
                            tonight?                                      interest

                   No     Don't know            Yes                       Opinion

                                                                           Agent


                                                                           Belief
               0                 Prior                1
                                                                          Updated with:
                                 Own observations
                                                                          sensors
                                Opinions' of others                       network


                                             ...
                                Yes      ?          No    No              neighbours


                                                                                                5 / 19
Introduction          Model           AAT              Experiments and Results   Conclusions



Model – Sample Dynamics




       red nodes are agents with sensors;
       green nodes are agents with undeter. opinion;
       white and black are agents that support the
       corresponding opinions. (b = white)
                                                                                       6 / 19
Introduction          Model           AAT              Experiments and Results      Conclusions



Model – Sample Dynamics




                                                                    opinions are shared in
                                                                    cascades




       red nodes are agents with sensors;
       green nodes are agents with undeter. opinion;
       white and black are agents that support the
       corresponding opinions. (b = white)
                                                                                          6 / 19
Introduction          Model           AAT              Experiments and Results      Conclusions



Model – Sample Dynamics




                                                                    opinions are shared in
                                                                    cascades
                                                                    cascades might be
                                                                    wrong and fragile




       red nodes are agents with sensors;
       green nodes are agents with undeter. opinion;
       white and black are agents that support the
       corresponding opinions. (b = white)
                                                                                          6 / 19
Introduction          Model           AAT              Experiments and Results      Conclusions



Model – Sample Dynamics




                                                                    opinions are shared in
                                                                    cascades
                                                                    cascades might be
                                                                    wrong and fragile
                                                                    cascades depend on
                                                                    trust levels

       red nodes are agents with sensors;
       green nodes are agents with undeter. opinion;
       white and black are agents that support the
       corresponding opinions. (b = white)
                                                                                          6 / 19
Introduction          Model           AAT              Experiments and Results      Conclusions



Model – Sample Dynamics




                                                                    opinions are shared in
                                                                    cascades
                                                                    cascades might be
                                                                    wrong and fragile
                                                                    cascades depend on
                                                                    trust levels
                                                                    double counting fallacy
       red nodes are agents with sensors;
       green nodes are agents with undeter. opinion;
       white and black are agents that support the
       corresponding opinions. (b = white)
                                                                                          6 / 19
Introduction                                      Model                    AAT                    Experiments and Results                 Conclusions



Settings for Improved Reliability – Metrics
                                     100
         Agents holding opinion, %


                                      80

                                      60                                                                                     correct
                                                                                                                             incorrect
                                      40                                                                                     undetermined


                                      20

                                       0
                                           0.55           0.6       tcritical 0.65          0.7               0.75

              Stable dynamics Scale-Invariant dynamics                                   Unstable dynamics
                                       1

                                     0.8
              Reliability




                                     0.6
                                                                                                                            Reliability
                                     0.4                                                                                    Awareness

                                     0.2

                                       0
                                           0.55           0.6      t
                                                                    critical 0.65          0.7               0.75
                                                           Trust level (common for all agents)                                                  7 / 19
Introduction                                       Model                                     AAT                       Experiments and Results                                      Conclusions



Cascades Distribution
                                   Stable Dynamics                                            Scale-Invariant Dynamics                                        Unstable Dynamics
                            4
                                           t=0.6                                       4
                                                                                                         t=0.63                                        2
                                                                                                                                                                      t=0.66
                          10                                                         10                                                              10



                            3                                                          3
                          10                                                         10
      Cascade Frequency




                                                                 Cascade Frequency




                                                                                                                                 Cascade Frequency
                            2                                                          2                                                               1
                          10                                                         10                                                              10



                            1                                                          1
                          10                                                         10



                            0                                                          0                                                               0
                          10                                                         10                                                              10
                              0        1             2       3                           0           1             2         3                           0        1             2       3
                            10       10            10       10                         10          10             10       10                          10       10             10      10
                                  Size of Opinion Cascade                                      Size of Opinion Cascade                                       Size of Opinion Cascade




                                                                                                                                                                                            8 / 19
Introduction                                         Model                                     AAT                       Experiments and Results                                      Conclusions



Cascades Distribution
                                      Stable Dynamics                                           Scale-Invariant Dynamics                                        Unstable Dynamics
                            4
                                             t=0.6                                       4
                                                                                                           t=0.63                                        2
                                                                                                                                                                        t=0.66
                          10                                                           10                                                              10



                            3                                                            3
                          10                                                           10
      Cascade Frequency




                                                                   Cascade Frequency




                                                                                                                                   Cascade Frequency
                            2                                                            2                                                               1
                          10                                                           10                                                              10



                            1                                                            1
                          10                                                           10



                            0                                                            0                                                               0
                          10                                                           10                                                              10
                              0          1             2       3                           0           1             2         3                           0        1             2       3
                            10          10           10       10                         10          10             10       10                          10       10             10      10
                                    Size of Opinion Cascade                                      Size of Opinion Cascade                                       Size of Opinion Cascade




   Branching factor of opinion sharing
          αimproved reliability = 1
                                  R. Glinton, P. Scerri, and K. Sycara. (2010)
                                  Exploiting scale invariant dynamics for efficient information propagation in large teams.
                                  In Proceedings of 9th International Conference on Autonomous Agents and Multiagent Systems
                                  (AAMAS’10), pages 21-28, Toronto, Canada.


                                                                                                                                                                                              8 / 19
Introduction          Model             AAT             Experiments and Results   Conclusions



DACOR
                                              Yes

                                ?                             ?




                                              α
                                                              Yes
                                    ?

                                                    ?




               introduces additional communication
                NumberOfNeighbours 2 additional messages for a single
               opinion change




                                                                                        9 / 19
Introduction           Model               AAT             Experiments and Results   Conclusions



DACOR
                                                 Yes

                                   ?                             ?




                                                 α
                                                                 Yes
                                       ?

                                                       ?




               introduces additional communication
                NumberOfNeighbours 2 additional messages for a single
               opinion change
               exhibits low adaptivity
               requires tuning of its parameters


                                                                                           9 / 19
Introduction        Model         AAT          Experiments and Results   Conclusions



Autonomous Adaptive Tuning of Trust Levels



       How to find the settings for improved reliability based on local
       observations only?




                                                                              10 / 19
Introduction                              Model                 AAT                      Experiments and Results                 Conclusions



Autonomous Adaptive Tuning of Trust Levels
       How to find the settings for improved reliability based on local
       observations only?
               Stable dynamics Scale-Invariant dynamics                          Unstable dynamics
                              1

                             0.8
               Reliability




                             0.6
                                                                                                                   Reliability
                             0.4                                                                                   Awareness

                             0.2

                              0
                                   0.55           0.6      tcritical 0.65          0.7              0.75
                                                   Trust level (common for all agents)




                                                                                                                                      10 / 19
Introduction                              Model                 AAT                      Experiments and Results                 Conclusions



Autonomous Adaptive Tuning of Trust Levels
       How to find the settings for improved reliability based on local
       observations only?
               Stable dynamics Scale-Invariant dynamics                          Unstable dynamics
                              1

                             0.8
               Reliability




                             0.6
                                                                                                                   Reliability
                             0.4                                                                                   Awareness

                             0.2

                              0
                                   0.55           0.6      tcritical 0.65          0.7              0.75
                                                   Trust level (common for all agents)


       Intuition
       An agent must use the minimal trust level that still enables it to
       form its opinion


                                                                                                                                      10 / 19
Introduction                              Model                 AAT                      Experiments and Results                 Conclusions



Autonomous Adaptive Tuning of Trust Levels
       How to find the settings for improved reliability based on local
       observations only?
               Stable dynamics Scale-Invariant dynamics                          Unstable dynamics
                              1

                             0.8
               Reliability




                             0.6
                                                                                                                   Reliability
                             0.4                                                                                   Awareness

                             0.2

                              0
                                   0.55           0.6      tcritical 0.65          0.7              0.75
                                                   Trust level (common for all agents)


       Intuition
       An agent must use the minimal trust level that still enables it to
       form its opinion

       However, the agent’s choice influences others in the team
                                                                                                                                      10 / 19
Introduction        Model         AAT           Experiments and Results     Conclusions



Autonomous Adaptive Tuning of Trust Levels



       Agent i has to select minimal trust level til from the candidates.




                                                                                 11 / 19
Introduction       Model         AAT          Experiments and Results   Conclusions



Autonomous Adaptive Tuning of Trust Levels



       Agent i has to select minimal trust level til from the candidates.
       The agent with til has to achieve the target awareness rate, hbest




                                                                             11 / 19
Introduction       Model           AAT             Experiments and Results   Conclusions



Autonomous Adaptive Tuning of Trust Levels



       Agent i has to select minimal trust level til from the candidates.
       The agent with til has to achieve the target awareness rate, hbest

                           ti = arg min |hi (til ) − hbest |
                                    til




                                                                                  11 / 19
Introduction           Model           AAT             Experiments and Results   Conclusions



Autonomous Adaptive Tuning of Trust Levels



       Agent i has to select minimal trust level til from the candidates.
       The agent with til has to achieve the target awareness rate, hbest

                               ti = arg min |hi (til ) − hbest |
                                        til


          1    How to select candidate trust levels?
          2    How to estimate their awareness rates?
          3    How to choose the trust level to use?




                                                                                      11 / 19
Introduction       Model                AAT         Experiments and Results      Conclusions



AAT – Candidate Trust Levels
                                        ck                                  te
                                     la                                  hi
                               k=3 =b                       k=1
                                                                 2   =w
                               oi                           oi


                                                                         Pki
                           0   1-σ            P'i       σ            1


       To form the most accurate opinion the agent must form its opinion
       when it observes the strongest support.




                                                                                      12 / 19
Introduction                    Model                 AAT               Experiments and Results            Conclusions



AAT – Candidate Trust Levels

                    ck                               te
                 la                                hi
         k=1   =b                          k= 1 = w
         oi                                oi
                                      1+
                 1−                  ti                                         2−
                                                                                                  2+
                                                                                                 ti
                ti                                                             ti
                                                          P   k
                                                               i                                                Pki
 0     1-σ               P'i   0.5         σ          1            0   1-σ           P'i   0.5         σ    1


       To form the most accurate opinion the agent must form its opinion
       when it observes the strongest support.




                                                                                                                12 / 19
Introduction                    Model                     AAT               Experiments and Results            Conclusions



AAT – Candidate Trust Levels

                    ck                                   te
                 la                                    hi
         k=1   =b                              k= 1 = w
         oi                                    oi
                                      1+
                 1−                  ti                                             2−
                                                                                                      2+
                                                                                                     ti
                ti                                                                 ti
                                                              P   k
                                                                   i                                                Pki
 0     1-σ               P'i   0.5             σ          1            0   1-σ           P'i   0.5         σ    1


       To form the most accurate opinion the agent must form its opinion
       when it observes the strongest support.

       Since the number of neighbours |Ni | is limited, the set of the
       candidate trust levels is:

                                           Ti = {til− , til+ : l = 1 . . . |Ni |}


                                                                                                                    12 / 19
Introduction                    Model                     AAT               Experiments and Results            Conclusions



AAT – Candidate Trust Levels

                    ck                                   te
                 la                                    hi
         k=1   =b                              k= 1 = w
         oi                                    oi
                                      1+
                 1−                  ti                                             2−
                                                                                                      2+
                                                                                                     ti
                ti                                                                 ti
                                                              P   k
                                                                   i                                                Pki
 0     1-σ               P'i   0.5             σ          1            0   1-σ           P'i   0.5         σ    1


       To form the most accurate opinion the agent must form its opinion
       when it observes the strongest support.

       Since the number of neighbours |Ni | is limited, the set of the
       candidate trust levels is:

                                           Ti = {til− , til+ : l = 1 . . . |Ni |}

       In the settings of dynamic topology and agent may use arbitrary Ti
                                                                                                                    12 / 19
Introduction       Model         AAT          Experiments and Results   Conclusions



AAT – Estimation of the Awareness Rates


       The awareness rates of the candidate trust levels cannot be
       calculated.




                                                                             13 / 19
Introduction       Model        AAT         Experiments and Results   Conclusions



AAT – Estimation of the Awareness Rates


       The awareness rates of the candidate trust levels cannot be
       calculated.
       There are two evidences that indicate that agent could have
       formed an opinion with til actually using ti :




                                                                           13 / 19
Introduction           Model         AAT          Experiments and Results    Conclusions



AAT – Estimation of the Awareness Rates


       The awareness rates of the candidate trust levels cannot be
       calculated.
       There are two evidences that indicate that agent could have
       formed an opinion with til actually using ti :
          1    Ev1: If an opinion was formed, then all higher trust levels
               (til ≥ ti ) would have led to opinion formation as well.




                                                                                  13 / 19
Introduction           Model         AAT          Experiments and Results    Conclusions



AAT – Estimation of the Awareness Rates


       The awareness rates of the candidate trust levels cannot be
       calculated.
       There are two evidences that indicate that agent could have
       formed an opinion with til actually using ti :
          1    Ev1: If an opinion was formed, then all higher trust levels
               (til ≥ ti ) would have led to opinion formation as well.
          2    Ev2: Otherwise, if til requires less updates to form an opinion
               then the observed strongest support.




                                                                                  13 / 19
Introduction           Model         AAT               Experiments and Results   Conclusions



AAT – Estimation of the Awareness Rates


       The awareness rates of the candidate trust levels cannot be
       calculated.
       There are two evidences that indicate that agent could have
       formed an opinion with til actually using ti :
          1    Ev1: If an opinion was formed, then all higher trust levels
               (til ≥ ti ) would have led to opinion formation as well.
          2    Ev2: Otherwise, if til requires less updates to form an opinion
               then the observed strongest support.

                                                ˆ
                                    hi (til ) ≈ hi (til )




                                                                                      13 / 19
Introduction         Model         AAT           Experiments and Results    Conclusions



AAT – Strategies to Select a Trust Level

                                                             ˆ
       The problem of selecting til ∈ Ti , accordingly their h(til ), resembles
       the standard multi-armed bandit (MAB) model.




                                                                                  14 / 19
Introduction             Model     AAT           Experiments and Results    Conclusions



AAT – Strategies to Select a Trust Level

                                                             ˆ
       The problem of selecting til ∈ Ti , accordingly their h(til ), resembles
       the standard multi-armed bandit (MAB) model.

   The agent can apply MAB
   strategies:
           Greedy
               -greedy
               -N-greedy
           Soft-max
   – assume that reward
   distribution is unknown.



                                                                                  14 / 19
Introduction             Model     AAT                                 Experiments and Results               Conclusions



AAT – Strategies to Select a Trust Level

                                                             ˆ
       The problem of selecting til ∈ Ti , accordingly their h(til ), resembles
       the standard multi-armed bandit (MAB) model.

   The agent can apply MAB            However, for ascendantly ordered Ti :
                                                           1




                                         Awareness Rate
   strategies:                                            0.8

           Greedy                                         0.6

                                                          0.4
               -greedy                                    0.2

               -N-greedy                                   0
                                                                0.55           0.6    tcritical 0.65   0.7

           Soft-max                                                           Trust Level

   – assume that reward               Hill-climbing: Select a trust level from
   distribution is unknown.           the closest to the currently used




                                                                                                                  14 / 19
Introduction             Model     AAT                                 Experiments and Results               Conclusions



AAT – Strategies to Select a Trust Level

                                                             ˆ
       The problem of selecting til ∈ Ti , accordingly their h(til ), resembles
       the standard multi-armed bandit (MAB) model.

   The agent can apply MAB            However, for ascendantly ordered Ti :
                                                           1




                                         Awareness Rate
   strategies:                                            0.8

           Greedy                                         0.6

                                                          0.4
               -greedy                                    0.2

               -N-greedy                                   0
                                                                0.55           0.6    tcritical 0.65   0.7

           Soft-max                                                           Trust Level

   – assume that reward          Hill-climbing: Select a trust level from
   distribution is unknown.      the closest to the currently used
     Since an agent’s choice influences others, strategies with less
     dramatic changes to the dynamics are expected to perform better.

                                                                                                                  14 / 19
Introduction                  Model          AAT             Experiments and Results      Conclusions



Selection of the Target Awareness Rate
               1


              0.9
Reliability




              0.8


              0.7


              0.6
                    0.8   0.85    0.9     0.95    1
                     Target awareness rate, hbest

                               random                 scalefree              smallworld
              The agents have to compromise their awareness rates to improve
              team’s reliability.

                                                                                               15 / 19
Introduction                  Model          AAT                                      Experiments and Results       Conclusions



Selection of the Target Awareness Rate
               1
                                                                                      0.75




                                                         Average trust level, 〈ti 〉
              0.9
                                                                                        0.7
Reliability




              0.8

                                                                                      0.65
              0.7


              0.6                                                                       0.6
                    0.8   0.85    0.9     0.95    1                                           0.8 0.85 0.9 0.95             1
                     Target awareness rate, hbest                                              Target awareness rate, hbest

                               random                 scalefree                                       smallworld
              The agents have to compromise their awareness rates to improve
              team’s reliability.
              With a high target awareness rate, hbest , a team exhibits unstable
              dynamics, thus the reliability drops.                                                                      15 / 19
Introduction              Model             AAT            Experiments and Results       Conclusions



Reliability of a Team
                          (a) Random Network
                     1

                    0.9
                                                                       AAT
                    0.8
      Reliability




                                                                       DACOR
                                                                       Pre-tuned Trust Levels
                    0.7                                                Average Pre-tuned
                                                                       Trust Levels
                    0.6

                    0.5
                          500       1000     1500   2000
                                  Network Size

       AAT significantly outperforms prediction of the best parameters
       (average pre-tuned) and existing DACOR. Individually pre-tuned
       trust levels indicate on the upper-bound that can be achieved.
                                                                                                16 / 19
Introduction               Model             AAT            Experiments and Results       Conclusions



Reliability of a Team
                          (b) Scale−Free Network
                     1

                    0.9
                                                                        AAT
                    0.8
      Reliability




                                                                        DACOR
                                                                        Pre-tuned Trust Levels
                    0.7                                                 Average Pre-tuned
                                                                        Trust Levels
                    0.6

                    0.5
                          500        1000     1500   2000
                                   Network Size

       AAT significantly outperforms prediction of the best parameters
       (average pre-tuned) and existing DACOR. Individually pre-tuned
       trust levels indicate on the upper-bound that can be achieved.
                                                                                                 16 / 19
Introduction                Model             AAT            Experiments and Results       Conclusions



Reliability of a Team
                          (c) Small−World Network
                     1

                    0.9
                                                                         AAT
                    0.8
      Reliability




                                                                         DACOR
                                                                         Pre-tuned Trust Levels
                    0.7                                                  Average Pre-tuned
                                                                         Trust Levels
                    0.6

                    0.5
                           500        1000     1500   2000
                                    Network Size

       AAT significantly outperforms prediction of the best parameters
       (average pre-tuned) and existing DACOR. Individually pre-tuned
       trust levels indicate on the upper-bound that can be achieved.
                                                                                                  16 / 19
Introduction     Model     AAT             Experiments and Results   Conclusions



Communication Expense




         MinimalCommunication =            NumberOfNeighbours
                                  Agents




                                                                          17 / 19
Introduction                        Model                  AAT               Experiments and Results   Conclusions



Communication Expense

         MinimalCommunication =                                              NumberOfNeighbours
                                                                    Agents

                                    80
               Messages per Agent



                                    60
                                                                                      AAT
                                    40                                                DACOR
                                                                                      Minimal
                                                                                      Communication
                                    20


                                    0
                                            500     1000     1500     2000
                                                  Network Size
       AAT is communicationally efficient while DACOR requires 4-7
       times more messages to operate
                                                                                                            17 / 19
Introduction                 Model          AAT            Experiments and Results           Conclusions



Performance in the Presence of Indifferent Agents
                                 (a) Random Network
                   1


                 0.9
  Reliability




                 0.8                                                            AAT
                                                                                DACOR
                                                                                Pre-tuned Trust Levels
                 0.7                                                            Average Pre-tuned
                                                                                Trust Levels
                 0.6


                 0.5
                       0    20       40      60       80         100
                             % of Indifferent Agents
                AAT installed on a half of a team delivers higher reliability than we 18 / 19
Introduction                 Model              AAT            Experiments and Results           Conclusions



Performance in the Presence of Indifferent Agents
                                 (b) Scale−Free Network
                   1

                  0.9

                  0.8
    Reliability




                                                                              AAT
                  0.7                                                         DACOR
                                                                              Pre-tuned Trust Levels
                                                                              Average Pre-tuned
                  0.6                                                         Trust Levels

                  0.5

                  0.4
                        0   20        40       60         80    100
                             % of Indifferent Agents

           AAT installed on a half of a team delivers higher reliability than we
           can predict by using the average pre-tuned trust-levels.
                                                                                                       18 / 19
Introduction                 Model              AAT             Experiments and Results           Conclusions



Performance in the Presence of Indifferent Agents
                                 (c) Small−World Network
                   1

                  0.9

                  0.8
    Reliability




                                                                               AAT
                  0.7                                                          DACOR
                                                                               Pre-tuned Trust Levels
                                                                               Average Pre-tuned
                  0.6                                                          Trust Levels

                  0.5

                  0.4
                        0   20         40       60         80    100
                             % of Indifferent Agents

           AAT installed on a half of a team delivers higher reliability than we
           can predict by using the average pre-tuned trust-levels.
                                                                                                        18 / 19
Introduction          Model           AAT       Experiments and Results   Conclusions



Conclusions

       AAT exploits properties of social behaviour to improve accuracy of
       agents’ opinions. Contributions:
               improves Reliability
               minimises Communication – the first to operate under this
               restriction
               Computationally inexpensive
               Adaptive, Scalable, Robust to the presence of indifferent
               agents




                                                                               19 / 19
Introduction           Model          AAT         Experiments and Results   Conclusions



Conclusions

       AAT exploits properties of social behaviour to improve accuracy of
       agents’ opinions. Contributions:
               improves Reliability
               minimises Communication – the first to operate under this
               restriction
               Computationally inexpensive
               Adaptive, Scalable, Robust to the presence of indifferent
               agents
       Future work:
               Tuning an individual trust level for each neighbour
               Attack-resistant solution


                                                                                 19 / 19

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Efficient Sharing of Conflicting Opinions with Minimal Communication in Large Decentralised Teams

  • 1. Introduction Model AAT Experiments and Results Conclusions Efficient Sharing of Conflicting Opinions with Minimal Communication in Large Decentralised Teams Oleksandr Pryymak, Alex Rogers and Nicholas R. Jennings University of Southampton {op08r,acr,nrj}@ecs.soton.ac.uk July 20, 2011 0 / 19
  • 2. Introduction Model AAT Experiments and Results Conclusions Disaster response and large decentralised teams 2010, Haiti earthquake – Citizen and public news reporting, plotted on an online map (Ushahidi). 1 / 19
  • 3. Introduction Model AAT Experiments and Results Conclusions Disaster response and large decentralised teams 2010, Haiti earthquake – Citizen and public news reporting, plotted on an online map (Ushahidi). 2010, Chile earthquake – Twitter is one of the speediest, albeit not the most accurate, sources of real-time information (France24). 1 / 19
  • 4. Introduction Model AAT Experiments and Results Conclusions Disaster response and large decentralised teams 2010, Haiti earthquake – Citizen and public news reporting, plotted on an online map (Ushahidi). 2010, Chile earthquake – Twitter is one of the speediest, albeit not the most accurate, sources of real-time information (France24). Large teams of individuals 1 / 19
  • 5. Introduction Model AAT Experiments and Results Conclusions Disaster response and large decentralised teams 2010, Haiti earthquake – Citizen and public news reporting, plotted on an online map (Ushahidi). 2010, Chile earthquake – Twitter is one of the speediest, albeit not the most accurate, sources of real-time information (France24). Large teams of individuals Decentralised 1 / 19
  • 6. Introduction Model AAT Experiments and Results Conclusions Disaster response and large decentralised teams 2010, Haiti earthquake – Citizen and public news reporting, plotted on an online map (Ushahidi). 2010, Chile earthquake – Twitter is one of the speediest, albeit not the most accurate, sources of real-time information (France24). Large teams of individuals Decentralised Not every individual can make an observation 1 / 19
  • 7. Introduction Model AAT Experiments and Results Conclusions Disaster response and large decentralised teams 2010, Haiti earthquake – Citizen and public news reporting, plotted on an online map (Ushahidi). 2010, Chile earthquake – Twitter is one of the speediest, albeit not the most accurate, sources of real-time information (France24). Large teams of individuals Decentralised Not every individual can make an observation Observations are uncertain and conflicting 1 / 19
  • 8. Introduction Model AAT Experiments and Results Conclusions Disaster response and large decentralised teams 2010, Haiti earthquake – Citizen and public news reporting, plotted on an online map (Ushahidi). 2010, Chile earthquake – Twitter is one of the speediest, albeit not the most accurate, sources of real-time information (France24). Large teams of individuals Decentralised Not every individual can make an observation Observations are uncertain and conflicting Individuals share opinions without supporting information 1 / 19
  • 9. Introduction Model AAT Experiments and Results Conclusions Disaster response and large decentralised teams 2010, Haiti earthquake – Citizen and public news reporting, plotted on an online map (Ushahidi). 2010, Chile earthquake – Twitter is one of the speediest, albeit not the most accurate, sources of real-time information (France24). Large teams of individuals Decentralised Not every individual can make an observation Observations are uncertain and conflicting Individuals share opinions without supporting information How opinions are shared and how to improve their accuracy? 1 / 19
  • 10. Introduction Model AAT Experiments and Results Conclusions How opinions are shared – Can we trust what we share? 2 / 19
  • 11. Introduction Model AAT Experiments and Results Conclusions How opinions are shared – Can we trust what we share? Opinions are shared in cascades (avalanches) 2 / 19
  • 12. Introduction Model AAT Experiments and Results Conclusions How opinions are shared – Can we trust what we share? Can we trust what we share? Opinions are shared in cascades (avalanches) 2 / 19
  • 13. Introduction Model AAT Experiments and Results Conclusions How opinions are shared – Can we trust what we share? Can we trust what we share? Chile’10 : yes / no (Mendoza et al. 2010) Opinions are shared in cascades (avalanches) 2 / 19
  • 14. Introduction Model AAT Experiments and Results Conclusions How opinions are shared – Can we trust what we share? Can we trust what we share? Chile’10 : yes / no (Mendoza et al. 2010) Santiago airport is closed Fire at the University of Conceptcion Looting in Conceptcion Opinions are shared in cascades (avalanches) 2 / 19
  • 15. Introduction Model AAT Experiments and Results Conclusions How opinions are shared – Can we trust what we share? Can we trust what we share? Chile’10 : yes / no (Mendoza et al. 2010) Santiago airport is closed Fire at the University of Conceptcion Looting in Conceptcion Looting in Santiago Tsunami warning Active volcano Opinions are shared in cascades (avalanches) 2 / 19
  • 16. Introduction Model AAT Experiments and Results Conclusions How opinions are shared – Can we trust what we share? Can we trust what we share? Chile’10 : yes / no (Mendoza et al. 2010) Santiago airport is closed Fire at the University of Conceptcion Looting in Conceptcion Looting in Santiago Tsunami warning Active volcano Opinions are shared in cascades (avalanches) Even in cooperative settings opinions might be incorrect 2 / 19
  • 17. Introduction Model AAT Experiments and Results Conclusions Problem of Forming a Correct Opinion How do agents make a decision which opinion is correct? based on own priors, observations based on information from others 3 / 19
  • 18. Introduction Model AAT Experiments and Results Conclusions Problem of Forming a Correct Opinion How do agents make a decision which opinion is correct? based on own priors, observations based on information from others by analysing communicated information reaching agreements interactivity with others 3 / 19
  • 19. Introduction Model AAT Experiments and Results Conclusions Problem of Forming a Correct Opinion How do agents make a decision which opinion is correct? based on own priors, observations based on information from others by analysing communicated information reaching agreements interactivity with others The Problem However, if: agents’ processing abilities are limited communication is strictly limited to opinion sharing 3 / 19
  • 20. Introduction Model AAT Experiments and Results Conclusions Problem of Forming a Correct Opinion How do agents make a decision which opinion is correct? based on own priors, observations based on information from others by analysing communicated information reaching agreements interactivity with others The Problem However, if: agents’ processing abilities are limited communication is strictly limited to opinion sharing The Solution Agents have to exploit properties of opinion sharing dynamics, and filter out incorrect opinions in the sharing process 3 / 19
  • 21. Introduction Model AAT Experiments and Results Conclusions Problem of Forming a Correct Opinion How do agents make a decision which opinion is correct? based on own priors, observations based on information from others by analysing communicated information reaching agreements interactivity with others The Problem However, if: agents’ processing abilities are limited communication is strictly limited to opinion sharing The Solution Agents have to exploit properties of opinion sharing dynamics, and filter out incorrect opinions in the sharing process How to find such settings by independent actions of the agents? 3 / 19
  • 22. Introduction Model AAT Experiments and Results Conclusions Outline Remaining sections: 1 Model of opinion sharing 2 Existing message-passing algorithm 3 Our algorithm based on independent actions 4 Evaluation 4 / 19
  • 23. Introduction Model AAT Experiments and Results Conclusions Model – an Agent Agent 5 / 19
  • 24. Introduction Model AAT Experiments and Results Conclusions Model – an Agent Will it rain Subject of tonight? interest Agent 5 / 19
  • 25. Introduction Model AAT Experiments and Results Conclusions Model – an Agent Will it rain Subject of tonight? interest No Don't know Yes Opinion Agent 5 / 19
  • 26. Introduction Model AAT Experiments and Results Conclusions Model – an Agent Will it rain Subject of tonight? interest No Don't know Yes Opinion Agent 5 / 19
  • 27. Introduction Model AAT Experiments and Results Conclusions Model – an Agent Will it rain Subject of tonight? interest No Don't know Yes Opinion Agent Belief 0 Prior 1 5 / 19
  • 28. Introduction Model AAT Experiments and Results Conclusions Model – an Agent Will it rain Subject of tonight? interest No Don't know Yes Opinion Agent Belief 0 Prior 1 Updated with: Own observations sensors 5 / 19
  • 29. Introduction Model AAT Experiments and Results Conclusions Model – an Agent Will it rain Subject of tonight? interest No Don't know Yes Opinion Agent Belief 0 Prior 1 Updated with: Own observations sensors 5 / 19
  • 30. Introduction Model AAT Experiments and Results Conclusions Model – an Agent Will it rain Subject of tonight? interest No Don't know Yes Opinion Agent Belief 0 Prior 1 Updated with: Own observations sensors Opinions' of others network ... Yes ? No No neighbours 5 / 19
  • 31. Introduction Model AAT Experiments and Results Conclusions Model – an Agent Will it rain Subject of tonight? interest No Don't know Yes Opinion Agent Belief 0 Prior 1 Updated with: Own observations sensors Opinions' of others network ... Yes ? No No neighbours 5 / 19
  • 32. Introduction Model AAT Experiments and Results Conclusions Model – an Agent Will it rain Subject of tonight? interest No Don't know Yes Opinion Agent Belief 0 Prior 1 Updated with: Own observations sensors Opinions' of others network ... Yes ? No No neighbours 5 / 19
  • 33. Introduction Model AAT Experiments and Results Conclusions Model – Sample Dynamics red nodes are agents with sensors; green nodes are agents with undeter. opinion; white and black are agents that support the corresponding opinions. (b = white) 6 / 19
  • 34. Introduction Model AAT Experiments and Results Conclusions Model – Sample Dynamics opinions are shared in cascades red nodes are agents with sensors; green nodes are agents with undeter. opinion; white and black are agents that support the corresponding opinions. (b = white) 6 / 19
  • 35. Introduction Model AAT Experiments and Results Conclusions Model – Sample Dynamics opinions are shared in cascades cascades might be wrong and fragile red nodes are agents with sensors; green nodes are agents with undeter. opinion; white and black are agents that support the corresponding opinions. (b = white) 6 / 19
  • 36. Introduction Model AAT Experiments and Results Conclusions Model – Sample Dynamics opinions are shared in cascades cascades might be wrong and fragile cascades depend on trust levels red nodes are agents with sensors; green nodes are agents with undeter. opinion; white and black are agents that support the corresponding opinions. (b = white) 6 / 19
  • 37. Introduction Model AAT Experiments and Results Conclusions Model – Sample Dynamics opinions are shared in cascades cascades might be wrong and fragile cascades depend on trust levels double counting fallacy red nodes are agents with sensors; green nodes are agents with undeter. opinion; white and black are agents that support the corresponding opinions. (b = white) 6 / 19
  • 38. Introduction Model AAT Experiments and Results Conclusions Settings for Improved Reliability – Metrics 100 Agents holding opinion, % 80 60 correct incorrect 40 undetermined 20 0 0.55 0.6 tcritical 0.65 0.7 0.75 Stable dynamics Scale-Invariant dynamics Unstable dynamics 1 0.8 Reliability 0.6 Reliability 0.4 Awareness 0.2 0 0.55 0.6 t critical 0.65 0.7 0.75 Trust level (common for all agents) 7 / 19
  • 39. Introduction Model AAT Experiments and Results Conclusions Cascades Distribution Stable Dynamics Scale-Invariant Dynamics Unstable Dynamics 4 t=0.6 4 t=0.63 2 t=0.66 10 10 10 3 3 10 10 Cascade Frequency Cascade Frequency Cascade Frequency 2 2 1 10 10 10 1 1 10 10 0 0 0 10 10 10 0 1 2 3 0 1 2 3 0 1 2 3 10 10 10 10 10 10 10 10 10 10 10 10 Size of Opinion Cascade Size of Opinion Cascade Size of Opinion Cascade 8 / 19
  • 40. Introduction Model AAT Experiments and Results Conclusions Cascades Distribution Stable Dynamics Scale-Invariant Dynamics Unstable Dynamics 4 t=0.6 4 t=0.63 2 t=0.66 10 10 10 3 3 10 10 Cascade Frequency Cascade Frequency Cascade Frequency 2 2 1 10 10 10 1 1 10 10 0 0 0 10 10 10 0 1 2 3 0 1 2 3 0 1 2 3 10 10 10 10 10 10 10 10 10 10 10 10 Size of Opinion Cascade Size of Opinion Cascade Size of Opinion Cascade Branching factor of opinion sharing αimproved reliability = 1 R. Glinton, P. Scerri, and K. Sycara. (2010) Exploiting scale invariant dynamics for efficient information propagation in large teams. In Proceedings of 9th International Conference on Autonomous Agents and Multiagent Systems (AAMAS’10), pages 21-28, Toronto, Canada. 8 / 19
  • 41. Introduction Model AAT Experiments and Results Conclusions DACOR Yes ? ? α Yes ? ? introduces additional communication NumberOfNeighbours 2 additional messages for a single opinion change 9 / 19
  • 42. Introduction Model AAT Experiments and Results Conclusions DACOR Yes ? ? α Yes ? ? introduces additional communication NumberOfNeighbours 2 additional messages for a single opinion change exhibits low adaptivity requires tuning of its parameters 9 / 19
  • 43. Introduction Model AAT Experiments and Results Conclusions Autonomous Adaptive Tuning of Trust Levels How to find the settings for improved reliability based on local observations only? 10 / 19
  • 44. Introduction Model AAT Experiments and Results Conclusions Autonomous Adaptive Tuning of Trust Levels How to find the settings for improved reliability based on local observations only? Stable dynamics Scale-Invariant dynamics Unstable dynamics 1 0.8 Reliability 0.6 Reliability 0.4 Awareness 0.2 0 0.55 0.6 tcritical 0.65 0.7 0.75 Trust level (common for all agents) 10 / 19
  • 45. Introduction Model AAT Experiments and Results Conclusions Autonomous Adaptive Tuning of Trust Levels How to find the settings for improved reliability based on local observations only? Stable dynamics Scale-Invariant dynamics Unstable dynamics 1 0.8 Reliability 0.6 Reliability 0.4 Awareness 0.2 0 0.55 0.6 tcritical 0.65 0.7 0.75 Trust level (common for all agents) Intuition An agent must use the minimal trust level that still enables it to form its opinion 10 / 19
  • 46. Introduction Model AAT Experiments and Results Conclusions Autonomous Adaptive Tuning of Trust Levels How to find the settings for improved reliability based on local observations only? Stable dynamics Scale-Invariant dynamics Unstable dynamics 1 0.8 Reliability 0.6 Reliability 0.4 Awareness 0.2 0 0.55 0.6 tcritical 0.65 0.7 0.75 Trust level (common for all agents) Intuition An agent must use the minimal trust level that still enables it to form its opinion However, the agent’s choice influences others in the team 10 / 19
  • 47. Introduction Model AAT Experiments and Results Conclusions Autonomous Adaptive Tuning of Trust Levels Agent i has to select minimal trust level til from the candidates. 11 / 19
  • 48. Introduction Model AAT Experiments and Results Conclusions Autonomous Adaptive Tuning of Trust Levels Agent i has to select minimal trust level til from the candidates. The agent with til has to achieve the target awareness rate, hbest 11 / 19
  • 49. Introduction Model AAT Experiments and Results Conclusions Autonomous Adaptive Tuning of Trust Levels Agent i has to select minimal trust level til from the candidates. The agent with til has to achieve the target awareness rate, hbest ti = arg min |hi (til ) − hbest | til 11 / 19
  • 50. Introduction Model AAT Experiments and Results Conclusions Autonomous Adaptive Tuning of Trust Levels Agent i has to select minimal trust level til from the candidates. The agent with til has to achieve the target awareness rate, hbest ti = arg min |hi (til ) − hbest | til 1 How to select candidate trust levels? 2 How to estimate their awareness rates? 3 How to choose the trust level to use? 11 / 19
  • 51. Introduction Model AAT Experiments and Results Conclusions AAT – Candidate Trust Levels ck te la hi k=3 =b k=1 2 =w oi oi Pki 0 1-σ P'i σ 1 To form the most accurate opinion the agent must form its opinion when it observes the strongest support. 12 / 19
  • 52. Introduction Model AAT Experiments and Results Conclusions AAT – Candidate Trust Levels ck te la hi k=1 =b k= 1 = w oi oi 1+ 1− ti 2− 2+ ti ti ti P k i Pki 0 1-σ P'i 0.5 σ 1 0 1-σ P'i 0.5 σ 1 To form the most accurate opinion the agent must form its opinion when it observes the strongest support. 12 / 19
  • 53. Introduction Model AAT Experiments and Results Conclusions AAT – Candidate Trust Levels ck te la hi k=1 =b k= 1 = w oi oi 1+ 1− ti 2− 2+ ti ti ti P k i Pki 0 1-σ P'i 0.5 σ 1 0 1-σ P'i 0.5 σ 1 To form the most accurate opinion the agent must form its opinion when it observes the strongest support. Since the number of neighbours |Ni | is limited, the set of the candidate trust levels is: Ti = {til− , til+ : l = 1 . . . |Ni |} 12 / 19
  • 54. Introduction Model AAT Experiments and Results Conclusions AAT – Candidate Trust Levels ck te la hi k=1 =b k= 1 = w oi oi 1+ 1− ti 2− 2+ ti ti ti P k i Pki 0 1-σ P'i 0.5 σ 1 0 1-σ P'i 0.5 σ 1 To form the most accurate opinion the agent must form its opinion when it observes the strongest support. Since the number of neighbours |Ni | is limited, the set of the candidate trust levels is: Ti = {til− , til+ : l = 1 . . . |Ni |} In the settings of dynamic topology and agent may use arbitrary Ti 12 / 19
  • 55. Introduction Model AAT Experiments and Results Conclusions AAT – Estimation of the Awareness Rates The awareness rates of the candidate trust levels cannot be calculated. 13 / 19
  • 56. Introduction Model AAT Experiments and Results Conclusions AAT – Estimation of the Awareness Rates The awareness rates of the candidate trust levels cannot be calculated. There are two evidences that indicate that agent could have formed an opinion with til actually using ti : 13 / 19
  • 57. Introduction Model AAT Experiments and Results Conclusions AAT – Estimation of the Awareness Rates The awareness rates of the candidate trust levels cannot be calculated. There are two evidences that indicate that agent could have formed an opinion with til actually using ti : 1 Ev1: If an opinion was formed, then all higher trust levels (til ≥ ti ) would have led to opinion formation as well. 13 / 19
  • 58. Introduction Model AAT Experiments and Results Conclusions AAT – Estimation of the Awareness Rates The awareness rates of the candidate trust levels cannot be calculated. There are two evidences that indicate that agent could have formed an opinion with til actually using ti : 1 Ev1: If an opinion was formed, then all higher trust levels (til ≥ ti ) would have led to opinion formation as well. 2 Ev2: Otherwise, if til requires less updates to form an opinion then the observed strongest support. 13 / 19
  • 59. Introduction Model AAT Experiments and Results Conclusions AAT – Estimation of the Awareness Rates The awareness rates of the candidate trust levels cannot be calculated. There are two evidences that indicate that agent could have formed an opinion with til actually using ti : 1 Ev1: If an opinion was formed, then all higher trust levels (til ≥ ti ) would have led to opinion formation as well. 2 Ev2: Otherwise, if til requires less updates to form an opinion then the observed strongest support. ˆ hi (til ) ≈ hi (til ) 13 / 19
  • 60. Introduction Model AAT Experiments and Results Conclusions AAT – Strategies to Select a Trust Level ˆ The problem of selecting til ∈ Ti , accordingly their h(til ), resembles the standard multi-armed bandit (MAB) model. 14 / 19
  • 61. Introduction Model AAT Experiments and Results Conclusions AAT – Strategies to Select a Trust Level ˆ The problem of selecting til ∈ Ti , accordingly their h(til ), resembles the standard multi-armed bandit (MAB) model. The agent can apply MAB strategies: Greedy -greedy -N-greedy Soft-max – assume that reward distribution is unknown. 14 / 19
  • 62. Introduction Model AAT Experiments and Results Conclusions AAT – Strategies to Select a Trust Level ˆ The problem of selecting til ∈ Ti , accordingly their h(til ), resembles the standard multi-armed bandit (MAB) model. The agent can apply MAB However, for ascendantly ordered Ti : 1 Awareness Rate strategies: 0.8 Greedy 0.6 0.4 -greedy 0.2 -N-greedy 0 0.55 0.6 tcritical 0.65 0.7 Soft-max Trust Level – assume that reward Hill-climbing: Select a trust level from distribution is unknown. the closest to the currently used 14 / 19
  • 63. Introduction Model AAT Experiments and Results Conclusions AAT – Strategies to Select a Trust Level ˆ The problem of selecting til ∈ Ti , accordingly their h(til ), resembles the standard multi-armed bandit (MAB) model. The agent can apply MAB However, for ascendantly ordered Ti : 1 Awareness Rate strategies: 0.8 Greedy 0.6 0.4 -greedy 0.2 -N-greedy 0 0.55 0.6 tcritical 0.65 0.7 Soft-max Trust Level – assume that reward Hill-climbing: Select a trust level from distribution is unknown. the closest to the currently used Since an agent’s choice influences others, strategies with less dramatic changes to the dynamics are expected to perform better. 14 / 19
  • 64. Introduction Model AAT Experiments and Results Conclusions Selection of the Target Awareness Rate 1 0.9 Reliability 0.8 0.7 0.6 0.8 0.85 0.9 0.95 1 Target awareness rate, hbest random scalefree smallworld The agents have to compromise their awareness rates to improve team’s reliability. 15 / 19
  • 65. Introduction Model AAT Experiments and Results Conclusions Selection of the Target Awareness Rate 1 0.75 Average trust level, 〈ti 〉 0.9 0.7 Reliability 0.8 0.65 0.7 0.6 0.6 0.8 0.85 0.9 0.95 1 0.8 0.85 0.9 0.95 1 Target awareness rate, hbest Target awareness rate, hbest random scalefree smallworld The agents have to compromise their awareness rates to improve team’s reliability. With a high target awareness rate, hbest , a team exhibits unstable dynamics, thus the reliability drops. 15 / 19
  • 66. Introduction Model AAT Experiments and Results Conclusions Reliability of a Team (a) Random Network 1 0.9 AAT 0.8 Reliability DACOR Pre-tuned Trust Levels 0.7 Average Pre-tuned Trust Levels 0.6 0.5 500 1000 1500 2000 Network Size AAT significantly outperforms prediction of the best parameters (average pre-tuned) and existing DACOR. Individually pre-tuned trust levels indicate on the upper-bound that can be achieved. 16 / 19
  • 67. Introduction Model AAT Experiments and Results Conclusions Reliability of a Team (b) Scale−Free Network 1 0.9 AAT 0.8 Reliability DACOR Pre-tuned Trust Levels 0.7 Average Pre-tuned Trust Levels 0.6 0.5 500 1000 1500 2000 Network Size AAT significantly outperforms prediction of the best parameters (average pre-tuned) and existing DACOR. Individually pre-tuned trust levels indicate on the upper-bound that can be achieved. 16 / 19
  • 68. Introduction Model AAT Experiments and Results Conclusions Reliability of a Team (c) Small−World Network 1 0.9 AAT 0.8 Reliability DACOR Pre-tuned Trust Levels 0.7 Average Pre-tuned Trust Levels 0.6 0.5 500 1000 1500 2000 Network Size AAT significantly outperforms prediction of the best parameters (average pre-tuned) and existing DACOR. Individually pre-tuned trust levels indicate on the upper-bound that can be achieved. 16 / 19
  • 69. Introduction Model AAT Experiments and Results Conclusions Communication Expense MinimalCommunication = NumberOfNeighbours Agents 17 / 19
  • 70. Introduction Model AAT Experiments and Results Conclusions Communication Expense MinimalCommunication = NumberOfNeighbours Agents 80 Messages per Agent 60 AAT 40 DACOR Minimal Communication 20 0 500 1000 1500 2000 Network Size AAT is communicationally efficient while DACOR requires 4-7 times more messages to operate 17 / 19
  • 71. Introduction Model AAT Experiments and Results Conclusions Performance in the Presence of Indifferent Agents (a) Random Network 1 0.9 Reliability 0.8 AAT DACOR Pre-tuned Trust Levels 0.7 Average Pre-tuned Trust Levels 0.6 0.5 0 20 40 60 80 100 % of Indifferent Agents AAT installed on a half of a team delivers higher reliability than we 18 / 19
  • 72. Introduction Model AAT Experiments and Results Conclusions Performance in the Presence of Indifferent Agents (b) Scale−Free Network 1 0.9 0.8 Reliability AAT 0.7 DACOR Pre-tuned Trust Levels Average Pre-tuned 0.6 Trust Levels 0.5 0.4 0 20 40 60 80 100 % of Indifferent Agents AAT installed on a half of a team delivers higher reliability than we can predict by using the average pre-tuned trust-levels. 18 / 19
  • 73. Introduction Model AAT Experiments and Results Conclusions Performance in the Presence of Indifferent Agents (c) Small−World Network 1 0.9 0.8 Reliability AAT 0.7 DACOR Pre-tuned Trust Levels Average Pre-tuned 0.6 Trust Levels 0.5 0.4 0 20 40 60 80 100 % of Indifferent Agents AAT installed on a half of a team delivers higher reliability than we can predict by using the average pre-tuned trust-levels. 18 / 19
  • 74. Introduction Model AAT Experiments and Results Conclusions Conclusions AAT exploits properties of social behaviour to improve accuracy of agents’ opinions. Contributions: improves Reliability minimises Communication – the first to operate under this restriction Computationally inexpensive Adaptive, Scalable, Robust to the presence of indifferent agents 19 / 19
  • 75. Introduction Model AAT Experiments and Results Conclusions Conclusions AAT exploits properties of social behaviour to improve accuracy of agents’ opinions. Contributions: improves Reliability minimises Communication – the first to operate under this restriction Computationally inexpensive Adaptive, Scalable, Robust to the presence of indifferent agents Future work: Tuning an individual trust level for each neighbour Attack-resistant solution 19 / 19