this talk was an introduction to Reinforcement Learning based on the book by Andrew Barto and Richard S. Sutton. We explained the main components of an RL problem and detailed the tabular solutions and approximate solutions methods.
Partially observable Markov decision processes for spoken dialog systemsMartin Majlis
Paper presentation:
Partially observable Markov decision processes for spoken dialog systems
Jason D. Williams, Steve Young (AT&T Labs)
2007, Computer Speech and Language, 21(2)
Reinforcement learning is the training of machine learning models to make a sequence of decisions. The agent learns to achieve a goal in an uncertain, potentially complex environment. In reinforcement learning, an artificial intelligence faces a game-like situation.
this talk was an introduction to Reinforcement Learning based on the book by Andrew Barto and Richard S. Sutton. We explained the main components of an RL problem and detailed the tabular solutions and approximate solutions methods.
Partially observable Markov decision processes for spoken dialog systemsMartin Majlis
Paper presentation:
Partially observable Markov decision processes for spoken dialog systems
Jason D. Williams, Steve Young (AT&T Labs)
2007, Computer Speech and Language, 21(2)
Reinforcement learning is the training of machine learning models to make a sequence of decisions. The agent learns to achieve a goal in an uncertain, potentially complex environment. In reinforcement learning, an artificial intelligence faces a game-like situation.
An efficient use of temporal difference technique in Computer Game LearningPrabhu Kumar
A computer game using temporal difference algorithm of Machine learning which improves the ability of the computer to learn and also explore the best next move for the game by greedy movement techniques and exploration method techniques for the future states of the game.
Reinforcement learning is an area of machine learning inspired by behaviorist psychology, concerned with how software agents ought to take actions in an environment so as to maximize some notion of cumulative reward.
This chapter shows how to use knowledge about the wlorld to make decisions even when the
outcomes of an action are uncertain and the rewards for acting might not be reaped until many
actions have passed. The main points are as follows:
e Sequential decision problems in uncertain envirsinments,also called Markov decision
processes, or MDPs, are defined by a transition model specifying the probabilistic
outcomes of actions and a reward function specifying the reward in each state.
o The utility of a state sequence is the sum of all the rewards over the sequence, possibly
discounted over time. The solution of an MDP is a policy that associates a decision
with every state that the agent might reach. An optimal policy maximizes the utility of
the state sequences encountered when it is execut~ed.
e The utility of a state is the expected utility of the state sequences encountered when
an optimal policy is executed, starting in that state. The value iteration algorithm for
solving MDPs works by iteratively solving the equations relating the utilities of each
state to that of its neighbors.
Policy iteration alternates between calculating the utilities of states under the current
policy and improving the current policy with respect to the current utilities.
* Partially observable MDPs, or POMDPs, are much more difficult to solve than are
MDPs. They can be solved by conversion to an MDP in the continuous space of belief
states. Optimal behavior in POMDPs includes information gathering to reduce uncertainty and therefore make better decisions in the fiuture.
A decision-theoretic agent can be constructed for POMDP environments. The agent
uses a dynamic decision network to represent the transition and observation models,
to update its belief state, and to project forward possible action sequences.
Game theory describes rational behavior for agents in situations where multiple agents
interact simultaneously. Solutions of games are Nash equilibria-strategy profiles in
which no agent has an incentive to deviate from the specified strategy.
Mechanism design can be used to set the rules by which agents will interact, in order
to maximize some global utility through the operation of individually rational agents.
Sometimes, mechanisms exist that achieve this goal without requiring each agent to
consider the choices made by other agents.
We shall return to the world of MDPs and POMDP in Chapter 21, when we study reinforcement learning methods that allow an agent to improve its behavior from experience in sequential, uncertain environments.
An efficient use of temporal difference technique in Computer Game LearningPrabhu Kumar
A computer game using temporal difference algorithm of Machine learning which improves the ability of the computer to learn and also explore the best next move for the game by greedy movement techniques and exploration method techniques for the future states of the game.
Reinforcement learning is an area of machine learning inspired by behaviorist psychology, concerned with how software agents ought to take actions in an environment so as to maximize some notion of cumulative reward.
This chapter shows how to use knowledge about the wlorld to make decisions even when the
outcomes of an action are uncertain and the rewards for acting might not be reaped until many
actions have passed. The main points are as follows:
e Sequential decision problems in uncertain envirsinments,also called Markov decision
processes, or MDPs, are defined by a transition model specifying the probabilistic
outcomes of actions and a reward function specifying the reward in each state.
o The utility of a state sequence is the sum of all the rewards over the sequence, possibly
discounted over time. The solution of an MDP is a policy that associates a decision
with every state that the agent might reach. An optimal policy maximizes the utility of
the state sequences encountered when it is execut~ed.
e The utility of a state is the expected utility of the state sequences encountered when
an optimal policy is executed, starting in that state. The value iteration algorithm for
solving MDPs works by iteratively solving the equations relating the utilities of each
state to that of its neighbors.
Policy iteration alternates between calculating the utilities of states under the current
policy and improving the current policy with respect to the current utilities.
* Partially observable MDPs, or POMDPs, are much more difficult to solve than are
MDPs. They can be solved by conversion to an MDP in the continuous space of belief
states. Optimal behavior in POMDPs includes information gathering to reduce uncertainty and therefore make better decisions in the fiuture.
A decision-theoretic agent can be constructed for POMDP environments. The agent
uses a dynamic decision network to represent the transition and observation models,
to update its belief state, and to project forward possible action sequences.
Game theory describes rational behavior for agents in situations where multiple agents
interact simultaneously. Solutions of games are Nash equilibria-strategy profiles in
which no agent has an incentive to deviate from the specified strategy.
Mechanism design can be used to set the rules by which agents will interact, in order
to maximize some global utility through the operation of individually rational agents.
Sometimes, mechanisms exist that achieve this goal without requiring each agent to
consider the choices made by other agents.
We shall return to the world of MDPs and POMDP in Chapter 21, when we study reinforcement learning methods that allow an agent to improve its behavior from experience in sequential, uncertain environments.
Top mailing list providers in the USA.pptxJeremyPeirce1
Discover the top mailing list providers in the USA, offering targeted lists, segmentation, and analytics to optimize your marketing campaigns and drive engagement.
The 10 Most Influential Leaders Guiding Corporate Evolution, 2024.pdfthesiliconleaders
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FIA officials brutally tortured innocent and snatched 200 Bitcoins of worth 4...jamalseoexpert1978
Farman Ayaz Khattak and Ehtesham Matloob are government officials in CTW Counter terrorism wing Islamabad, in Federal Investigation Agency FIA Headquarters. CTW and FIA kidnapped crypto currency owner from Islamabad and snatched 200 Bitcoins those worth of 4 billion rupees in Pakistan currency. There is not Cryptocurrency Regulations in Pakistan & CTW is official dacoit and stealing digital assets from the innocent crypto holders and making fake cases of terrorism to keep them silent.
Digital Transformation and IT Strategy Toolkit and TemplatesAurelien Domont, MBA
This Digital Transformation and IT Strategy Toolkit was created by ex-McKinsey, Deloitte and BCG Management Consultants, after more than 5,000 hours of work. It is considered the world's best & most comprehensive Digital Transformation and IT Strategy Toolkit. It includes all the Frameworks, Best Practices & Templates required to successfully undertake the Digital Transformation of your organization and define a robust IT Strategy.
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This PowerPoint presentation is only a small preview of our Toolkits. For more details, visit www.domontconsulting.com
At Techbox Square, in Singapore, we're not just creative web designers and developers, we're the driving force behind your brand identity. Contact us today.
Implicitly or explicitly all competing businesses employ a strategy to select a mix
of marketing resources. Formulating such competitive strategies fundamentally
involves recognizing relationships between elements of the marketing mix (e.g.,
price and product quality), as well as assessing competitive and market conditions
(i.e., industry structure in the language of economics).
3. Objective
Markov Decision Processes (Sequences of decisions)
– Introduction to MDPs
– Computing optimal policies for MDPs
4. Markov Decision Process (MDP)
Sequential decision problems under uncertainty
– Not just the immediate utility, but the longer-term utility
as well
– Uncertainty in outcomes
Roots in operations research
Also used in economics, communications engineering,
ecology, performance modeling and of course, AI!
– Also referred to as stochastic dynamic programs
5. Markov Decision Process (MDP)
Defined as a tuple: <S, A, P, R>
– S: State
– A: Action
– P: Transition function
Table P(s’| s, a), prob of s’ given action “a” in state “s”
– R: Reward
R(s, a) = cost or reward of taking action a in state s
Choose a sequence of actions (not just one decision or one action)
– Utility based on a sequence of decisions
6. Example: What SEQUENCE of actions
should our agent take?
Reward
-1
Blocked
CELL
Reward
+1
Start1 2 3 4
1
2
3
0.8
0.1
0.1
• Each action costs –1/25
• Agent can take action N, E, S, W
• Faces uncertainty in every state
N
7. MDP Tuple: <S, A, P, R>
S: State of the agent on the grid (4,3)
– Note that cell denoted by (x,y)
A: Actions of the agent, i.e., N, E, S, W
P: Transition function
– Table P(s’| s, a), prob of s’ given action “a” in state “s”
– E.g., P( (4,3) | (3,3), N) = 0.1
– E.g., P((3, 2) | (3,3), N) = 0.8
– (Robot movement, uncertainty of another agent’s actions,…)
R: Reward (more comments on the reward function later)
– R( (3, 3), N) = -1/25
– R (4,1) = +1
8. ??Terminology
• Before describing policies, lets go through some terminology
• Terminology useful throughout this set of lectures
•Policy: Complete mapping from states to actions
9. MDP Basics and Terminology
An agent must make a decision or control a probabilistic
system
Goal is to choose a sequence of actions for optimality
Defined as <S, A, P, R>
MDP models:
– Finite horizon: Maximize the expected reward for the
next n steps
– Infinite horizon: Maximize the expected discounted
reward.
– Transition model: Maximize average expected reward
per transition.
– Goal state: maximize expected reward (minimize expected
cost) to some target state G.
10. ???Reward Function
According to chapter2, directly associated with state
– Denoted R(I)
– Simplifies computations seen later in algorithms presented
Sometimes, reward is assumed associated with state,action
– R(S, A)
– We could also assume a mix of R(S,A) and R(S)
Sometimes, reward associated with state,action,destination-state
– R(S,A,J)
– R(S,A) = S R(S,A,J) * P(J | S, A)
J
11. Markov Assumption
Markov Assumption: Transition probabilities (and rewards) from
any given state depend only on the state and not on previous
history
Where you end up after action depends only on current state
– After Russian Mathematician A. A. Markov (1856-1922)
– (He did not come up with markov decision processes
however)
– Transitions in state (1,2) do not depend on prior state (1,1)
or (1,2)
12. ???MDP vs POMDPs
Accessibility: Agent’s percept in any given state identify the
state that it is in, e.g., state (4,3) vs (3,3)
– Given observations, uniquely determine the state
– Hence, we will not explicitly consider observations, only states
Inaccessibility: Agent’s percepts in any given state DO NOT
identify the state that it is in, e.g., may be (4,3) or (3,3)
– Given observations, not uniquely determine the state
– POMDP: Partially observable MDP for inaccessible environments
We will focus on MDPs in this presentation.
15. Policy
Policy is like a plan, but not quite
– Certainly, generated ahead of time, like a plan
Unlike traditional plans, it is not a sequence of
actions that an agent must execute
– If there are failures in execution, agent can continue to
execute a policy
Prescribes an action for all the states
Maximizes expected reward, rather than just
reaching a goal state
16. MDP problem
The MDP problem consists of:
– Finding the optimal control policy for all possible states;
– Finding the sequence of optimal control functions for a specific
initial state
– Finding the best control action(decision) for a specific state.
17. Non-Optimal Vs Optimal Policy
-1
+1
Start
1 2 3 4
1
2
3
• Choose Red policy or Yellow policy?
• Choose Red policy or Blue policy?
Which is optimal (if any)?
• Value iteration: One popular algorithm to determine optimal policy
18. Value Iteration: Key Idea
• Iterate: update utility of state “I” using old utility of
neighbor states “J”; given actions “A”
– U t+1 (I) = max [R(I,A) + S P(J|I,A)* U t (J)]
A J
– P(J|I,A): Probability of J if A is taken in state I
– max F(A) returns highest F(A)
– Immediate reward & longer term reward taken into
account
19. Value Iteration: Algorithm
• Initialize: U0 (I) = 0
• Iterate:
U t+1 (I) = max [ R(I,A) + S P(J|I,A)* U t (J) ]
A J
– Until close-enough (U t+1, Ut)
At the end of iteration, calculate optimal policy:
Policy(I) = argmax [R(I,A) + S P(J|I,A)* U t+1 (J) ]
A J
21. ??Markov Chain
Given fixed policy, you get a markov chain from the MDP
– Markov chain: Next state is dependent only on previous state
– Next state: Not dependent on action (there is only one action)
– Next state: History dependency only via the previous state
– P(S t+1 | St, S t-1, S t-2 …..) = P(S t+1 | St)
How to evaluate the markov chain?
• Could we try simulations?
• Are there other sophisticated methods around?
26. Dynamic Construction
of the Decision Tree
Incrémental expansion(MDP,γ, sI, є, VL, VU)
Initialize tree T with sI and ubound (sI), lbound (sI) using VL, VU;
repeat until(single action remains for sI or ubound (sI) - lbound (sI) <= є
call Improve-tree(T,MDP,γ, VL, VU)
return action with greatest lover bound as a result;
Improve-tree (T,MDP,γ, VL, VU)
if root(T) is a leaf
then expand root(T)
set bouds lbound, ubound of new leaves using VL, VU;
else for all decision subtrees T’ of T
do call Improve-tree (T,MDP,γ, VL, VU)
recompute bounds lbound(root(T)), ubound(root(T))for root(T);
when root(T) is a decision node
prune suboptimal action branches from T;
return;
27. Incremental expansion function:
Basic Method for the Dynamic Construction of the Decision Tree
start
MDP, γ, SI, ε, VL,
VU
OR SI)-bound(SI)
initialize leaf node of the partially
built decision tree
return
call Improve-tree(T,MDP, γ, ε, VL, VU)
Terminate
28. Computer Decisions
using Bound Iteration
Incrémental expansion(MDP,γ, sI, є, VL, VU)
Initialize tree T with sI and ubound (sI), lbound (sI) using VL, VU;
repeat until(single action remains for sI or ubound (sI) - lbound (sI) <= є
call Improve-tree(T,MDP,γ, VL, VU)
return action with greatest lover bound as a result;
Improve-tree (T,MDP,γ, VL, VU)
if root(T) is a leaf
then expand root(T)
set bouds lbound, ubound of new leaves using VL, VU;
else for all decision subtrees T’ of T
do call Improve-tree (T,MDP,γ, VL, VU)
recompute bounds lbound(root(T)), ubound(root(T))for root(T);
when root(T) is a decision node
prune suboptimal action branches from T;
return;
29. Incremental expansion function:
Basic Method for the Dynamic Construction of the Decision Tree
start
MDP, γ, SI, ε, VL,
VU
OR (SI)-bound(SI)
initialize leaf node of the partially
built decision tree
return
call Improve-tree(T,MDP, γ, ε, VL, VU)
Terminate
31. If You Want to Read More
on MDPs
If You Want to Read More
on MDPs
Book:
– Martin L. Puterman
Markov Decision Processes
Wiley Series in Probability
– Available on Amazon.com