[DL輪読会]Learning Deep Mean Field Games for Modeling Large Population...

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1
DEEP LEARNING JP
[DL Papers]
http://deeplearning.jp/
“Learning deep mean field games for modeling large
population behav...

• : Learning deep mean fieldgamse for modeling large population behavior
• : Jiachen Yang, Xiaojing Ye, Rakshit Trivedi, H...

• :
• Collective Behavior( )
• Mean Field Games(MFG)
• Pros:
• Cons: (= )
• : Inference of MFG via Markov Decision Process...

• :
• Arab Spring , Black Lives Matter movement, fake news, etc.
• 1:
• "Nothing takes place in the world whose meaning is...

• 2: ⇄
•
topic1 topic2 topic1 topic2
:
topic1

•
• MFG(discrete-time graph-state)
• e.g., , etc.
topic1 topic2 topic1 topic2
:
topic1

•
1. ( ⇄ )
2.
3.
• Mean Filed Game
1. 2. 3.
Time-Series-Analysis
(e.g., VAR)
Network-Analysis , ?,
Mean Field Game

Mean Field Game (MFG)
•
ØN-player ! → ∞
Ø
• e.g.,
•
•
•
• opinion network
• etc. ( : Gueant+ 2011)

Mean Field Game (MFG)
• MFG (Guent 2009):
•
• ! → ∞
•
• Social Interactions of the mean field type
•
•

Mean Field Game (MFG)
• Social Interactions of the mean field type
DL
1 5 5 9
DL
1 5 5 9
5
5
5
•
• N
……
I

( ) Multi Agent Reinforcement Learning (MARL)
• Mean Field Multi-Agent Reinforcement Learning (Yang+ 2018)
• MARL
ØMARL j ...

Mean Field Game (MFG)
• MFG : (=- )
ØMFG agnostic
Ø
Ø MFG Toy-Problem
• Contribution:
• MFG Toy-Problem

Discrete-time graph-state MFG
• : Discrete-time graph-state MFG
• d
• !" # : t i
• $"%
&
: t, t+1 i j
• (Mean)
topic1 topi...

Discrete-time graph-state MFG
• : Discrete-time graph-state MFG
• !"($ % , '" % ):
• $ % = $" % "*+
,
'"
-
= '",+
-
, … , ...

Discrete-time graph-state MFG
• MFG
• !"
#
= max
()
*
[," -#
, /"
#
+ ∑2 /"2
#
!2
#34
] (backward Hamilton-Jacobi-Bellman ...

Inference on MFG via MDP optimization
•
…
MDP
MFG Trajectory

Inference on MFG via MDP optimization
• MFG MDP
•
• MFG MDP
Ø
Ø MFG Forward-Path
• Settings
• States: !"
, n
• Actions: #"...

Inference on MFG via MDP optimization
• : MDP
MFG HJB, Fokker-Planck
HJB
Fokker-Planck
!
Nash-Maximizer!"

Inference on MFG via MDP optimization
•
1. ( ⇄ )
2.
3.
• MFG MDP
Øsingle-agent RL V∗
(%&
) = max
,
[. %&
, 0 + V∗
%&23
]
Ø...

Experiments
• : Twitter
• d = 15 topics 15 ( ( , etc.) )
• n_timesteps=16, 16 1episode
• n_episodes = 27, 27
• Guided Cost...

Experiments
• state-action
•
S0:
A0:
S2:

Experiments
• Jensen-Shannon-Divergence
VAE, RNN
• MFG
( ⇄ , )
•
MFG RNN
• RNN

Experiments
•
• ( )

Conslusion
•
• MFG MDP
• MFG Toy-Problem
•
• !"($ % , ' % )= !"($ % , '" % )
• ( )
• Network-Based Social
Dynamics Model
•

• MFG VAR
or
•

References
• Gueant, Olivier. (2009). A reference case for mean field games models. Journal de
Mathématiques Pures et Appl...

• MFG :
• https://link.springer.com/content/pdf/10.1007%2Fs11537-007-0657-8.pdf
• MFG :
• https://www.sciencedirect.com/sc...

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