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Convergence of Deep Fictitious Play for Stochastic Differential Games [article]

Jiequn Han, Ruimeng Hu, Jihao Long
2021 arXiv   pre-print
The recently proposed machine learning algorithm, deep fictitious play, provides a novel efficient tool for finding Markovian Nash equilibrium of large N-player asymmetric stochastic differential games  ...  By incorporating the idea of fictitious play, the algorithm decouples the game into N sub-optimization problems, and identifies each player's optimal strategy with the deep backward stochastic differential  ...  For stochastic differential games, besides [27] , the most related work is [34] , where fictitious play is used to design numerical algorithms for finding open-loop Nash equilibria.  ... 
arXiv:2008.05519v2 fatcat:oeecmh7t6bhspbakvde6rghew4

Deep Fictitious Play for Stochastic Differential Games [article]

Ruimeng Hu
2020 arXiv   pre-print
stochastic differential games, for which we refer as deep fictitious play, a multi-stage learning process.  ...  The resulted deep learning algorithm based on fictitious play is scalable, parallel and model-free, i.e., using GPU parallelization, it can be applied to any N-player stochastic differential game with  ...  I am grateful to Professor Marcel Nutz for the stimulating and fruitful discussions on fictitious play and convergence of linear quadratic case.  ... 
arXiv:1903.09376v3 fatcat:qmqw7xeylbaqjlkvg2mjcqt7ui

Smooth Fictitious Play in Stochastic Games with Perturbed Payoffs and Unknown Transitions [article]

Lucas Baudin, Rida Laraki
2022 arXiv   pre-print
Recent extensions to dynamic games of the well-known fictitious play learning procedure in static games were proved to globally converge to stationary Nash equilibria in two important classes of dynamic  ...  Our procedures can be seen as extensions to stochastic games of the classical smooth fictitious play learning procedures in static games (where the players best responses are regularized, thanks to a smooth  ...  play with known transitions and deterministic payoff To extend smooth fictitious play to stochastic games, we use two sets of variables.  ... 
arXiv:2207.03109v1 fatcat:lhkfmyexj5ef7fitviv5m7i2kq

Deep Fictitious Play for Finding Markovian Nash Equilibrium in Multi-Agent Games [article]

Jiequn Han, Ruimeng Hu
2020 arXiv   pre-print
We propose a deep neural network-based algorithm to identify the Markovian Nash equilibrium of general large N-player stochastic differential games.  ...  Following the idea of fictitious play, we recast the N-player game into N decoupled decision problems (one for each player) and solve them iteratively.  ...  They really appreciate the hospitality of the institute, and thank Professor Weinan E for hosting and useful discussions.  ... 
arXiv:1912.01809v2 fatcat:f5zln73xzvgxvnpzvle4lr5zbq

Large-Scale Multi-Agent Deep FBSDEs [article]

Tianrong Chen, Ziyi Wang, Ioannis Exarchos, Evangelos A. Theodorou
2021 arXiv   pre-print
In this paper we present a scalable deep learning framework for finding Markovian Nash Equilibria in multi-agent stochastic games using fictitious play.  ...  We showcase superior performance of our framework over the state-of-the-art deep fictitious play algorithm on an inter-bank lending/borrowing problem in terms of multiple metrics.  ...  We would also like to thank Professor Matthieu Bloch and Guan-Horng Liu for the helpful discussions.  ... 
arXiv:2011.10890v3 fatcat:rdttsdxsczdblan2qmo2yyg7ve

Signatured Deep Fictitious Play for Mean Field Games with Common Noise [article]

Ming Min, Ruimeng Hu
2021 arXiv   pre-print
Existing deep learning methods for solving mean-field games (MFGs) with common noise fix the sampling common noise paths and then solve the corresponding MFGs.  ...  In this paper, based on the rough path theory, we propose a novel single-loop algorithm, named signatured deep fictitious play, by which we can work with the unfixed common noise setup to avoid the nested-loop  ...  We integrate the signature from rough path theory, and fictitious play from game theory for efficiency and accuracy, and term the algorithm Signatured Deep Fictitious Play (Sig-DFP).  ... 
arXiv:2106.03272v1 fatcat:wtcdkn2pcnhwxbwstvxsc3kdiy

Optimal Policies for a Pandemic: A Stochastic Game Approach and a Deep Learning Algorithm [article]

Yao Xuan, Robert Balkin, Jiequn Han, Ruimeng Hu, Hector D. Ceniceros
2021 arXiv   pre-print
In this paper, we propose a multi-region SEIR model based on stochastic differential game theory, aiming to formulate optimal regional policies for infectious diseases.  ...  This significant numerical difficulty of the model structure motivates us to generalize the deep fictitious algorithm introduced in [Han and Hu, MSML2020, pp.221--245, PMLR, 2020] and develop an improved  ...  Left: validation losses versus rounds M of the enhanced deep fictitious play; Right: log 10 validation loss versus rounds M of the enhanced deep fictitious play.  ... 
arXiv:2012.06745v2 fatcat:txrhsivtpbf6vmdstisifa6pca

Multi-Agent Reinforcement Learning: A Selective Overview of Theories and Algorithms [article]

Kaiqing Zhang, Zhuoran Yang, Tamer Başar
2021 arXiv   pre-print
the mean-field regime, (non-)convergence of policy-based methods for learning in games, etc.  ...  More specifically, we review the theoretical results of MARL algorithms mainly within two representative frameworks, Markov/stochastic games and extensive-form games, in accordance with the types of tasks  ...  Moreover, in a more recent work, [162] has proposed a smooth fictitious play algorithm [265] for zero-sum multi-stage games with simultaneous moves (a special case of zero-sum stochastic games).  ... 
arXiv:1911.10635v2 fatcat:ihlhtjlhnrdizbkcfzsnz5urfq

Generalization in Mean Field Games by Learning Master Policies [article]

Sarah Perrin and Mathieu Laurière and Julien Pérolat and Romuald Élie and Matthieu Geist and Olivier Pietquin
2021 arXiv   pre-print
and Fictitious Play.  ...  Mean Field Games (MFGs) can potentially scale multi-agent systems to extremely large populations of agents.  ...  E On the Convergence of Master Fictitious Play In this section we study the evolution of the averaged MF flow generated by the Master Fictitious Play algorithm, see Alg. 1.  ... 
arXiv:2109.09717v1 fatcat:wwgozospdnbpblbyv6u5bo7zqu

Game of GANs: Game-Theoretical Models for Generative Adversarial Networks [article]

Monireh Mohebbi Moghadam, Bahar Boroomand, Mohammad Jalali, Arman Zareian, Alireza DaeiJavad, Mohammad Hossein Manshaei, Marwan Krunz
2022 arXiv   pre-print
This paper reviews the literature on the game theoretic aspects of GANs and addresses how game theory models can address specific challenges of generative model and improve the GAN's performance.  ...  We then present taxonomy to classify state-of-the-art solutions into three main categories: modified game models, modified architectures, and modified learning methods.  ...  Furthermore, they show that the minimax objective of the generator's equilibrium strategy is optimal for the minimax objective. 2) Fictitious play: GAN is a two-player zero-sum game with a repeated game  ... 
arXiv:2106.06976v3 fatcat:mecyjeopxnesjfj7bcoiim3p3a

Learning High-Dimensional McKean-Vlasov Forward-Backward Stochastic Differential Equations with General Distribution Dependence [article]

Jiequn Han, Ruimeng Hu, Jihao Long
2022 arXiv   pre-print
One of the core problems in mean-field control and mean-field games is to solve the corresponding McKean-Vlasov forward-backward stochastic differential equations (MV-FBSDEs).  ...  In this paper, we propose a novel deep learning method for computing MV-FBSDEs with a general form of mean-field interactions.  ...  of fictitious play.  ... 
arXiv:2204.11924v1 fatcat:4uvsyh563vhxpamvauvkyxbvzu

Scaling Mean Field Games by Online Mirror Descent

Julien Pérolat, Sarah Perrin, Romuald Elie, Mathieu Laurière, Georgios Piliouras, Matthieu Geist, Karl Tuyls, Olivier Pietquin
2022 International Joint Conference on Autonomous Agents & Multiagent Systems  
We empirically show that OMD scales and converges significantly faster than Fictitious Play by solving, for the first time to our knowledge, examples of MFGs with hundreds of billions states.  ...  We address the scaling of equilibrium computation in Mean Field Games (MFGs) by using Online Mirror Descent (OMD).  ...  In our framework, it is a consequence of the convergence of the Fictitious Play dynamics in monotone games, which is detailed in Appx. C. Proposition 1 (Existence and uniqeness of Nash).  ... 
dblp:conf/atal/PerolatPELPGTP22 fatcat:pvyun7redfgirnhx3jltmewtuy

On the Convergence of Model Free Learning in Mean Field Games [article]

Romuald Elie, Julien Pérolat, Mathieu Laurière, Matthieu Geist, Olivier Pietquin
2020 arXiv   pre-print
a deep RL algorithm.  ...  We illustrate our theoretical results with a numerical experiment in a continuous action-space environment, where the approximate best response of the iterative fictitious play scheme is computed with  ...  Fictitious Play Algorithms for MFG Fictitious play (Robinson 1951 ) is an iterative learning scheme for repeated games, where each agent calibrates its belief to the empirical frequency of previously  ... 
arXiv:1907.02633v3 fatcat:enhfu4622newvf2ey4q4vajiqm

On the Convergence of Model Free Learning in Mean Field Games

Romuald Elie, Julien Pérolat, Mathieu Laurière, Matthieu Geist, Olivier Pietquin
2020 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
a deep RL algorithm.  ...  We illustrate our theoretical results with a numerical experiment in a continuous action-space environment, where the approximate best response of the iterative fictitious play scheme is computed with  ...  Fictitious Play Algorithms for MFG Fictitious play (Robinson 1951 ) is an iterative learning scheme for repeated games, where each agent calibrates its belief to the empirical frequency of previously  ... 
doi:10.1609/aaai.v34i05.6203 fatcat:37v32bxk6vd53jdpqs3ydjwsiy

Deep Reinforcement Learning from Self-Play in No-limit Texas Hold'em Poker

T.-V. Pricope
2021 Studia Universitatis Babes-Bolyai: Series Informatica  
Neural Fictitious Self Play (NFSP) is a powerful algorithm for learning approximate Nash equilibrium of imperfect information games from self-play.  ...  When applied to no-limit Hold'em Poker, the agents trained through self-play outperformed the ones that used fictitious play with a normal-form single-step approach to the game.  ...  Neural Fictitious Self-Play. Neural Fictitious Self-Play [10] is a model of learning approximate Nash Equilibrium in imperfect-information games using deep learning.  ... 
doi:10.24193/subbi.2021.2.04 fatcat:obzv6wscrnfdtepsf3xaijhtvu
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