Learning to Compute Approximate Nash Equilibrium for Normal-form Games

• URL: http://arxiv.org/abs/2108.07472v1
• Date: Tue, 17 Aug 2021 07:06:46 GMT
• Title: Learning to Compute Approximate Nash Equilibrium for Normal-form Games
• Authors: Zhijian Duan, Yali Du, Jun Wang, Xiaotie Deng
• Abstract summary: We propose a general meta learning approach to computing approximate Nash equilibrium for finite $n$-player normal-form games. Unlike existing solutions that approximate or learn a Nash equilibrium from scratch for each of the games, our meta solver directly constructs a mapping from a game utility matrix to a joint strategy profile.
• Score: 15.321036952379488
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we propose a general meta learning approach to computing approximate Nash equilibrium for finite $n$-player normal-form games. Unlike existing solutions that approximate or learn a Nash equilibrium from scratch for each of the games, our meta solver directly constructs a mapping from a game utility matrix to a joint strategy profile. The mapping is parameterized and learned in a self-supervised fashion by a proposed Nash equilibrium approximation metric without ground truth data informing any Nash equilibrium. As such, it can immediately predict the joint strategy profile that approximates a Nash equilibrium for any unseen new game under the same game distribution. Moreover, the meta-solver can be further fine-tuned and adaptive to a new game if iteration updates are allowed. We theoretically prove that our meta-solver is not affected by the non-smoothness of exact Nash equilibrium solutions, and derive a sample complexity bound to demonstrate its generalization ability across normal-form games. Experimental results demonstrate its substantial approximation power against other strong baselines in both adaptive and non-adaptive cases.

Related papers

• Nash Equilibria via Stochastic Eigendecomposition [4.190518009892366]
  We show a Nash equilibrium can be approximated with purely calls to parameter, iterative variants of value decomposition and power. We provide pseudocode and experiments demonstrating solving for all equilibria of a general-sum game using only readily available linear algebra tools.
  arXiv  Detail & Related papers  (2024-11-04T17:32:21Z)
• Differentiable Arbitrating in Zero-sum Markov Games [59.62061049680365]
  We study how to perturb the reward in a zero-sum Markov game with two players to induce a desirable Nash equilibrium, namely arbitrating. The lower level requires solving the Nash equilibrium under a given reward function, which makes the overall problem challenging to optimize in an end-to-end way. We propose a backpropagation scheme that differentiates through the Nash equilibrium, which provides the gradient feedback for the upper level.
  arXiv  Detail & Related papers  (2023-02-20T16:05:04Z)
• Abstracting Imperfect Information Away from Two-Player Zero-Sum Games [85.27865680662973]
  Nayyar et al. (2013) showed that imperfect information can be abstracted away from common-payoff games by having players publicly announce their policies as they play. This work shows that certain regularized equilibria do not possess the aforementioned non-correspondence problem. Because these regularized equilibria can be made arbitrarily close to Nash equilibria, our result opens the door to a new perspective to solving two-player zero-sum games.
  arXiv  Detail & Related papers  (2023-01-22T16:54:06Z)
• Global Nash Equilibrium in Non-convex Multi-player Game: Theory and Algorithms [66.8634598612777]
  We show that Nash equilibrium (NE) is acceptable to all players in a multi-player game. We also show that no one can benefit unilaterally from the general theory step by step.
  arXiv  Detail & Related papers  (2023-01-19T11:36:50Z)
• Finding mixed-strategy equilibria of continuous-action games without gradients using randomized policy networks [83.28949556413717]
  We study the problem of computing an approximate Nash equilibrium of continuous-action game without access to gradients. We model players' strategies using artificial neural networks. This paper is the first to solve general continuous-action games with unrestricted mixed strategies and without any gradient information.
  arXiv  Detail & Related papers  (2022-11-29T05:16:41Z)
• Learning Correlated Equilibria in Mean-Field Games [62.14589406821103]
  We develop the concepts of Mean-Field correlated and coarse-correlated equilibria. We show that they can be efficiently learnt in emphall games, without requiring any additional assumption on the structure of the game.
  arXiv  Detail & Related papers  (2022-08-22T08:31:46Z)
• Safe Equilibrium [1.7132914341329848]
  The standard game-theoretic solution concept, Nash equilibrium, assumes that all players behave rationally. We propose a new solution concept called safe equilibrium that models opponents as behaving rationally with a specified probability. We prove that a safe equilibrium exists in all strategic-form games, and prove that its computation is PPAD-hard.
  arXiv  Detail & Related papers  (2022-01-12T01:45:51Z)
• Multiplayer Performative Prediction: Learning in Decision-Dependent Games [18.386569111954213]
  This paper formulates a new game theoretic framework for multi-player performative prediction. We focus on two distinct solution concepts, namely (i) performatively stable equilibria and (ii) Nash equilibria of the game. We show that under mild assumptions, the performatively stable equilibria can be found efficiently by a variety of algorithms.
  arXiv  Detail & Related papers  (2022-01-10T15:31:10Z)
• Towards convergence to Nash equilibria in two-team zero-sum games [17.4461045395989]
  Two-team zero-sum games are defined as multi-player games where players are split into two competing sets of agents. We focus on the solution concept of Nash equilibria (NE) We show that computing NE for this class of games is $textithard$ for the complexity class $mathrm$.
  arXiv  Detail & Related papers  (2021-11-07T21:15:35Z)
• Sample-Efficient Learning of Stackelberg Equilibria in General-Sum Games [78.65798135008419]
  It remains vastly open how to learn the Stackelberg equilibrium in general-sum games efficiently from samples. This paper initiates the theoretical study of sample-efficient learning of the Stackelberg equilibrium in two-player turn-based general-sum games.
  arXiv  Detail & Related papers  (2021-02-23T05:11:07Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.