Near-Optimal Pure Exploration in Matrix Games: A Generalization of Stochastic Bandits & Dueling Bandits

• URL: http://arxiv.org/abs/2310.16252v2
• Date: Mon, 27 Nov 2023 21:33:05 GMT
• Title: Near-Optimal Pure Exploration in Matrix Games: A Generalization of Stochastic Bandits & Dueling Bandits
• Authors: Arnab Maiti, Ross Boczar, Kevin Jamieson, Lillian J. Ratliff
• Abstract summary: We study the sample complexity of identifying the pure strategy Nash equilibrium (PSNE) in a two-player zero-sum matrix game with noise. We find a near-optimal algorithm whose complexity matches lower bound, up to log factors. The problem of identifying the PSNE is also generalizes the problem of pure exploration in multi-armed bandits and dueling bandits, and our result matches the optimal bounds, up to log factors.
• Score: 21.49682459678413
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the sample complexity of identifying the pure strategy Nash equilibrium (PSNE) in a two-player zero-sum matrix game with noise. Formally, we are given a stochastic model where any learner can sample an entry $(i,j)$ of the input matrix $A\in[-1,1]^{n\times m}$ and observe $A_{i,j}+\eta$ where $\eta$ is a zero-mean 1-sub-Gaussian noise. The aim of the learner is to identify the PSNE of $A$, whenever it exists, with high probability while taking as few samples as possible. Zhou et al. (2017) presents an instance-dependent sample complexity lower bound that depends only on the entries in the row and column in which the PSNE lies. We design a near-optimal algorithm whose sample complexity matches the lower bound, up to log factors. The problem of identifying the PSNE also generalizes the problem of pure exploration in stochastic multi-armed bandits and dueling bandits, and our result matches the optimal bounds, up to log factors, in both the settings.

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