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.

这篇研究论文探讨了具有噪声的两人零和矩阵博弈中，识别纯策略纳什均衡（PSNE）的样本复杂度。研究人员设计了一个接近最优的算法，其样本复杂度与已知的下界相匹配，同时解决了纯探索问题和dueling bandits问题，且结果与最优边界相匹配。

矩阵博弈中的接近最优纯探索：随机赌博机和决斗赌博机的一般化