  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.
