  Recent applications in machine learning have renewed the interest of the
community in min-max optimization problems. While gradient-based optimization
methods are widely used to solve such problems, there are however many
scenarios where these techniques are not well-suited, or even not applicable
when the gradient is not accessible. We investigate the use of direct-search
methods that belong to a class of derivative-free techniques that only access
the objective function through an oracle. In this work, we design a novel
algorithm in the context of min-max saddle point games where one sequentially
updates the min and the max player. We prove convergence of this algorithm
under mild assumptions, where the objective of the max-player satisfies the
Polyak-\L{}ojasiewicz (PL) condition, while the min-player is characterized by
a nonconvex objective. Our method only assumes dynamically adjusted accurate
estimates of the oracle with a fixed probability. To the best of our knowledge,
our analysis is the first one to address the convergence of a direct-search
method for min-max objectives in a stochastic setting.
