An Eecient Stochastic Approximation Algorithm for Stochastic Saddle Point Problems

We show that Polyak's (1990) stochastic approximation algorithm with averaging originally developed for unconstrained minimization of a smooth strongly convex objective function observed with noise can be naturally modiied to solve convex-concave stochas-tic saddle point problems. We also show that the extended algorithm, considered on general families of stochastic convex-concave saddle point problems, possesses a rate of convergence unimprovable in order in the minimax sense. We nally present supporting numerical results for the proposed algorithm.