Gradient-free algorithm for saddle point problems under overparametrization

Abstract: This paper focuses on solving a stochastic saddle point problem (SPP) under an overparameterized regime for the case, when the gradient computation is impractical. As an intermediate step, we generalize Same-sample Stochastic Extra-gradient algorithm (Gorbunov et al., 2022) to a biased oracle and estimate novel convergence rates. As the result of the paper we introduce an algorithm, which uses gradient approximation instead of a gradient oracle. We also conduct an analysis to find the maximum admissible level of adversarial noise and the optimal number of iterations at which our algorithm can guarantee achieving the desired accuracy.