#optazur High Probability and Risk-Averse Guarantees for Stochastic Saddle Point Problems

par Yassine Laguel (UniCA)

lundi 18 déc. 2023, 15:15 → 16:15 Europe/Paris

I3S

We investigate the stochastic accelerated primal-dual algorithm for strongly-convex-strongly-concave saddle point problems, common in distributionally robust learning, game theory, and fairness in machine learning. Our algorithm offers optimal complexity in several settings and we provide high probability guarantees for convergence to a neighborhood of the saddle point. We derive analytical formulas for the limit covariance matrix and develop lower bounds to show that our analysis is tight. Our risk- averse convergence analysis characterizes the trade-offs between bias and risk in approximate solutions. We present numerical experiments on zero-sum games and robust learning problems.