Stochastic Optimization Methods for Variational Inequalities

The seminar will explore optimization methods for variational inequalities (VIs), a broader class of problems encompassing minimization and min-max problems. The presentation will start with a brief historical overview, delving into classical deterministic methods for solving VIs. It will then transition to modern results, covering various stochastic approaches tailored to different problem formulations and randomness nature. In particularly, topics include finite-sum formulations and variance reduction techniques for them. The emphasis will be on the theoretical aspects of algorithms, aiming to establish a unified theory for obtaining convergence bounds of stochastic algorithms for VIs. The talk is based on one of the chapters of the speaker's thesis.