We develop a new stochastic algorithm with variance reduction for solving pseudo-monotone stochastic variational inequalities. Our method builds on Tseng's forward-backward-forward (FBF) algorithm, which is known in the deterministic literature to be a valuable alternative to Korpelevich's extragradient method when solving variational inequalities over a convex and closed set governed by pseudo-monotone, Lipschitz continuous operators. The main computational advantage of Tseng's algorithm is that it relies only on a single projection step and two independent queries of a stochastic oracle. Our algorithm incorporates a variance reduction mechanism and leads to almost sure (a.s.) convergence to an optimal solution. To the best of our knowledge, this is the first stochastic look-ahead algorithm achieving this by using only a single projection at each iteration.
|Publisher||arXiv.org at Cornell University Library|
|Number of pages||34|
|Publication status||Published - 2019|
Mertikopoulos, P., Staudigl, M., University of Vienna, & University of Vienna (2019). Forward-backward-forward methods with variance reduction for stochastic variational inequalities. arXiv.org at Cornell University Library.