Stochastic Proximal Point Methods for Monotone Inclusions under Expected Similarity

Abdurakhmon Sadiev, Laurent Condat, Peter Richtárik

Keywords: Monotone Inclusions, Proximal Point Method, Stochastic Proximal Point Method, Data Similarity

Abstract: Monotone inclusions have a wide range of applications, including minimization, saddle-point, and equilibria problems. We introduce new stochastic algorithms, with or without variance reduction, to estimate a root of the expectation of possibly set-valued monotone operators, using at every iteration one call to the resolvent of a randomly sampled operator. We also introduce a notion of similarity between the operators, which holds even for discontinuous operators. We leverage it to derive linear convergence results in the strongly monotone setting.

Submission Number: 66