Almost-Surely Convergent Randomly Activated Monotone Operator Splitting Methods

Abstract

We propose stochastic splitting algorithms for solving large-scale composite inclusion problems involving monotone and linear operators. They activate at each iteration blocks of randomly selected resolvents of monotone operators and, unlike existing methods, achieve almost sure convergence of the iterates to a solution without any regularity assumptions or knowledge of the norms of the linear operators. Applications to image recovery and machine learning are provided.