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It is common to encounter large-scale monotone inclusion problems where theobjective has a finite sum structure. We develop a general framework forvariance-reduced forward-backward splitting algorithms for this problem. Thisframework includes a number of existing deterministic and variance-reducedalgorithms for function minimization as special cases, and it is alsoapplicable to more general problems such as saddle-point problems andvariational inequalities. With a carefully constructed Lyapunov function, weshow that the algorithms covered by our framework enjoy a linear convergencerate in expectation under mild assumptions. We further consider Catalystacceleration and asynchronous implementation to reduce the algorithmiccomplexity and computation time. We apply our proposed framework to a policyevaluation problem and a strongly monotone two-player game, both of which falloutside of function minimization.

A Unifying Framework for Variance Reduction Algorithms for Finding Zeroes of Monotone Operators