A Generic Acceleration Framework for Stochastic Composite Optimization
This work provides a generic acceleration framework for stochastic optimization, which is incremental as it builds on existing deterministic methods.
The authors tackled the problem of accelerating stochastic composite optimization for convex and strongly convex objectives by extending the Catalyst approach to the stochastic setting, achieving optimal worst-case complexity dependent on gradient noise variance.
In this paper, we introduce various mechanisms to obtain accelerated first-order stochastic optimization algorithms when the objective function is convex or strongly convex. Specifically, we extend the Catalyst approach originally designed for deterministic objectives to the stochastic setting. Given an optimization method with mild convergence guarantees for strongly convex problems, the challenge is to accelerate convergence to a noise-dominated region, and then achieve convergence with an optimal worst-case complexity depending on the noise variance of the gradients. A side contribution of our work is also a generic analysis that can handle inexact proximal operators, providing new insights about the robustness of stochastic algorithms when the proximal operator cannot be exactly computed.