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Conference Papers Year : 2019

A Generic Acceleration Framework for Stochastic Composite Optimization

Abstract

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.
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Dates and versions

hal-02139489 , version 1 (29-05-2019)
hal-02139489 , version 2 (03-10-2019)
hal-02139489 , version 3 (07-10-2019)

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Andrei Kulunchakov, Julien Mairal. A Generic Acceleration Framework for Stochastic Composite Optimization. NeurIPS 2019 - Thirty-third Conference Neural Information Processing Systems, Dec 2019, Vancouver, Canada. pp.12556-12567. ⟨hal-02139489v3⟩
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