Estimate Sequences for Stochastic Composite Optimization: Variance Reduction, Acceleration, and Robustness to Noise

Andrei Kulunchakov; Julien Mairal

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arXiv · 1901.08788

Estimate Sequences for Stochastic Composite Optimization: Variance Reduction, Acceleration, and Robustness to Noise

Andrei Kulunchakov·Julien Mairal

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Abstract

In this paper, we propose a unified view of gradient-based algorithms for stochastic convex composite optimization by extending the concept of estimate sequence introduced by Nesterov. More precisely, we interpret a large class of stochastic optimization methods as procedures that iteratively minimize a surrogate of the objective, which covers the stochastic gradient descent method and variants of the incremental approaches SAGA, SVRG, and MISO/Finito/SDCA. This point of view has several advantages: (i) we provide a simple generic proof of convergence for all of the aforementioned methods; (ii) we naturally obtain new algorithms with the same guarantees; (iii) we derive generic strategies to make these algorithms robust to stochastic noise, which is useful when data is corrupted by small random perturbations. Finally, we propose a new accelerated stochastic gradient descent algorithm and an accelerated SVRG algorithm with optimal complexity that is robust to stochastic noise.

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BibTeX RIS

Andrei Kulunchakov, Julien Mairal. 2019-01-25. Estimate Sequences for Stochastic Composite Optimization: Variance Reduction, Acceleration, and Robustness to Noise. https://arxiv.org/abs/1901.08788

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