SVRG Meets AdaGrad: Painless Variance Reduction

TL;DR

This paper introduces AdaSVRG, an adaptive variance reduction method that combines SVRG with AdaGrad, making it robust to step-size choices and eliminating the need for problem-dependent constants, with proven convergence and empirical success.

Contribution

We propose AdaSVRG, a novel variance reduction algorithm integrating AdaGrad, which is robust to step-size selection and does not require prior knowledge of problem constants.

Findings

Achieves optimal convergence rate without problem-dependent constants.

Demonstrates superior empirical performance over existing methods.

Provides a heuristic for adaptive inner-loop length determination.

Abstract

Variance reduction (VR) methods for finite-sum minimization typically require the knowledge of problem-dependent constants that are often unknown and difficult to estimate. To address this, we use ideas from adaptive gradient methods to propose AdaSVRG, which is a more robust variant of SVRG, a common VR method. AdaSVRG uses AdaGrad in the inner loop of SVRG, making it robust to the choice of step-size. When minimizing a sum of n smooth convex functions, we prove that a variant of AdaSVRG requires $\tilde{O}(n + 1/\epsilon)$ gradient evaluations to achieve an $O(\epsilon)$-suboptimality, matching the typical rate, but without needing to know problem-dependent constants. Next, we leverage the properties of AdaGrad to propose a heuristic that adaptively determines the length of each inner-loop in AdaSVRG. Via experiments on synthetic and real-world datasets, we validate the robustness and effectiveness of AdaSVRG, demonstrating its superior performance over standard and other "tune-free" VR methods.