Almost Tune-Free Variance Reduction

TL;DR

This paper introduces almost tune-free variants of SVRG and SARAH algorithms using Barzilai-Borwein step sizes and adaptive inner loop lengths, improving convergence and reducing parameter tuning.

Contribution

It develops new almost tune-free SVRG and SARAH algorithms with BB step sizes and adaptive inner loop adjustments, backed by theoretical analysis and empirical validation.

Findings

Enhanced convergence rates through averaging methods.

Reduced need for parameter tuning in variance reduction algorithms.

Numerical tests demonstrate improved performance.

Abstract

The variance reduction class of algorithms including the representative ones, SVRG and SARAH, have well documented merits for empirical risk minimization problems. However, they require grid search to tune parameters (step size and the number of iterations per inner loop) for optimal performance. This work introduces `almost tune-free' SVRG and SARAH schemes equipped with i) Barzilai-Borwein (BB) step sizes; ii) averaging; and, iii) the inner loop length adjusted to the BB step sizes. In particular, SVRG, SARAH, and their BB variants are first reexamined through an `estimate sequence' lens to enable new averaging methods that tighten their convergence rates theoretically, and improve their performance empirically when the step size or the inner loop length is chosen large. Then a simple yet effective means to adjust the number of iterations per inner loop is developed to enhance the merits of the proposed averaging schemes and BB step sizes. Numerical tests corroborate the proposed methods.