Almost Tune-Free Variance Reduction
This work addresses the practical issue of parameter tuning for researchers and practitioners using variance reduction methods in empirical risk minimization, though it is incremental as it builds on existing SVRG and SARAH frameworks.
The paper tackles the need for manual parameter tuning in variance reduction algorithms like SVRG and SARAH by introducing 'almost tune-free' variants with Barzilai-Borwein step sizes, averaging, and adjusted inner loop lengths, resulting in improved convergence rates and empirical performance.
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.