Almost Tune-Free Variance Reduction
Bingcong Li,u00a0Lingda Wang,u00a0Georgios B. Giannakis
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 u2018almost tune-freeu2019 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 u2018estimate sequenceu2019 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.
