Almost Tune-Free Variance Reduction

Bingcong Li, Lingda Wang, Georgios B. Giannakis
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:5969-5978, 2020.

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.

Cite this Paper


BibTeX
@InProceedings{pmlr-v119-li20n, title = {Almost Tune-Free Variance Reduction}, author = {Li, Bingcong and Wang, Lingda and Giannakis, Georgios B.}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {5969--5978}, year = {2020}, editor = {Hal Daumé III and Aarti Singh}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/li20n/li20n.pdf}, url = { http://proceedings.mlr.press/v119/li20n.html }, 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.} }
Endnote
%0 Conference Paper %T Almost Tune-Free Variance Reduction %A Bingcong Li %A Lingda Wang %A Georgios B. Giannakis %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-li20n %I PMLR %P 5969--5978 %U http://proceedings.mlr.press/v119/li20n.html %V 119 %X 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.
APA
Li, B., Wang, L. & Giannakis, G.B.. (2020). Almost Tune-Free Variance Reduction. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:5969-5978 Available from http://proceedings.mlr.press/v119/li20n.html .

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