Stochastic Extragradient with Random Reshuffling: Improved Convergence for Variational Inequalities

Konstantinos Emmanouilidis, Rene Vidal, Nicolas Loizou
Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, PMLR 238:3682-3690, 2024.

Abstract

The Stochastic Extragradient (SEG) method is one of the most popular algorithms for solving finite-sum min-max optimization and variational inequality problems (VIPs) appearing in various machine learning tasks. However, existing convergence analyses of SEG focus on its with-replacement variants, while practical implementations of the method randomly reshuffle components and sequentially use them. Unlike the well-studied with-replacement variants, SEG with Random Reshuffling (SEG-RR) lacks established theoretical guarantees. In this work, we provide a convergence analysis of SEG-RR for three classes of VIPs: (i) strongly monotone, (ii) affine, and (iii) monotone. We derive conditions under which SEG-RR achieves a faster convergence rate than the uniform with-replacement sampling SEG. In the monotone setting, our analysis of SEG-RR guarantees convergence to an arbitrary accuracy without large batch sizes, a strong requirement needed in the classical with-replacement SEG. As a byproduct of our results, we provide convergence guarantees for Shuffle Once SEG (shuffles the data only at the beginning of the algorithm) and the Incremental Extragradient (does not shuffle the data). We supplement our analysis with experiments validating empirically the superior performance of SEG-RR over the classical with-replacement sampling SEG.

Cite this Paper

BibTeX
@InProceedings{pmlr-v238-emmanouilidis24a, title = { Stochastic Extragradient with Random Reshuffling: Improved Convergence for Variational Inequalities }, author = {Emmanouilidis, Konstantinos and Vidal, Rene and Loizou, Nicolas}, booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics}, pages = {3682--3690}, year = {2024}, editor = {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen}, volume = {238}, series = {Proceedings of Machine Learning Research}, month = {02--04 May}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v238/emmanouilidis24a/emmanouilidis24a.pdf}, url = {https://proceedings.mlr.press/v238/emmanouilidis24a.html}, abstract = { The Stochastic Extragradient (SEG) method is one of the most popular algorithms for solving finite-sum min-max optimization and variational inequality problems (VIPs) appearing in various machine learning tasks. However, existing convergence analyses of SEG focus on its with-replacement variants, while practical implementations of the method randomly reshuffle components and sequentially use them. Unlike the well-studied with-replacement variants, SEG with Random Reshuffling (SEG-RR) lacks established theoretical guarantees. In this work, we provide a convergence analysis of SEG-RR for three classes of VIPs: (i) strongly monotone, (ii) affine, and (iii) monotone. We derive conditions under which SEG-RR achieves a faster convergence rate than the uniform with-replacement sampling SEG. In the monotone setting, our analysis of SEG-RR guarantees convergence to an arbitrary accuracy without large batch sizes, a strong requirement needed in the classical with-replacement SEG. As a byproduct of our results, we provide convergence guarantees for Shuffle Once SEG (shuffles the data only at the beginning of the algorithm) and the Incremental Extragradient (does not shuffle the data). We supplement our analysis with experiments validating empirically the superior performance of SEG-RR over the classical with-replacement sampling SEG. } }
Endnote
%0 Conference Paper %T Stochastic Extragradient with Random Reshuffling: Improved Convergence for Variational Inequalities %A Konstantinos Emmanouilidis %A Rene Vidal %A Nicolas Loizou %B Proceedings of The 27th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2024 %E Sanjoy Dasgupta %E Stephan Mandt %E Yingzhen Li %F pmlr-v238-emmanouilidis24a %I PMLR %P 3682--3690 %U https://proceedings.mlr.press/v238/emmanouilidis24a.html %V 238 %X The Stochastic Extragradient (SEG) method is one of the most popular algorithms for solving finite-sum min-max optimization and variational inequality problems (VIPs) appearing in various machine learning tasks. However, existing convergence analyses of SEG focus on its with-replacement variants, while practical implementations of the method randomly reshuffle components and sequentially use them. Unlike the well-studied with-replacement variants, SEG with Random Reshuffling (SEG-RR) lacks established theoretical guarantees. In this work, we provide a convergence analysis of SEG-RR for three classes of VIPs: (i) strongly monotone, (ii) affine, and (iii) monotone. We derive conditions under which SEG-RR achieves a faster convergence rate than the uniform with-replacement sampling SEG. In the monotone setting, our analysis of SEG-RR guarantees convergence to an arbitrary accuracy without large batch sizes, a strong requirement needed in the classical with-replacement SEG. As a byproduct of our results, we provide convergence guarantees for Shuffle Once SEG (shuffles the data only at the beginning of the algorithm) and the Incremental Extragradient (does not shuffle the data). We supplement our analysis with experiments validating empirically the superior performance of SEG-RR over the classical with-replacement sampling SEG.
APA
Emmanouilidis, K., Vidal, R. & Loizou, N.. (2024). Stochastic Extragradient with Random Reshuffling: Improved Convergence for Variational Inequalities . Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 238:3682-3690 Available from https://proceedings.mlr.press/v238/emmanouilidis24a.html.

Related Material