dc.contributor.author Malinovsky, Grigory dc.contributor.author Sailanbayev, Alibek dc.contributor.author Richtarik, Peter dc.date.accessioned 2021-04-21T06:55:59Z dc.date.available 2021-04-21T06:55:59Z dc.date.issued 2021-04-19 dc.identifier.uri http://hdl.handle.net/10754/668880 dc.description.abstract Virtually all state-of-the-art methods for training supervised machine learning models are variants of SGD enhanced with a number of additional tricks, such as minibatching, momentum, and adaptive stepsizes. One of the tricks that works so well in practice that it is used as default in virtually all widely used machine learning software is {\em random reshuffling (RR)}. However, the practical benefits of RR have until very recently been eluding attempts at being satisfactorily explained using theory. Motivated by recent development due to Mishchenko, Khaled and Richt\'{a}rik (2020), in this work we provide the first analysis of SVRG under Random Reshuffling (RR-SVRG) for general finite-sum problems. First, we show that RR-SVRG converges linearly with the rate $\mathcal{O}(\kappa^{3/2})$ in the strongly-convex case, and can be improved further to $\mathcal{O}(\kappa)$ in the big data regime (when $n > \mathcal{O}(\kappa)$), where $\kappa$ is the condition number. This improves upon the previous best rate $\mathcal{O}(\kappa^2)$ known for a variance reduced RR method in the strongly-convex case due to Ying, Yuan and Sayed (2020). Second, we obtain the first sublinear rate for general convex problems. Third, we establish similar fast rates for Cyclic-SVRG and Shuffle-Once-SVRG. Finally, we develop and analyze a more general variance reduction scheme for RR, which allows for less frequent updates of the control variate. We corroborate our theoretical results with suitably chosen experiments on synthetic and real datasets. dc.publisher arXiv dc.relation.url https://arxiv.org/pdf/2104.09342.pdf dc.rights Archived with thanks to arXiv dc.title Random Reshuffling with Variance Reduction: New Analysis and Better Rates dc.type Preprint dc.contributor.department Applied Mathematics & Computational Sci dc.contributor.department Applied Mathematics and Computational Science Program dc.contributor.department Computer Science Program dc.contributor.department Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division dc.eprint.version Pre-print dc.identifier.arxivid 2104.09342 kaust.person Malinovsky, Grigory kaust.person Sailanbayev, Alibek kaust.person Richtarik, Peter refterms.dateFOA 2021-04-21T06:56:27Z
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