{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/towards-closing-the-gap-between-the-theory","title":"Towards closing the gap between the theory and practice of SVRG","arxiv_id":"1908.02725","date":"2019-07-31","proceeding":"NeurIPS 2019 12","authors":["Othmane Sebbouh","Nidham Gazagnadou","Samy Jelassi","Francis Bach","Robert M. Gower"],"abstract":"Among the very first variance reduced stochastic methods for solving the empirical risk minimization problem was the SVRG method (Johnson & Zhang 2013). SVRG is an inner-outer loop based method, where in the outer loop a reference full gradient is evaluated, after which $m \\in \\mathbb{N}$ steps of an inner loop are executed where the reference gradient is used to build a variance reduced estimate of the current gradient. The simplicity of the SVRG method and its analysis have led to multiple extensions and variants for even non-convex optimization. We provide a more general analysis of SVRG than had been previously done by using arbitrary sampling, which allows us to analyse virtually all forms of mini-batching through a single theorem. Furthermore, our analysis is focused on more practical variants of SVRG including a new variant of the loopless SVRG (Hofman et al 2015, Kovalev et al 2019, Kulunchakov and Mairal 2019) and a variant of k-SVRG (Raj and Stich 2018) where $m=n$ and where $n$ is the number of data points. Since our setup and analysis reflect what is done in practice, we are able to set the parameters such as the mini-batch size and step size using our theory in such a way that produces a more efficient algorithm in practice, as we show in extensive numerical experiments.","url_abs":"https://arxiv.org/abs/1908.02725v2","url_pdf":"https://arxiv.org/pdf/1908.02725v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"towards-closing-the-gap-between-the-theory","repo_url":"https://github.com/gowerrobert/StochOpt.jl","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok","spdx":"GPL-3.0"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1908.02725","atlas_url":"https://app.syntology.ai/?focus=1908.02725","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}