{"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/fast-stochastic-composite-minimization-and-an","title":"Fast Stochastic Composite Minimization and an Accelerated Frank-Wolfe Algorithm under Parallelization","arxiv_id":"2205.12751","date":"2022-05-25","proceeding":null,"authors":["Benjamin Dubois-Taine","Francis Bach","Quentin Berthet","Adrien Taylor"],"abstract":"We consider the problem of minimizing the sum of two convex functions. One of those functions has Lipschitz-continuous gradients, and can be accessed via stochastic oracles, whereas the other is \"simple\". We provide a Bregman-type algorithm with accelerated convergence in function values to a ball containing the minimum. The radius of this ball depends on problem-dependent constants, including the variance of the stochastic oracle. We further show that this algorithmic setup naturally leads to a variant of Frank-Wolfe achieving acceleration under parallelization. More precisely, when minimizing a smooth convex function on a bounded domain, we show that one can achieve an $\\epsilon$ primal-dual gap (in expectation) in $\\tilde{O}(1/ \\sqrt{\\epsilon})$ iterations, by only accessing gradients of the original function and a linear maximization oracle with $O(1/\\sqrt{\\epsilon})$ computing units in parallel. We illustrate this fast convergence on synthetic numerical experiments.","url_abs":"https://arxiv.org/abs/2205.12751v3","url_pdf":"https://arxiv.org/pdf/2205.12751v3.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":"fast-stochastic-composite-minimization-and-an","repo_url":"https://github.com/bpauld/pfw","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2205.12751","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}