{"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/a-stochastic-halpern-iteration-with-variance","title":"Stochastic Halpern Iteration with Variance Reduction for Stochastic Monotone Inclusions","arxiv_id":"2203.09436","date":"2022-03-17","proceeding":null,"authors":["Xufeng Cai","Chaobing Song","Cristóbal Guzmán","Jelena Diakonikolas"],"abstract":"We study stochastic monotone inclusion problems, which widely appear in machine learning applications, including robust regression and adversarial learning. We propose novel variants of stochastic Halpern iteration with recursive variance reduction. In the cocoercive -- and more generally Lipschitz-monotone -- setup, our algorithm attains $\\epsilon$ norm of the operator with $\\mathcal{O}(\\frac{1}{\\epsilon^3})$ stochastic operator evaluations, which significantly improves over state of the art $\\mathcal{O}(\\frac{1}{\\epsilon^4})$ stochastic operator evaluations required for existing monotone inclusion solvers applied to the same problem classes. We further show how to couple one of the proposed variants of stochastic Halpern iteration with a scheduled restart scheme to solve stochastic monotone inclusion problems with ${\\mathcal{O}}(\\frac{\\log(1/\\epsilon)}{\\epsilon^2})$ stochastic operator evaluations under additional sharpness or strong monotonicity assumptions.","url_abs":"https://arxiv.org/abs/2203.09436v4","url_pdf":"https://arxiv.org/pdf/2203.09436v4.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":"a-stochastic-halpern-iteration-with-variance","repo_url":"https://github.com/zephyr-cai/halpern","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2203.09436","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2203.09436"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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