{"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/parameter-free-stochastic-optimization-of","title":"Parameter-free Stochastic Optimization of Variationally Coherent Functions","arxiv_id":"2102.00236","date":"2021-01-30","proceeding":null,"authors":["Francesco Orabona","Dávid Pál"],"abstract":"We design and analyze an algorithm for first-order stochastic optimization of a large class of functions on $\\mathbb{R}^d$. In particular, we consider the \\emph{variationally coherent} functions which can be convex or non-convex. The iterates of our algorithm on variationally coherent functions converge almost surely to the global minimizer $\\boldsymbol{x}^*$. Additionally, the very same algorithm with the same hyperparameters, after $T$ iterations guarantees on convex functions that the expected suboptimality gap is bounded by $\\widetilde{O}(\\|\\boldsymbol{x}^* - \\boldsymbol{x}_0\\| T^{-1/2+\\epsilon})$ for any $\\epsilon>0$. It is the first algorithm to achieve both these properties at the same time. Also, the rate for convex functions essentially matches the performance of parameter-free algorithms. Our algorithm is an instance of the Follow The Regularized Leader algorithm with the added twist of using \\emph{rescaled gradients} and time-varying linearithmic regularizers.","url_abs":"https://arxiv.org/abs/2102.00236v1","url_pdf":"https://arxiv.org/pdf/2102.00236v1.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":"parameter-free-stochastic-optimization-of","repo_url":"https://github.com/bremen79/parameterfree","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"unanswered"}}],"tasks":[{"task_slug":"stochastic-optimization","task_name":"Stochastic Optimization"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2102.00236","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}