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[Submitted on 17 Sep 2026] Title:From Switching to Dynamic Regret: A Simple Reduction via Unbiased Random Sequences View a PDF of the paper titled From Switching to Dynamic Regret: A Simple Reduction via Unbiased Random Sequences, by Yibo Wang and 4 other authors View PDF HTML (experimental) Abstract:In non-stationary online learning, dynamic regret has attracted increasing attention as a measure of how well an online learner performs against a time-varying comparator sequence. Despite considerable advances, attaining optimal bounds for strongly convex and exp-concave losses often involves intricate analysis. In this paper, we present a \textit{simple} framework that reduces dynamic regret minimization to switching regret minimization. As a result, we can derive dynamic regret bounds by using off-the-shelf algorithms with switching regret guarantees. The key idea of our reduction is to construct, for \textit{any} comparator sequence, an auxiliary random sequence that is unbiased at each round, with the controlled variance and a manageable number of switches. Combining this construction with suitable surrogate losses, we can decompose dynamic regret into the expected switching regret against the random sequence and its controlled variance. Theoretically, for strongly convex and exp-concave losses, we establish the $\widetilde{O}(T^{1/3}P_T^{2/3})$ dynamic regret bounds, where $T$ denotes the time horizon and $P_T$ denotes the path-length of the comparator sequence. Moreover, for general convex losses, the same reduction also recovers the $O(\sqrt{T(1+P_T)})$ dynamic regret bound. Notably, all our findings match the minimax optimal results for these three types of losses, highlighting the versatility of our proposed framework. Subjects: Machine Learning (cs.LG) Cite as: arXiv:2609.20968 [cs.LG] (or arXiv:2609.20968v1 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2609.20968 arXiv-issued DOI via DataCite (pending registration) Submission history From: Yibo Wang [view email] [v1] Thu, 17 Sep 2026 18:25:43 UTC (57 KB) Full-text links: Access Paper: View a PDF of the paper titled From Switching to Dynamic Regret: A Simple Reduction via Unbiased Random Sequences, by Yibo Wang and 4 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cs.LG new | recent | 2026-09 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar Loading... Data provided by: Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) IArxiv recommender toggle IArxiv Recommender (What is IArxiv?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)