Delayed Feedback in Online Non-Convex Optimization: A Non-Stationary Approach with Applications

Delayed Feedback in Online Non-Convex Optimization: A Non-Stationary Approach with Applications | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Delayed Feedback in Online Non-Convex Optimization: A Non-Stationary Approach with Applications Felipe Lara, Cristian Vega This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6708570/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 29 Nov, 2025 Read the published version in Numerical Algorithms → Version 1 posted 8 You are reading this latest preprint version Abstract We study non-convex delayed-noise online optimization problems by evaluating dynamic regret in the non-stationary setting when the loss functions are quasar-convex. In particular, we consider scenarios involving quasar-convex functions either with a Lipschitz gradient or weakly smooth and, for each case, we ensure bounded dynamic regret in terms of cumulative path variation achieving sub-linear regret rates. Furthermore, we illustrate the flexibility of our framework by applying it to both theoretical settings such as zeroth-order (bandit) and also to practical applications with quadratic fractional functions. Moreover, we provide new examples of non-convex functions that are quasar-convex by proving that the class of differentiable strongly quasiconvex functions are strongly quasar-convex on convex compact sets. Finally, several numerical experiments validate our theoretical findings, illustrating the effectiveness of our approach. Non-convex online optimization Delayed algorithms Quasar-convexity Bandit Quadratic fractional programming Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 29 Nov, 2025 Read the published version in Numerical Algorithms → Version 1 posted Editorial decision: Revision requested 03 Aug, 2025 Reviews received at journal 25 Jul, 2025 Reviewers agreed at journal 28 May, 2025 Reviewers agreed at journal 23 May, 2025 Reviewers invited by journal 23 May, 2025 Editor assigned by journal 22 May, 2025 Submission checks completed at journal 22 May, 2025 First submitted to journal 20 May, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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