Abstract:We study offline-to-online learning in linear contextual bandits with biased offline regression data: the offline parameter need not match the online one, so history should not be treated as a single warm start. We model directional transfer with a shift certificate $(M_{\mathrm{shift}},\rho)$ and offline ridge estimation, yielding a geometry-aware confidence region for the online parameter rather than an isotropic radius. We propose \emph{Ellipsoidal-MINUCB}, which combines a standard online branch with an offline-informed pooled branch and uses offline information only when it tightens uncertainty. With high probability, regret is bounded by the minimum of a standard SupLinUCB-style fallback and a pooled term that separates statistical width from a certificate-weighted shift penalty. Under a simple alignment condition, the pooled term further simplifies to a rate governed by an effective dimension induced by the offline geometry. We also show that a purely Euclidean (scalar) shift bound, by itself, does not determine which feature directions are transferable. Beyond this fixed certificate, we show how to learn a data-driven certificate from data at finitely many refresh times and establish a high-probability regret bound for Ellipsoidal-MINUCB with epoch-wise learned certificates. Experiments match the main prediction: gains are strongest at intermediate horizons when offline coverage and transferability align, while the method otherwise tracks the safe online baseline.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2604.24016 [cs.LG] |
| (or arXiv:2604.24016v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2604.24016 arXiv-issued DOI via DataCite (pending registration) |
From: Jiheng Zhang [view email]
[v1]
Mon, 27 Apr 2026 03:53:30 UTC (11,820 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。