Geometry-Aware Offline-to-Online Learning in Linear Contextual Bandits

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 $(M_{\mathrm{shift}},ρ)$ 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.

Make Optimization Once and for All with Fine-grained Guidance

Learning to Optimize (L2O) enhances optimization efficiency with integrated neural networks. L2O paradigms achieve great outcomes, e.g., refitting optimizer, generating unseen solutions iteratively or directly. However, conventional L2O methods require intricate design and rely on specific optimization processes, limiting scalability and generalization. Our analyses explore general framework for learning optimization, called Diff-L2O, focusing on augmenting sampled solutions from a wider view rather than local updates in real optimization process only. Meanwhile, we give the related generalization bound, showing that the sample diversity of Diff-L2O brings better performance. This bound can be simply applied to other fields, discussing diversity, mean-variance, and different tasks. Diff-L2O's strong compatibility is empirically verified with only minute-level training, comparing with other hour-levels.