Noise-Adaptive High-Probability Regret Bounds for Online Convex Optimization
We study high-probability regret bounds for online convex optimization (OCO) with strongly convex losses and establish three results that resolve open questions at the intersection of noise adaptivity, feedback structure, and constraint satisfaction. For the full-information setting with sub-Gaussian stochastic gradients, we prove a noise-adaptive high-probability regret bound in which the martingale deviation term scales with the noise level $σ$ rather than the gradient bound $G$, yielding a multiplicative improvement of $G/σ$ over the classical Azuma-Hoeffding baseline. Our analysis introduces an exponential supermartingale argument that bypasses the bounded-difference requirement of Fr...
| Authors | Wentao Zhang, Yutong Zhang, Wentao Mo |
|---|---|
| Primary category | cs.LG |
| Published | 6 June 2026 |
| Last updated at source | 6 June 2026 |
Silytics shows public metadata from arXiv and links to the original. Information may be incomplete or out of date. Last refreshed 17 October 2026. Licenses and terms of the original apply to the work itself. Not financial, legal or professional advice.