Gradient-Variation Regret Bounds for Unconstrained Online Learning
Machine Learning
2026-04-14 v1 Machine Learning
Abstract
We develop parameter-free algorithms for unconstrained online learning with regret guarantees that scale with the gradient variation . For -smooth convex loss, we provide fully-adaptive algorithms achieving regret of order without requiring prior knowledge of comparator norm , Lipschitz constant , or smoothness . The update in each round can be computed efficiently via a closed-form expression. Our results extend to dynamic regret and find immediate implications to the stochastically-extended adversarial (SEA) model, which significantly improves upon the previous best-known result [Wang et al., 2025].
Cite
@article{arxiv.2604.11151,
title = {Gradient-Variation Regret Bounds for Unconstrained Online Learning},
author = {Yuheng Zhao and Andrew Jacobsen and Nicolò Cesa-Bianchi and Peng Zhao},
journal= {arXiv preprint arXiv:2604.11151},
year = {2026}
}