The paper explores the use of set membership estimation (SME) for uncertainty quantification in linear contextual bandits, contrasting it with the more common confidence‑interval approach. An SME‑based optimism‑in‑the‑face‑of‑uncertainty (OFU) algorithm is proposed, and a sublinear regret bound is proven under suitable assumptions. Simulations show that SME‑OFU performs favorably compared to existing methods.
By Haonan Xu, Yingying Li
arXiv:2610.28136v1 Announce Type: cross
Abstract: Gaussian process upper confidence bound (GP-UCB) has been widely studied, though its known regret upper bound is suboptimal. To obtain near-optimal r...
By Shion Takeno, Shogo Iwazaki, Ichiro Takeuchi
arXiv:2607. 23679v1 Announce Type: new Abstract: Recent years have witnessed increasing interests in tackling heteroscedastic noise in bandits and reinforcement learning.
By Heyang Zhao, Tianyuan Jin, Weixin Wang, Vincent Y. F. Tan, Pan Xu, Quanquan Gu
arXiv:2606. 08028v1 Announce Type: new Abstract: 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.
By Wentao Zhang, Yutong Zhang, Wentao Mo
arXiv:2502. 13467v2 Announce Type: replace Abstract: The $K$-Max combinatorial multi-armed bandit problem arises in applications such as recommendation and distributed decision making, where the reward is determined by the maximum outcome among $K$ selected arms.
By Yu Chen, Siwei Wang, Longbo Huang, Wei Chen
arXiv:2608. 16492v1 Announce Type: cross Abstract: This paper studies the regret analysis for parallel Gaussian process (GP) bandit optimization.
By Shion Takeno, Shogo Iwazaki
arXiv:2610. 29381v1 Announce Type: new Abstract: We propose a novel stochastic cascading bandit setup where probing an ordered shortlist of $K$ out of $L$ arms incurs position-dependent costs, and the learner observes only noisy feedback regarding each arm's true output.
By Yashaswini Kaluguri, Nikhil Karamchandani
The paper investigates how offline data can improve online learning in stochastic linear bandits, focusing on the case where only a subset of feature directions is poorly covered. It shows that previous regret bounds of ≥O(√{dkT}) stem from loose reward prediction error control and derives tighter bounds using concentration of Lipschitz functions of Gaussian vectors. The authors propose a phased elimination algorithm achieving regret ≥O(k√T) and establish matching lower bounds for both partial and uniform coverage, while also addressing pure exploration with offline data and providing matching bounds for simple regret.
By Kushagra Chandak, Volodymyr Tkachuk, Xiaoqi Tan, Csaba Szepesv\'ari
arXiv:2608. 18863v1 Announce Type: cross Abstract: We study Bayesian optimization in a time-varying environment where the unknown reward function evolves according to a Gaussian process drift model.
By Matthias Mandl, Hanne Kekkonen
arXiv:2606. 28616v1 Announce Type: new Abstract: In stochastic linear bandits, the canonical Upper Confidence Bound (UCB) algorithm admits a simple frequentist regret analysis but can be computationally demanding, while Thompson Sampling (TS) is computationally attractive yet typically harder to analyze due to its non-optimistic nature.
By Toshinori Kitamura, Shuai Liu, Csaba Szepesv\'ari
arXiv:2602.10727v3 Announce Type: replace
Abstract: Rising Multi-Armed Bandits (RMABs) model sequential decision problems where each arm's expected reward improves with repeated pulls. In such proble...
By Seockbean Song, Chenyu Gan, Youngsik Yoon, Siwei Wang, Wei Chen, Jungseul Ok
arXiv:2512. 00517v3 Announce Type: replace-cross Abstract: Sequential optimization of black-box functions from noisy evaluations has been widely studied, with Gaussian Process bandit algorithms such as GP-UCB guaranteeing no-regret in stationary settings.
By Eliabelle Mauduit, Elo\"ise Berthier, Andrea Simonetto