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.
arXiv:2608. 16492v1 Announce Type: cross Abstract: This paper studies the regret analysis for parallel Gaussian process (GP) bandit optimization.
The paper analyzes Bayesian linear bandits with isotropic Gaussian parameters, independent Gaussian arms, and Gaussian reward noise when the time horizon scales with the dimension. It derives explicit limits for the normalized posterior uncertainty and parameter overlaps, yielding exact regret curves for several policies—including Thompson sampling, posterior‑mean greedy selection, and scaled‑covariance variants. The results show that posterior‑mean greedy selection achieves the optimal Bayes regret, while Thompson sampling incurs a strictly larger leading regret whose ratio to greedy lies between one and two, approaching two for long horizons.
arXiv:2502. 01226v4 Announce Type: replace Abstract: Gaussian process (GP) bandits provide a powerful framework for performing blackbox optimization of unknown functions.
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.
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.
arXiv:2603. 09276v2 Announce Type: replace-cross Abstract: We study a widely used Bayesian optimization method, Gaussian process Thompson sampling (GP-TS), under the assumption that the objective function is a sample path from a GP.
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.
arXiv:2606. 20022v1 Announce Type: cross Abstract: This paper considers stochastic linear contextual bandits (SLCB) with bounded reward noise.
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.
arXiv:2409. 18909v2 Announce Type: replace Abstract: Motivated by real-world applications that necessitate responsible experimentation, we introduce the problem of best arm identification (BAI) with minimal regret.
arXiv:2604. 00531v2 Announce Type: replace Abstract: Multi-task representation learning exploits the shared structure among related tasks by learning a common latent representation, thereby improving sample efficiency.