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Stochastic linear bandits are a fundamental model for sequential decision making, where an agent selects a vector-valued action and receives a noisy reward with expected value given by an unknown linear function. Although well studied in…

Machine Learning · Computer Science 2025-06-23 Bruce Huang , Ruida Zhou , Lin F. Yang , Suhas Diggavi

We consider the stochastic multi-armed bandit problem with a prior distribution on the reward distributions. We are interested in studying prior-free and prior-dependent regret bounds, very much in the same spirit as the usual…

Machine Learning · Statistics 2013-10-04 Sébastien Bubeck , Che-Yu Liu

The most prominent feedback models for the best expert problem are the full information and bandit models. In this work we consider a simple feedback model that generalizes both, where on every round, in addition to a bandit feedback, the…

Machine Learning · Computer Science 2020-12-18 Eyal Gofer , Guy Gilboa

Gaussian process optimization is a successful class of algorithms(e.g. GP-UCB) to optimize a black-box function through sequential evaluations. However, for functions with continuous domains, Gaussian process optimization has to rely on…

Machine Learning · Computer Science 2022-03-15 Marco Rando , Luigi Carratino , Silvia Villa , Lorenzo Rosasco

Safe Bayesian optimization (BO) algorithms promise to find optimal control policies without knowing the system dynamics while at the same time guaranteeing safety with high probability. In exchange for those guarantees, popular algorithms…

Machine Learning · Computer Science 2025-10-22 Abdullah Tokmak , Thomas B. Schön , Dominik Baumann

Bayesian optimisation (BO) is a well-known efficient algorithm for finding the global optimum of expensive, black-box functions. The current practical BO algorithms have regret bounds ranging from $\mathcal{O}(\frac{logN}{\sqrt{N}})$ to…

Machine Learning · Computer Science 2026-04-28 Hung Tran-The , Sunil Gupta , Santu Rana , Svetha Venkatesh

This paper considers the use of a simple posterior sampling algorithm to balance between exploration and exploitation when learning to optimize actions such as in multi-armed bandit problems. The algorithm, also known as Thompson Sampling,…

Machine Learning · Computer Science 2014-02-04 Daniel Russo , Benjamin Van Roy

We revisit the challenge of designing online algorithms for the bandit convex optimization problem (BCO) which are also scalable to high dimensional problems. Hence, we consider algorithms that are \textit{projection-free}, i.e., based on…

Machine Learning · Computer Science 2019-10-09 Dan Garber , Ben Kretzu

We address a generalization of the bandit with knapsacks problem, where a learner aims to maximize rewards while satisfying an arbitrary set of long-term constraints. Our goal is to design best-of-both-worlds algorithms that perform…

Machine Learning · Computer Science 2024-05-28 Martino Bernasconi , Matteo Castiglioni , Andrea Celli , Federico Fusco

We motivate and analyse a new Tree Search algorithm, GPTS, based on recent theoretical advances in the use of Gaussian Processes for Bandit problems. We consider tree paths as arms and we assume the target/reward function is drawn from a GP…

Machine Learning · Computer Science 2011-01-18 Louis Dorard , John Shawe-Taylor

Bayesian Optimization is critically vulnerable to extreme outliers. Existing provably robust methods typically assume a bounded cumulative corruption budget, which makes them defenseless against even a single corruption of sufficient…

Machine Learning · Statistics 2026-02-17 Abdelhamid Ezzerg , Ilija Bogunovic , Jeremias Knoblauch

We consider the Lipschitz bandit optimization problem with an emphasis on practical efficiency. Although there is rich literature on regret analysis of this type of problem, e.g., [Kleinberg et al. 2008, Bubeck et al. 2011, Slivkins 2014],…

Machine Learning · Computer Science 2019-07-11 Xu Zhu

We study linear contextual bandits under adversarial corruption and heavy-tailed noise with finite $(1+\epsilon)$-th moments for some $\epsilon \in (0,1]$. Existing work that addresses both adversarial corruption and heavy-tailed noise…

Machine Learning · Computer Science 2026-03-17 Naoto Tani , Futoshi Futami

We revisit the study of optimal regret rates in bandit combinatorial optimization---a fundamental framework for sequential decision making under uncertainty that abstracts numerous combinatorial prediction problems. We prove that the…

Machine Learning · Computer Science 2017-02-27 Alon Cohen , Tamir Hazan , Tomer Koren

Recent studies have shown that reinforcement learning with KL-regularized objectives can enjoy faster rates of convergence or logarithmic regret, in contrast to the classical $\sqrt{T}$-type regret in the unregularized setting. However, the…

Machine Learning · Computer Science 2026-03-03 Kaixuan Ji , Qingyue Zhao , Heyang Zhao , Qiwei Di , Quanquan Gu

This paper studies bandit convex optimization in non-stationary environments with two-point feedback, using dynamic regret as the performance measure. We propose an algorithm based on bandit mirror descent that extends naturally to…

Optimization and Control · Mathematics 2026-05-26 Chang He , Bo Jiang , Shuzhong Zhang

This paper is devoted to regret lower bounds in the classical model of stochastic multi-armed bandit. A well-known result of Lai and Robbins, which has then been extended by Burnetas and Katehakis, has established the presence of a…

Machine Learning · Statistics 2011-12-19 Antoine Salomon , Jean-Yves Audibert , Issam El Alaoui

Stochastic high dimensional bandit problems with low dimensional structures are useful in different applications such as online advertising and drug discovery. In this work, we propose a simple unified algorithm for such problems and…

Machine Learning · Computer Science 2022-09-12 Wenjie Li , Adarsh Barik , Jean Honorio

This paper establishes error bounds for the convergence of a piecewise linear approximation of the constrained optimal smoothing problem posed in a reproducing kernel Hilbert space (RKHS). This problem can be reformulated as a Bayesian…

Statistics Theory · Mathematics 2025-06-24 Laurence Grammont , François Bachoc , Andrés F. López-Lopera

Motivated by applications in online bidding and sleeping bandits, we examine the problem of contextual bandits with cross learning, where the learner observes the loss associated with the action across all possible contexts, not just the…

Machine Learning · Computer Science 2025-01-27 Ruiyuan Huang , Zengfeng Huang