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We analyse the convergence of sampling algorithms for functions in reproducing kernel Hilbert spaces (RKHS). To this end, we discuss approximation properties of kernel regression under minimalistic assumptions on both the kernel and the…

Machine Learning · Statistics 2025-04-21 Armin Iske

We consider the sequential optimization of an unknown, continuous, and expensive to evaluate reward function, from noisy and adversarially corrupted observed rewards. When the corruption attacks are subject to a suitable budget $C$ and the…

Machine Learning · Statistics 2022-03-30 Ilija Bogunovic , Zihan Li , Andreas Krause , Jonathan Scarlett

Popular safe Bayesian optimization (BO) algorithms learn control policies for safety-critical systems in unknown environments. However, most algorithms make a smoothness assumption, which is encoded by a known bounded norm in a reproducing…

Machine Learning · Computer Science 2025-03-14 Abdullah Tokmak , Kiran G. Krishnan , Thomas B. Schön , Dominik Baumann

We study a stochastic bandit problem with a general unknown reward function and a general unknown constraint function. Both functions can be non-linear (even non-convex) and are assumed to lie in a reproducing kernel Hilbert space (RKHS)…

Machine Learning · Computer Science 2022-03-30 Xingyu Zhou , Bo Ji

In this paper, we present a unified approach to function approximation in reproducing kernel Hilbert spaces (RKHS) that establishes a previously unrecognized optimality property for several well-known function approximation techniques, such…

Statistics Theory · Mathematics 2013-01-08 Richard J. Barton

We consider bandit optimization of a smooth reward function, where the goal is cumulative regret minimization. This problem has been studied for $\alpha$-H\"older continuous (including Lipschitz) functions with $0<\alpha\leq 1$. Our main…

Machine Learning · Computer Science 2020-12-14 Yusha Liu , Yining Wang , Aarti Singh

Contextual bandits are a rich model for sequential decision making given side information, with important applications, e.g., in recommender systems. We propose novel algorithms for contextual bandits harnessing neural networks to…

Machine Learning · Statistics 2022-03-01 Parnian Kassraie , Andreas Krause

We propose a new point of view for regularizing deep neural networks by using the norm of a reproducing kernel Hilbert space (RKHS). Even though this norm cannot be computed, it admits upper and lower approximations leading to various…

Machine Learning · Statistics 2019-05-15 Alberto Bietti , Grégoire Mialon , Dexiong Chen , Julien Mairal

In this paper, we consider the nonparametric least square regression in a Reproducing Kernel Hilbert Space (RKHS). We propose a new randomized algorithm that has optimal generalization error bounds with respect to the square loss, closing a…

Machine Learning · Computer Science 2019-05-28 Kwang-Sung Jun , Ashok Cutkosky , Francesco Orabona

Many applications require a learner to make sequential decisions given uncertainty regarding both the system's payoff function and safety constraints. In safety-critical systems, it is paramount that the learner's actions do not violate the…

Machine Learning · Computer Science 2020-05-06 Sanae Amani , Mahnoosh Alizadeh , Christos Thrampoulidis

We consider Kernelized Bandits (KBs) to optimize a function $f : \mathcal{X} \rightarrow [0,1]$ belonging to the Reproducing Kernel Hilbert Space (RKHS) $\mathcal{H}_k$. Mainstream works on kernelized bandits focus on a subgaussian noise…

Machine Learning · Statistics 2024-07-10 Marco Mussi , Simone Drago , Alberto Maria Metelli

We consider distributed kernel bandits where $N$ agents aim to collaboratively maximize an unknown reward function that lies in a reproducing kernel Hilbert space. Each agent sequentially queries the function to obtain noisy observations at…

Machine Learning · Computer Science 2024-02-21 Nikola Pavlovic , Sudeep Salgia , Qing Zhao

We consider the sequential Bayesian optimization problem with bandit feedback, adopting a formulation that allows for the reward function to vary with time. We model the reward function using a Gaussian process whose evolution obeys a…

Machine Learning · Statistics 2016-01-26 Ilija Bogunovic , Jonathan Scarlett , Volkan Cevher

We consider the problem of contextual kernel bandits with stochastic contexts, where the underlying reward function belongs to a known Reproducing Kernel Hilbert Space (RKHS). We study this problem under the additional constraint of joint…

Machine Learning · Statistics 2025-01-14 Nikola Pavlovic , Sudeep Salgia , Qing Zhao

This paper addresses the Bayesian optimization problem (also referred to as the Bayesian setting of the Gaussian process bandit), where the learner seeks to minimize the regret under a function drawn from a known Gaussian process (GP).…

Machine Learning · Computer Science 2025-12-12 Shogo Iwazaki

In recent years methods from optimal linear experimental design have been leveraged to obtain state of the art results for linear bandits. A design returned from an objective such as $G$-optimal design is actually a probability distribution…

Machine Learning · Computer Science 2021-05-13 Romain Camilleri , Julian Katz-Samuels , Kevin Jamieson

Current methods for stochastic hyperparameter learning in Gaussian Processes (GPs) rely on approximations, such as computing biased stochastic gradients or using inducing points in stochastic variational inference. However, when using such…

Machine Learning · Computer Science 2025-08-29 Neta Shoham , Haim Avron

We consider the neural contextual bandit problem. In contrast to the existing work which primarily focuses on ReLU neural nets, we consider a general set of smooth activation functions. Under this more general setting, (i) we derive…

Machine Learning · Statistics 2022-06-02 Sudeep Salgia , Sattar Vakili , Qing Zhao

We study a generalization of the problem of online learning in adversarial linear contextual bandits by incorporating loss functions that belong to a reproducing kernel Hilbert space, which allows for a more flexible modeling of complex…

Machine Learning · Statistics 2023-10-04 Gergely Neu , Julia Olkhovskaya , Sattar Vakili

Consider the sequential optimization of an expensive to evaluate and possibly non-convex objective function $f$ from noisy feedback, that can be considered as a continuum-armed bandit problem. Upper bounds on the regret performance of…

Machine Learning · Statistics 2021-03-11 Sattar Vakili , Kia Khezeli , Victor Picheny