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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…
Obtaining reliable, adaptive confidence sets for prediction functions (hypotheses) is a central challenge in sequential decision-making tasks, such as bandits and model-based reinforcement learning. These confidence sets typically rely on…
Under mild assumptions on the kernel, we obtain the best known error rates in a regularized learning scenario taking place in the corresponding reproducing kernel Hilbert space (RKHS). The main novelty in the analysis is a proof that one…
We consider the $\epsilon$-greedy strategy for the multi-arm bandit with covariates (MABC) problem, where the mean reward functions are assumed to lie in a reproducing kernel Hilbert space (RKHS). We propose to estimate the unknown mean…
We consider the kernelized contextual bandit problem with a large feature space. This problem involves $K$ arms, and the goal of the forecaster is to maximize the cumulative rewards through learning the relationship between the contexts and…
We consider the problem of optimising functions in the reproducing kernel Hilbert space (RKHS) of a Mat\'ern kernel with smoothness parameter $\nu$ over the domain $[0,1]^d$ under noisy bandit feedback. Our contribution, the $\pi$-GP-UCB…
This paper develops a frequentist solution to the functional calibration problem, where the value of a calibration parameter in a computer model is allowed to vary with the value of control variables in the physical system. The need of…
We tackle the communication efficiency challenge of learning kernelized contextual bandits in a distributed setting. Despite the recent advances in communication-efficient distributed bandit learning, existing solutions are restricted to…
We propose an algorithm for non-stationary kernel bandits that does not require prior knowledge of the degree of non-stationarity. The algorithm follows randomized strategies obtained by solving optimization problems that balance…
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…
This paper generalizes regularized regression problems in a hyper-reproducing kernel Hilbert space (hyper-RKHS), illustrates its utility for kernel learning and out-of-sample extensions, and proves asymptotic convergence results for the…
This paper investigates the convergence properties of spectral algorithms -- a class of regularization methods originating from inverse problems -- under covariate shift. In this setting, the marginal distributions of inputs differ between…
A major research direction in contextual bandits is to develop algorithms that are computationally efficient, yet support flexible, general-purpose function approximation. Algorithms based on modeling rewards have shown strong empirical…
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…
We study the regret minimization problem in the novel setting of generalized kernelized bandits (GKBs), where we optimize an unknown function $f^*$ belonging to a reproducing kernel Hilbert space (RKHS) having access to samples generated by…
Kernel methods are one of the cornerstones of learning-based control, modern system identification, surrogate modelling, and related fields. A key advantage of this class of learning and function approximation methods is the availability of…
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…
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…
Fast changing states or volatile environments pose a significant challenge to online optimization, which needs to perform rapid adaptation under limited observation. In this paper, we give query and regret optimal bandit algorithms under…
When concept shifts and sample scarcity are present in the target domain of interest, nonparametric regression learners often struggle to generalize effectively. The technique of transfer learning remedies these issues by leveraging data or…