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We study the kernelized bandit problem, that involves designing an adaptive strategy for querying a noisy zeroth-order-oracle to efficiently learn about the optimizer of an unknown function $f$ with a norm bounded by $M<\infty$ in a…
In this work we investigate the relationship between kernel regularity and algorithmic performance in the bandit optimization of RKHS functions. While reproducing kernel Hilbert space (RKHS) methods traditionally rely on global kernel…
The optimization of black-box functions with noisy observations is a fundamental problem with widespread applications, and has been widely studied under the assumption that the function lies in a reproducing kernel Hilbert space (RKHS).…
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)…
We study the adversarial kernel bandit problem, in which the loss at each round is induced by an arbitrary bounded element of a reproducing kernel Hilbert space (RKHS). We propose an exponential-weights algorithm built on a regularized…
In this paper, we consider the problem of black-box optimization with noisy feedback revealed in batches, where the unknown function to optimize has a bounded norm in some Reproducing Kernel Hilbert Space (RKHS). We refer to this as the…
Confidence intervals are a crucial building block in the analysis of various online learning problems. The analysis of kernel based bandit and reinforcement learning problems utilize confidence intervals applicable to the elements of a…
Ridgeless regression has garnered attention among researchers, particularly in light of the ``Benign Overfitting'' phenomenon, where models interpolating noisy samples demonstrate robust generalization. However, kernel ridgeless regression…
The RKHS bandit problem (also called kernelized multi-armed bandit problem) is an online optimization problem of non-linear functions with noisy feedback. Although the problem has been extensively studied, there are unsatisfactory results…
In this paper, we consider algorithm-independent lower bounds for the problem of black-box optimization of functions having a bounded norm is some Reproducing Kernel Hilbert Space (RKHS), which can be viewed as a non-Bayesian Gaussian…
Kernel methods approximate nonlinear maps in a data-driven manner by projecting the target map onto a finite-dimensional Hilbert space called the solution space. Traditionally, this space is a subspace of a fixed ambient reproducing kernel…
Kernel-based bandit is an extensively studied black-box optimization problem, in which the objective function is assumed to live in a known reproducing kernel Hilbert space. While nearly optimal regret bounds (up to logarithmic factors) are…
We study contextual bandits with finitely many actions in which the reward of each arm follows a single-index model with an arm-specific index parameter and an unknown nonparametric link function. We consider a regime in which arms…
We consider the stochastic bandit problem with a continuous set of arms, with the expected reward function over the arms assumed to be fixed but unknown. We provide two new Gaussian process-based algorithms for continuous bandit…
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…
We consider a kernelized bandit problem with a compact arm set ${X} \subset \mathbb{R}^d $ and a fixed but unknown reward function $f^*$ with a finite norm in some Reproducing Kernel Hilbert Space (RKHS). We propose a class of…
We consider the problem of streaming kernel regression, when the observations arrive sequentially and the goal is to recover the underlying mean function, assumed to belong to an RKHS. The variance of the noise is not assumed to be known.…
Cooperative multi-agent decision making involves a group of agents cooperatively solving learning problems while communicating over a network with delays. In this paper, we consider the kernelised contextual bandit problem, where the reward…
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…
We tackle the problem of online reward maximisation over a large finite set of actions described by their contexts. We focus on the case when the number of actions is too big to sample all of them even once. However we assume that we have…