Related papers: Gaussian Process bandits with adaptive discretizat…
In this paper, we consider the time-varying Bayesian optimization problem. The unknown function at each time is assumed to lie in an RKHS (reproducing kernel Hilbert space) with a bounded norm. We adopt the general variation budget model to…
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…
The contextual bandit framework is widely used to solve sequential optimization problems where the reward of each decision depends on auxiliary context variables. In settings such as medicine, business, and engineering, the decision maker…
Gaussian process upper confidence bound (GP-UCB) is a theoretically established algorithm for Bayesian optimization (BO), where we assume the objective function $f$ follows a GP. One notable drawback of GP-UCB is that the theoretical…
In federated multi-armed bandit problems, maximizing global reward while satisfying minimum privacy requirements to protect clients is the main goal. To formulate such problems, we consider a combinatorial contextual bandit setting with…
Bayesian optimization is a popular framework for efficiently tackling black-box search problems. As a rule, these algorithms operate by iteratively choosing what to evaluate next until some predefined budget has been exhausted. We…
Some real-world problems revolve to solve the optimization problem \max_{x\in\mathcal{X}}f\left(x\right) where f\left(.\right) is a black-box function and X might be the set of non-vectorial objects (e.g., distributions) where we can only…
Machine learning algorithms frequently require careful tuning of model hyperparameters, regularization terms, and optimization parameters. Unfortunately, this tuning is often a "black art" that requires expert experience, unwritten rules of…
Gaussian Process bandit optimization has emerged as a powerful tool for optimizing noisy black box functions. One example in machine learning is hyper-parameter optimization where each evaluation of the target function requires training a…
We study the problem of preferential Bayesian optimization (BO), where we aim to optimize a black-box function with only preference feedback over a pair of candidate solutions. Inspired by the likelihood ratio idea, we construct a…
Bayesian optimization is a powerful global optimization technique for expensive black-box functions. One of its shortcomings is that it requires auxiliary optimization of an acquisition function at each iteration. This auxiliary…
Bayesian optimization is a powerful tool for optimizing an expensive-to-evaluate black-box function. In particular, the effectiveness of expected improvement (EI) has been demonstrated in a wide range of applications. However, theoretical…
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. Compared with the GP upper confidence bound (GP-UCB) with…
In this paper, we analyze a generic algorithm scheme for sequential global optimization using Gaussian processes. The upper bounds we derive on the cumulative regret for this generic algorithm improve by an exponential factor the previously…
Bayesian Optimization is a popular approach for optimizing expensive black-box functions. Its key idea is to use a surrogate model to approximate the objective and, importantly, quantify the associated uncertainty that allows a sequential…
We consider the model selection task in the stochastic contextual bandit setting. Suppose we are given a collection of base contextual bandit algorithms. We provide a master algorithm that combines them and achieves the same performance, up…
We propose a novel sparse spectrum approximation of Gaussian process (GP) tailored for Bayesian optimization. Whilst the current sparse spectrum methods provide desired approximations for regression problems, it is observed that this…
This paper studies kernelized bandits (also known as Gaussian process bandits) in an adversarial environment, where the reward functions in a known reproducing kernel Hilbert space (RKHS) may be adversarially chosen at each round. We show…
Gaussian Processes (GPs) are a generic modelling tool for supervised learning. While they have been successfully applied on large datasets, their use in safety-critical applications is hindered by the lack of good performance guarantees. To…
Computing a Gaussian process (GP) posterior has a computational cost cubical in the number of historical points. A reformulation of the same GP posterior highlights that this complexity mainly depends on how many \emph{unique} historical…