Related papers: Gaussian Process bandits with adaptive discretizat…
This paper analyzes the problem of Gaussian process (GP) bandits with deterministic observations. The analysis uses a branch and bound algorithm that is related to the UCB algorithm of (Srinivas et al, 2010). For GPs with Gaussian…
In the kernelized bandit problem, a learner aims to sequentially compute the optimum of a function lying in a reproducing kernel Hilbert space given only noisy evaluations at sequentially chosen points. In particular, the learner aims to…
In this paper, the problem of estimating the level set of a black-box function from noisy and expensive evaluation queries is considered. A new algorithm for this problem in the Bayesian framework with a Gaussian Process (GP) prior is…
We aim to optimize a black-box function $f:\mathcal{X} \mapsto \mathbb{R}$ under the assumption that $f$ is H\"older smooth and has bounded norm in the RKHS associated with a given kernel $K$. This problem is known to have an agnostic…
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…
Optimization problems with uncertain black-box constraints, modeled by warped Gaussian processes, have recently been considered in the Bayesian optimization setting. This work introduces a new class of constraints in which the same…
We consider the problem of optimizing a grey-box objective function, i.e., nested function composed of both black-box and white-box functions. A general formulation for such grey-box problems is given, which covers the existing grey-box…
We consider sequential optimization of an unknown function in a reproducing kernel Hilbert space. We propose a Gaussian process-based algorithm and establish its order-optimal regret performance (up to a poly-logarithmic factor). This is…
The expected improvement (EI) algorithm is one of the most popular strategies for optimization under uncertainty due to its simplicity and efficiency. Despite its popularity, the theoretical aspects of this algorithm have not been properly…
We consider the problem of optimizing an unknown (typically non-convex) function with a bounded norm in some Reproducing Kernel Hilbert Space (RKHS), based on noisy bandit feedback. We consider a novel variant of this problem in which the…
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…
We study a time-varying Bayesian optimization problem with bandit feedback, where the reward function belongs to a Reproducing Kernel Hilbert Space (RKHS). We approach the problem via an upper-confidence bound Gaussian Process algorithm,…
We consider the continuum-armed bandits problem, under a novel setting of recommending the best arms within a fixed budget under aggregated feedback. This is motivated by applications where the precise rewards are impossible or expensive to…
In this paper, we consider the challenge of maximizing an unknown function f for which evaluations are noisy and are acquired with high cost. An iterative procedure uses the previous measures to actively select the next estimation of f…
Gaussian processes (GP) are one of the most successful frameworks to model uncertainty. However, GP optimization (e.g., GP-UCB) suffers from major scalability issues. Experimental time grows linearly with the number of evaluations, unless…
In this work, we investigate black-box optimization from the perspective of frequentist kernel methods. We propose a novel batch optimization algorithm, which jointly maximizes the acquisition function and select points from a whole batch…
We study the problem of constrained efficient global optimization, where both the objective and constraints are expensive black-box functions that can be learned with Gaussian processes. We propose CONFIG (CONstrained efFIcient Global…
Bayesian optimization usually assumes that a Bayesian prior is given. However, the strong theoretical guarantees in Bayesian optimization are often regrettably compromised in practice because of unknown parameters in the prior. In this…
We consider black box optimization of an unknown function in the nonparametric Gaussian process setting when the noise in the observed function values can be heavy tailed. This is in contrast to existing literature that typically assumes…
Sequential optimization of black-box functions from noisy evaluations has been widely studied, with Gaussian Process bandit algorithms such as GP-UCB guaranteeing no-regret in stationary settings. However, for time-varying objectives, it is…