Gaussian Process bandits with adaptive discretization

12/05/2017
by   Shubhanshu Shekhar, et al.
0

In this paper, the problem of maximizing a black-box function f:X→R is studied in the Bayesian framework with a Gaussian Process (GP) prior. In particular, a new algorithm for this problem is proposed, and high probability bounds on its simple and cumulative regret are established. The query point selection rule in most existing methods involves an exhaustive search over an increasingly fine sequence of uniform discretizations of X. The proposed algorithm, in contrast, adaptively refines X which leads to a lower computational complexity, particularly when X is a subset of a high dimensional Euclidean space. In addition to the computational gains, sufficient conditions are identified under which the regret bounds of the new algorithm improve upon the known results. Finally an extension of the algorithm to the case of contextual bandits is proposed, and high probability bounds on the contextual regret are presented.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
02/26/2019

Multiscale Gaussian Process Level Set Estimation

In this paper, the problem of estimating the level set of a black-box fu...
research
03/09/2012

Regret Bounds for Deterministic Gaussian Process Bandits

This paper analyses the problem of Gaussian process (GP) bandits with de...
research
06/27/2012

Exponential Regret Bounds for Gaussian Process Bandits with Deterministic Observations

This paper analyzes the problem of Gaussian process (GP) bandits with de...
research
10/27/2020

A Computationally Efficient Approach to Black-box Optimization using Gaussian Process Models

We consider the sequential optimization of an unknown function from nois...
research
02/07/2021

Bandits for Learning to Explain from Explanations

We introduce Explearn, an online algorithm that learns to jointly output...
research
07/06/2021

Weighted Gaussian Process Bandits for Non-stationary Environments

In this paper, we consider the Gaussian process (GP) bandit optimization...
research
11/25/2018

Robust Super-Level Set Estimation using Gaussian Processes

This paper focuses on the problem of determining as large a region as po...

Please sign up or login with your details

Forgot password? Click here to reset