Regret Bounds for Expected Improvement Algorithms in Gaussian Process Bandit Optimization

by   Hung Tran-The, et al.

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 analyzed. In particular, whether in the noisy setting, the EI strategy with a standard incumbent converges is still an open question of the Gaussian process bandit optimization problem. We aim to answer this question by proposing a variant of EI with a standard incumbent defined via the GP predictive mean. We prove that our algorithm converges, and achieves a cumulative regret bound of 𝒪(γ_T√(T)), where γ_T is the maximum information gain between T observations and the Gaussian process model. Based on this variant of EI, we further propose an algorithm called Improved GP-EI that converges faster than previous counterparts. In particular, our proposed variants of EI do not require the knowledge of the RKHS norm and the noise's sub-Gaussianity parameter as in previous works. Empirical validation in our paper demonstrates the effectiveness of our algorithms compared to several baselines.


page 1

page 2

page 3

page 4

∙ 11/09/2021

Misspecified Gaussian Process Bandit Optimization

We consider the problem of optimizing a black-box function based on nois...
∙ 10/29/2020

Gaussian Process Bandit Optimization of the Thermodynamic Variational Objective

Achieving the full promise of the Thermodynamic Variational Objective (T...
∙ 08/03/2016

A supermartingale approach to Gaussian process based sequential design of experiments

Gaussian process (GP) models have become a well-established frameworkfor...
∙ 06/09/2020

Scalable Thompson Sampling using Sparse Gaussian Process Models

Thompson Sampling (TS) with Gaussian Process (GP) models is a powerful t...
∙ 10/19/2015

Optimization for Gaussian Processes via Chaining

In this paper, we consider the problem of stochastic optimization under ...
∙ 03/04/2020

Corruption-Tolerant Gaussian Process Bandit Optimization

We consider the problem of optimizing an unknown (typically non-convex) ...
∙ 03/23/2020

Efficient Gaussian Process Bandits by Believing only Informative Actions

Bayesian optimization is a framework for global search via maximum a pos...

Please sign up or login with your details

Forgot password? Click here to reset