Multi-fidelity Gaussian Process Bandit Optimisation

TL;DR

This paper introduces MF-GP-UCB, a novel multi-fidelity Gaussian process bandit optimization method that efficiently leverages cheap approximations to accelerate the search for the global maximum of expensive black-box functions.

Contribution

It formalizes multi-fidelity optimization as a Gaussian process bandit problem and proposes MF-GP-UCB, which outperforms existing strategies in theory and practice.

Findings

MF-GP-UCB achieves lower regret than single-fidelity methods.

The method effectively uses cheap approximations to focus expensive evaluations.

Empirical results show superior performance on synthetic and real problems.

Abstract

In many scientific and engineering applications, we are tasked with the maximisation of an expensive to evaluate black box function $f$. Traditional settings for this problem assume just the availability of this single function. However, in many cases, cheap approximations to $f$ may be obtainable. For example, the expensive real world behaviour of a robot can be approximated by a cheap computer simulation. We can use these approximations to eliminate low function value regions cheaply and use the expensive evaluations of $f$ in a small but promising region and speedily identify the optimum. We formalise this task as a \emph{multi-fidelity} bandit problem where the target function and its approximations are sampled from a Gaussian process. We develop MF-GP-UCB, a novel method based on upper confidence bound techniques. In our theoretical analysis we demonstrate that it exhibits precisely the above behaviour, and achieves better regret than strategies which ignore multi-fidelity information. Empirically, MF-GP-UCB outperforms such naive strategies and other multi-fidelity methods on several synthetic and real experiments.