Portfolio Allocation for Bayesian Optimization

TL;DR

This paper introduces a portfolio approach for Bayesian optimization that combines multiple acquisition functions using an online bandit strategy, outperforming individual functions and providing theoretical performance guarantees.

Contribution

It proposes a novel portfolio method, GP-Hedge, for selecting acquisition functions in Bayesian optimization, improving performance over single-function strategies.

Findings

GP-Hedge outperforms individual acquisition functions

The portfolio approach adapts effectively to different optimization scenarios

Theoretical bounds on the algorithm's performance are established.

Abstract

Bayesian optimization with Gaussian processes has become an increasingly popular tool in the machine learning community. It is efficient and can be used when very little is known about the objective function, making it popular in expensive black-box optimization scenarios. It uses Bayesian methods to sample the objective efficiently using an acquisition function which incorporates the model's estimate of the objective and the uncertainty at any given point. However, there are several different parameterized acquisition functions in the literature, and it is often unclear which one to use. Instead of using a single acquisition function, we adopt a portfolio of acquisition functions governed by an online multi-armed bandit strategy. We propose several portfolio strategies, the best of which we call GP-Hedge, and show that this method outperforms the best individual acquisition function. We also provide a theoretical bound on the algorithm's performance.