Cost-aware Bayesian Optimization via the Pandora's Box Gittins Index

TL;DR

This paper introduces a novel approach to cost-aware Bayesian optimization by leveraging the Gittins index from the Pandora's Box problem, improving efficiency especially in higher dimensions.

Contribution

It establishes a new connection between cost-aware Bayesian optimization and the Pandora's Box problem, applying Gittins index as an acquisition function.

Findings

Gittins index-based acquisition performs well in medium-high dimensions.

The approach improves efficiency in cost-aware Bayesian optimization.

Performance benefits extend to classical Bayesian optimization without explicit costs.

Abstract

Bayesian optimization is a technique for efficiently optimizing unknown functions in a black-box manner. To handle practical settings where gathering data requires use of finite resources, it is desirable to explicitly incorporate function evaluation costs into Bayesian optimization policies. To understand how to do so, we develop a previously-unexplored connection between cost-aware Bayesian optimization and the Pandora's Box problem, a decision problem from economics. The Pandora's Box problem admits a Bayesian-optimal solution based on an expression called the Gittins index, which can be reinterpreted as an acquisition function. We study the use of this acquisition function for cost-aware Bayesian optimization, and demonstrate empirically that it performs well, particularly in medium-high dimensions. We further show that this performance carries over to classical Bayesian optimization without explicit evaluation costs. Our work constitutes a first step towards integrating techniques from Gittins index theory into Bayesian optimization.