Cost-aware Bayesian Optimization via the Pandora's Box Gittins Index
This work addresses the challenge of resource-efficient optimization for practitioners in fields like machine learning and engineering, though it is incremental as it adapts an existing economic theory to a new context.
The paper tackles the problem of incorporating evaluation costs into Bayesian optimization by connecting it to the Pandora's Box problem from economics, using the Gittins index as an acquisition function. The result is a method that performs well empirically, especially in medium-high dimensions, and also improves classical Bayesian optimization without explicit costs.
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.