Price-aware Bayesian optimization by way of the Pandora’s Field Gittins index
Authors: Qian Xie, Raul Astudillo, Peter Frazier, Ziv Scully, Alexander Terenin
Summary: Bayesian optimization is a way for effectively optimizing unknown features in a black-box method. To deal with sensible settings the place gathering knowledge requires use of finite assets, it’s fascinating to explicitly incorporate perform analysis prices into Bayesian optimization insurance policies. To grasp how to take action, we develop a previously-unexplored connection between cost-aware Bayesian optimization and the Pandora’s Field drawback, a call drawback from economics. The Pandora’s Field drawback admits a Bayesian-optimal resolution primarily based on an expression referred to as the Gittins index, which may be reinterpreted as an acquisition perform. We examine the usage of this acquisition perform for cost-aware Bayesian optimization, and display empirically that it performs effectively, significantly in medium-high dimensions. We additional present that this efficiency carries over to classical Bayesian optimization with out express analysis prices. Our work constitutes a primary step in direction of integrating methods from Gittins index idea into Bayesian optimization.