Efficient computation of the Knowledge Gradient for Bayesian Optimization

TL;DR

This paper introduces a new, efficient method for computing the Knowledge Gradient acquisition function in Bayesian optimization, combining previous approaches to reduce computational cost while maintaining or improving performance.

Contribution

The paper proposes One-shot Hybrid KG, a novel approach that unifies existing methods for Knowledge Gradient computation, offering theoretical guarantees and empirical efficiency improvements.

Findings

Reduced computational overhead compared to existing methods

Maintains or improves optimization performance

Implemented in BOTorch with publicly available code

Abstract

Bayesian optimization is a powerful collection of methods for optimizing stochastic expensive black box functions. One key component of a Bayesian optimization algorithm is the acquisition function that determines which solution should be evaluated in every iteration. A popular and very effective choice is the Knowledge Gradient acquisition function, however there is no analytical way to compute it. Several different implementations make different approximations. In this paper, we review and compare the spectrum of Knowledge Gradient implementations and propose One-shot Hybrid KG, a new approach that combines several of the previously proposed ideas and is cheap to compute as well as powerful and efficient. We prove the new method preserves theoretical properties of previous methods and empirically show the drastically reduced computational overhead with equal or improved performance. All experiments are implemented in BOTorch and code is available on github.