Fast Calculation of the Knowledge Gradient for Optimization of Deterministic Engineering Simulations

TL;DR

This paper introduces an efficient method for computing the Knowledge-Gradient policy in deterministic optimization, compares it with existing policies, and demonstrates its advantages in complex, multi-modal problems.

Contribution

It derives a novel efficient computation method for the Knowledge-Gradient policy and compares its performance with Expected Improvement and UCB policies.

Findings

KGCP performs similarly to EI on many problems

KGCP shows better convergence on complex, multi-modal problems

The relationship between MLE and slice sampling for hyperparameter estimation is analyzed

Abstract

A novel efficient method for computing the Knowledge-Gradient policy for Continuous Parameters (KGCP) for deterministic optimization is derived. The differences with Expected Improvement (EI), a popular choice for Bayesian optimization of deterministic engineering simulations, are explored. Both policies and the Upper Confidence Bound (UCB) policy are compared on a number of benchmark functions including a problem from structural dynamics. It is empirically shown that KGCP has similar performance as the EI policy for many problems, but has better convergence properties for complex (multi-modal) optimization problems as it emphasizes more on exploration when the model is confident about the shape of optimal regions. In addition, the relationship between Maximum Likelihood Estimation (MLE) and slice sampling for estimation of the hyperparameters of the underlying models, and the complexity of the problem at hand, is studied.