Improved Gaussian Process Acquisition for Targeted Bayesian Optimization

17 Pages Posted: 11 Feb 2020

See all articles by Peter Mitic

Peter Mitic

Santander Bank; Dept. of Computer Science, UCL

Date Written: January 17, 2020

Abstract

A black-box optimization problem is considered, in which the function to be optimized can only be expressed in terms of a complicated stochastic algorithm that takes a long time to evaluate. The value returned is required to be sufficiently near to a target value, and uses data that has a significant noise component. Bayesian Optimization with an underlying Gaussian Process is used as an optimization solution, and its effectiveness is measured in terms of the number of function evaluations required to attain the target. To improve results, a simple modification of the Gaussian Process ‘Lower Confidence Bound’ acquisition function is proposed. With this change, much improved results compared to random selection methods and to other commonly used acquisition functions are obtained. Additional modifications result in further improvement. An intuitive explanation and a formal proof are given to explain the reduction in the number of lengthy function evaluations needed to reach the target.

Keywords: Acquisition function, Bayesian Optimization, Gaussian Process, Loss Distribution, Monte Carlo

JEL Classification: C11, C61

Suggested Citation

Mitic, Peter, Improved Gaussian Process Acquisition for Targeted Bayesian Optimization (January 17, 2020). Available at SSRN: https://ssrn.com/abstract=3521188 or http://dx.doi.org/10.2139/ssrn.3521188

Peter Mitic (Contact Author)

Santander Bank ( email )

Ciudad Financiera
Edificio Amazonia
Boadilla del Monte, 28660
Spain

Dept. of Computer Science, UCL ( email )

Gower Street
London, WC1E 6BT
United Kingdom

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