TREGO: a Trust-Region Framework for Efficient Global Optimization

TL;DR

TREGO enhances Bayesian optimization by integrating a trust-region approach, improving scalability and convergence guarantees for high-dimensional black-box problems, and demonstrating superior performance over traditional EGO in numerical tests.

Contribution

This paper introduces TREGO, a trust-region framework for EGO that provides global convergence guarantees and improves scalability in high-dimensional optimization tasks.

Findings

TREGO outperforms EGO in numerical experiments.

TREGO is competitive with state-of-the-art black-box optimization methods.

The algorithm's sensitivity to parameters is thoroughly analyzed.

Abstract

Efficient Global Optimization (EGO) is the canonical form of Bayesian optimization that has been successfully applied to solve global optimization of expensive-to-evaluate black-box problems. However, EGO struggles to scale with dimension, and offers limited theoretical guarantees. In this work, a trust-region framework for EGO (TREGO) is proposed and analyzed. TREGO alternates between regular EGO steps and local steps within a trust region. By following a classical scheme for the trust region (based on a sufficient decrease condition), the proposed algorithm enjoys global convergence properties, while departing from EGO only for a subset of optimization steps. Using extensive numerical experiments based on the well-known COCO {bound constrained problems}, we first analyze the sensitivity of TREGO to its own parameters, then show that the resulting algorithm is consistently outperforming EGO and getting competitive with other state-of-the-art black-box optimization methods.