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TREGO: a Trust-Region Framework for Efficient Global Optimization

Y. Diouane (youssef.diouane***at***isae-supaero.fr)
V. Picheny (victor***at***secondmind.ai)
R. Le Riche (leriche***at***emse.fr)
A. Scotto Di Perrotolo (alexandre.scotto-di-perrotolo***at***isae-supaero.fr)

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, we propose and analyze a trust-region-like EGO method (TREGO). 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), we demonstrate that our algorithm enjoys strong global convergence properties, while departing from EGO only for a subset of optimization steps. Using extensive numerical experiments based on the well-known COCO benchmark, 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 global optimization methods. The method is available both in the R package DiceOptim (https://cran.r-project.org/package=DiceOptim) and Python library trieste (https://secondmind-labs.github.io/trieste/).

Keywords: nonlinear optimization; Gaussian processes; Bayesian optimization; trust-region.

Category 1: Global Optimization


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Entry Submitted: 01/17/2021
Entry Accepted: 01/18/2021
Entry Last Modified: 02/02/2021

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