TREGO: a Trust-Region Framework for Efficient Global Optimization

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

Correcting Boundary Over-Exploration Deficiencies In Bayesian Optimization With Virtual Derivative Sign Observations

Bayesian optimization (BO) is a global optimization strategy designed to find the minimum of an expensive black-box function, typically defined on a compact subset of ℛ d , by using a Gaussian process (GP) as a surrogate model for the objective. Although currently available acquisition functions address this goal with different degree of success, an over-exploration effect of the contour of the search space is typically observed. However, in problems like the configuration of machine learning algorithms, the function domain is conservatively large and with a high probability the global minimum does not sit on the boundary of the domain. We propose a method to incorporate this knowledge into the search process by adding virtual derivative observations in the GP at the boundary of the search space. We use the properties of GPs to impose conditions on the partial derivatives of the objective. The method is applicable with any acquisition function, it is easy to use and consistently reduces the number of evaluations required to optimize the objective irrespective of the acquisition used. We illustrate the benefits of our approach in an extensive experimental comparison.Peer reviewe