Enhancing Gaussian Process Surrogates for Optimization and Posterior Approximation via Random Exploration

• URL: http://arxiv.org/abs/2401.17037v2
• Date: Wed, 17 Jul 2024 10:42:12 GMT
• Title: Enhancing Gaussian Process Surrogates for Optimization and Posterior Approximation via Random Exploration
• Authors: Hwanwoo Kim, Daniel Sanz-Alonso,
• Abstract summary: novel noise-free Bayesian optimization strategies that rely on a random exploration step to enhance the accuracy of Gaussian process surrogate models. New algorithms retain the ease of implementation of the classical GP-UCB, but an additional exploration step facilitates their convergence.
• Score: 2.984929040246293
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper proposes novel noise-free Bayesian optimization strategies that rely on a random exploration step to enhance the accuracy of Gaussian process surrogate models. The new algorithms retain the ease of implementation of the classical GP-UCB algorithm, but the additional random exploration step accelerates their convergence, nearly achieving the optimal convergence rate. Furthermore, to facilitate Bayesian inference with an intractable likelihood, we propose to utilize optimization iterates for maximum a posteriori estimation to build a Gaussian process surrogate model for the unnormalized log-posterior density. We provide bounds for the Hellinger distance between the true and the approximate posterior distributions in terms of the number of design points. We demonstrate the effectiveness of our Bayesian optimization algorithms in non-convex benchmark objective functions, in a machine learning hyperparameter tuning problem, and in a black-box engineering design problem. The effectiveness of our posterior approximation approach is demonstrated in two Bayesian inference problems for parameters of dynamical systems.

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