A General Recipe for Likelihood-free Bayesian Optimization

• URL: http://arxiv.org/abs/2206.13035v1
• Date: Mon, 27 Jun 2022 03:55:27 GMT
• Title: A General Recipe for Likelihood-free Bayesian Optimization
• Authors: Jiaming Song, Lantao Yu, Willie Neiswanger, Stefano Ermon
• Abstract summary: We propose likelihood-free BO (LFBO) to extend BO to a broader class of models and utilities. LFBO directly models the acquisition function without having to separately perform inference with a probabilistic surrogate model. We show that computing the acquisition function in LFBO can be reduced to optimizing a weighted classification problem.
• Score: 115.82591413062546
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The acquisition function, a critical component in Bayesian optimization (BO), can often be written as the expectation of a utility function under a surrogate model. However, to ensure that acquisition functions are tractable to optimize, restrictions must be placed on the surrogate model and utility function. To extend BO to a broader class of models and utilities, we propose likelihood-free BO (LFBO), an approach based on likelihood-free inference. LFBO directly models the acquisition function without having to separately perform inference with a probabilistic surrogate model. We show that computing the acquisition function in LFBO can be reduced to optimizing a weighted classification problem, where the weights correspond to the utility being chosen. By choosing the utility function for expected improvement (EI), LFBO outperforms various state-of-the-art black-box optimization methods on several real-world optimization problems. LFBO can also effectively leverage composite structures of the objective function, which further improves its regret by several orders of magnitude.

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