Batch Bayesian optimisation via density-ratio estimation with guarantees

• URL: http://arxiv.org/abs/2209.10715v1
• Date: Thu, 22 Sep 2022 00:42:18 GMT
• Title: Batch Bayesian optimisation via density-ratio estimation with guarantees
• Authors: Rafael Oliveira, Louis Tiao and Fabio Ramos
• Abstract summary: We present a theoretical analysis of BORE's regret and an extension of the algorithm with improved uncertainty estimates. We also show that BORE can be naturally extended to a batch optimisation setting by recasting the problem as approximate Bayesian inference.
• Score: 26.052368583196426
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Bayesian optimisation (BO) algorithms have shown remarkable success in applications involving expensive black-box functions. Traditionally BO has been set as a sequential decision-making process which estimates the utility of query points via an acquisition function and a prior over functions, such as a Gaussian process. Recently, however, a reformulation of BO via density-ratio estimation (BORE) allowed reinterpreting the acquisition function as a probabilistic binary classifier, removing the need for an explicit prior over functions and increasing scalability. In this paper, we present a theoretical analysis of BORE's regret and an extension of the algorithm with improved uncertainty estimates. We also show that BORE can be naturally extended to a batch optimisation setting by recasting the problem as approximate Bayesian inference. The resulting algorithm comes equipped with theoretical performance guarantees and is assessed against other batch BO baselines in a series of experiments.

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