qEUBO: A Decision-Theoretic Acquisition Function for Preferential Bayesian Optimization

• URL: http://arxiv.org/abs/2303.15746v1
• Date: Tue, 28 Mar 2023 06:02:56 GMT
• Title: qEUBO: A Decision-Theoretic Acquisition Function for Preferential Bayesian Optimization
• Authors: Raul Astudillo, Zhiyuan Jerry Lin, Eytan Bakshy, Peter I. Frazier
• Abstract summary: We introduce the expected utility of the best option (qEUBO) as a novel acquisition function for PBO. We show that qEUBO is one-step Bayes optimal and thus equivalent to the popular knowledge gradient acquisition function. We demonstrate that qEUBO outperforms the state-of-the-art acquisition functions for PBO across many settings.
• Score: 17.300690315775572
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Preferential Bayesian optimization (PBO) is a framework for optimizing a decision maker's latent utility function using preference feedback. This work introduces the expected utility of the best option (qEUBO) as a novel acquisition function for PBO. When the decision maker's responses are noise-free, we show that qEUBO is one-step Bayes optimal and thus equivalent to the popular knowledge gradient acquisition function. We also show that qEUBO enjoys an additive constant approximation guarantee to the one-step Bayes-optimal policy when the decision maker's responses are corrupted by noise. We provide an extensive evaluation of qEUBO and demonstrate that it outperforms the state-of-the-art acquisition functions for PBO across many settings. Finally, we show that, under sufficient regularity conditions, qEUBO's Bayesian simple regret converges to zero at a rate $o(1/n)$ as the number of queries, $n$, goes to infinity. In contrast, we show that simple regret under qEI, a popular acquisition function for standard BO often used for PBO, can fail to converge to zero. Enjoying superior performance, simple computation, and a grounded decision-theoretic justification, qEUBO is a promising acquisition function for PBO.

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