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arXiv · 2402.05367

Principled Preferential Bayesian Optimization

Wenjie Xu·Wenbin Wang·Yuning Jiang·Bratislav Svetozarevic·Colin N. Jones
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Abstract

We study the problem of preferential Bayesian optimization (BO), where we aim to optimize a black-box function with only preference feedback over a pair of candidate solutions. Inspired by the likelihood ratio idea, we construct a confidence set of the black-box function using only the preference feedback. An optimistic algorithm with an efficient computational method is then developed to solve the problem, which enjoys an information-theoretic bound on the total cumulative regret, a first-of-its-kind for preferential BO. This bound further allows us to design a scheme to report an estimated best solution, with a guaranteed convergence rate. Experimental results on sampled instances from Gaussian processes, standard test functions, and a thermal comfort optimization problem all show that our method stably achieves better or competitive performance as compared to the existing state-of-the-art heuristics, which, however, do not have theoretical guarantees on regret bounds or convergence.

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Wenjie Xu, Wenbin Wang, Yuning Jiang, Bratislav Svetozarevic, Colin N. Jones. 2024-02-08. Principled Preferential Bayesian Optimization. https://arxiv.org/abs/2402.05367

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