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This paper introduces DOVE, a novel sequential sampling policy for preference learning that addresses the challenge of non-Gaussian posteriors in Gaussian process regression through moment-matching approximations. By combining information gain with randomized sampling to control error accumulation, the authors establish theoretical convergence rates for statistical error and simple regret in continuous global optimization where direct function evaluation is unavailable. This work advances the mathematical foundations of Bayesian inference for preference-based learning, offering a rigorous framework for optimizing systems based on pairwise comparisons rather than explicit reward signals.
Fully sequential Gaussian process regression for preference learning
arXiv:2610.19391v1 Announce Type: new Abstract: We study continuous global optimization problems in which the objective function cannot be directly evaluated; rather, we observe only which of two selected design points appears to perform better, subject to noise. Such comparisons complicate the use of Gaussian process regression because they yield non-Gaussian posteriors. We consider a fully sequential approximation, based on moment-matching, that yields a fast closed-form update of the metamodel's mean and covariance. We then propose DOVE, a fully sequential sampling policy that combines an information gain criterion with randomized sampling designed to control error accumulation. Under fairly standard regularity conditions, we prove convergence rates for both statistical error and expected simple regret that depend on kernel smoothness. To our knowledge, these are the first such rates for fully sequential approximate Bayesian inference in continuous global optimization.
Abstract:We study continuous global optimization problems in which the objective function cannot be directly evaluated; rather, we observe only which of two selected design points appears to perform better, subject to noise. Such comparisons complicate the use of Gaussian process regression because they yield non-Gaussian posteriors. We consider a fully sequential approximation, based on moment-matching, that yields a fast closed-form update of the metamodel's mean and covariance. We then propose DOVE, a fully sequential sampling policy that combines an information gain criterion with randomized sampling designed to control error accumulation. Under fairly standard regularity conditions, we prove convergence rates for both statistical error and expected simple regret that depend on kernel smoothness. To our knowledge, these are the first such rates for fully sequential approximate Bayesian inference in continuous global optimization.
Machine Learning (cs.LG)
arXiv:2610.19391 [cs.LG]
(or arXiv:2610.19391v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.19391 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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