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This paper introduces a Thompson Sampling (TS) algorithm for Bayesian Optimization that handles preferential feedback by modeling pairwise comparisons via a monotone link on latent utility differences and a dueling kernel. The key result is a finite-time analysis demonstrating that the proposed TS method achieves performance comparable to standard TS in Bayesian optimization with scalar feedback. The analysis leverages anchor invariance of TS and a novel double-TS pairing strategy.
Thompson Sampling can be just as efficient with pairwise preference feedback as it is with scalar rewards, opening up new avenues for optimization in human-in-the-loop and experimental design scenarios.
Preference feedback, in the form of pairwise comparisons rather than scalar scores, has seen increasing use in applications such as human-, laboratory-, and expert-in-the-loop design, as well as scientific discovery. We propose a Thompson Sampling (TS) approach to Bayesian optimization with preferential feedback that models comparisons using a monotone link on latent utility differences and leverages the dueling kernel induced by a base kernel. We provide a finite-time analysis showing that the performance of the proposed method matches that of standard TS for conventional Bayesian optimization with scalar feedback. The analysis exploits the anchor invariance of TS for challenger selection and introduces a double-TS pairing variant. We also demonstrate the performance of the method on both synthetic and real-world examples.
