A Finite Time Analysis of Thompson Sampling for Bayesian Optimization with Preferential Feedback
For practitioners using human-in-the-loop or expert-in-the-loop optimization where pairwise comparisons are easier to obtain than scalar scores, this work provides a theoretically grounded method with performance guarantees.
The paper proposes a Thompson Sampling method for Bayesian optimization with preferential feedback (pairwise comparisons) and proves it achieves finite-time performance matching standard TS for scalar feedback. Experiments on synthetic and real-world data validate the approach.
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.