Distributionally Robust Bayesian Optimization via Sinkhorn-Based Wasserstein Barycenter

This paper introduces a novel framework for Distributionally Robust Bayesian Optimization (DRBO) with continuous context that integrates optimal transport theory and entropic regularization. We propose the sampling from the Wasserstein Barycenter Bayesian Optimization (SWBBO) method to deal with uncertainty about the context; that is, the unknown stochastic component affecting the observations of the black-box objective function. This approach captures the geometric structure of the underlying distributional uncertainty and enables robust acquisition strategies without incurring excessive computational costs. The method incorporates adaptive robustness scheduling, Lipschitz regularization, and efficient barycenter construction to balance exploration and exploitation. Theoretical analysis establishes convergence guarantees for the robust Bayesian Optimization acquisition function. Empirical evaluations on standard global optimization problems and real-life inspired benchmarks demonstrate that SWBBO consistently achieves faster convergence, good final regret, and greater stability than other recently proposed methods for DRBO with continuous context. Indeed, SWBBO outperforms all of them in terms of both optimization performance and robustness under repeated evaluations.