Wasserstein Distributionally Robust Bayesian Optimization with Continuous Context

• URL: http://arxiv.org/abs/2503.20341v1
• Date: Wed, 26 Mar 2025 09:11:17 GMT
• Title: Wasserstein Distributionally Robust Bayesian Optimization with Continuous Context
• Authors: Francesco Micheli, Efe C. Balta, Anastasios Tsiamis, John Lygeros,
• Abstract summary: We address the challenge of sequential data-driven decision-making under context distributional uncertainty.<n>We propose a novel algorithm for Wasserstein Distributionally Robust Bayesian Optimization.<n>Our theoretical analysis combines recent results in self-normalized concentration in Hilbert spaces and finite-sample bounds for distributionally robust optimization.
• Score: 5.4147994801415145
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We address the challenge of sequential data-driven decision-making under context distributional uncertainty. This problem arises in numerous real-world scenarios where the learner optimizes black-box objective functions in the presence of uncontrollable contextual variables. We consider the setting where the context distribution is uncertain but known to lie within an ambiguity set defined as a ball in the Wasserstein distance. We propose a novel algorithm for Wasserstein Distributionally Robust Bayesian Optimization that can handle continuous context distributions while maintaining computational tractability. Our theoretical analysis combines recent results in self-normalized concentration in Hilbert spaces and finite-sample bounds for distributionally robust optimization to establish sublinear regret bounds that match state-of-the-art results. Through extensive comparisons with existing approaches on both synthetic and real-world problems, we demonstrate the simplicity, effectiveness, and practical applicability of our proposed method.

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