Wasserstein Distributionally Robust Bayesian Optimization with Continuous Context

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.

@article{micheli2025_2503.20341,
  title={ Wasserstein Distributionally Robust Bayesian Optimization with Continuous Context },
  author={ Francesco Micheli and Efe C. Balta and Anastasios Tsiamis and John Lygeros },
  journal={arXiv preprint arXiv:2503.20341},
  year={ 2025 }
}