Wasserstein Distributionally Robust Bayesian Optimization with Continuous Context
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912294895616000 |
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| author | Micheli, Francesco Balta, Efe C. Tsiamis, Anastasios Lygeros, John |
| author_facet | Micheli, Francesco Balta, Efe C. Tsiamis, Anastasios Lygeros, John |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_20341 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Wasserstein Distributionally Robust Bayesian Optimization with Continuous Context Micheli, Francesco Balta, Efe C. Tsiamis, Anastasios Lygeros, John Machine Learning Artificial Intelligence 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. |
| title | Wasserstein Distributionally Robust Bayesian Optimization with Continuous Context |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2503.20341 |