Wasserstein Distributionally Robust Bayesian Optimization with Continuous Context
This addresses the challenge of optimizing black-box functions with uncontrollable contextual variables in real-world scenarios, representing an incremental improvement with specific theoretical and practical gains.
The paper tackles the problem of sequential decision-making under uncertain context distributions by proposing a novel algorithm for Wasserstein Distributionally Robust Bayesian Optimization that handles continuous contexts with computational tractability, achieving sublinear regret bounds that match state-of-the-art results.
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.