Fast Online Distributionally Robust Optimization via Data Compression

We propose an online data compression approach for efficiently solving distributionally robust optimization (DRO) problems with streaming data while maintaining out-of-sample performance guarantees. Our method dynamically constructs ambiguity sets using online clustering, allowing the clustered configuration to evolve over time for an accurate representation of the underlying distribution. We establish theoretical conditions for clustering algorithms to ensure robustness, and show that the performance gap between our online solution and the nominal DRO solution can be written in terms of the distance between the true and compressed distributions. Therefore, by varying the number of clusters, our method effectively balances robustness and online computational efficiency. We show that our analysis is compatible with well-established finite-sample and asymptotic guarantees for Wasserstein DRO. Numerical experiments in mixed-integer portfolio optimization demonstrate significant computational savings, with minimal loss in solution quality.