Citation
Fang, L., Cheng, J., Hanasusanto, G. A., and Wang, Y. (2026). Distributionally Robust Optimization via Targeted Integral Probability Metrics for General Data Processes. Optimization Online.
Distributionally Robust Optimization via Targeted Integral Probability Metrics for General Data Processes
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Distributionally robust optimization (DRO) has been successful in addressing decision-making problems under uncertainty when the underlying distribution is unknown. Existing data-driven DRO frameworks, however, often impose restrictive assumptions on the data-generating process. We propose a new DRO framework based on targeted integral probability metrics. The ambiguity set is defined directly through the loss functions induced by feasible decisions, leading to an expected hinge-constrained formulation that is equivalent to an infinitely constrained ambiguity set. This targeted construction aligns the discrepancy measure with the downstream task and yields finite-sample guarantees that bypass the curse of dimensionality: whenever a scalar pointwise concentration inequality is available, the ambiguity radius can be calibrated at the canonical \(\widetilde{\mathcal O}(N^{-1/2})\) rate. As a result, the framework applies broadly to settings including heavier-tailed distributions, Markovian data, outlier-corrupted observations, incomplete data, and contextual optimization. We derive exact infinite-dimensional dual reformulations, establish out-of-sample and excess-risk guarantees, and develop a Monte Carlo approximation scheme that yields conservative sampled ambiguity sets together with convergence and suboptimality guarantees. For piecewise affine losses, the sampled problems admit tractable conic reformulations, and the Monte Carlo approximation converges at a provably fast rate. Numerical experiments in inventory management under heavy-tailed demand and regression with outlier corruption demonstrate the performance of our framework.