Bulk-Calibrated Credal Ambiguity Sets: Fast, Tractable Decision Making under Out-of-Sample Contamination
This work addresses the problem of making robust decisions under distributional shifts for practitioners in fields like inventory management and machine learning, though it is incremental as it builds on existing DRO and imprecise probability frameworks.
The paper tackles the challenge of infinite worst-case risk in distributionally robust optimization under Huber contamination by introducing bulk-calibrated credal ambiguity sets, which learn a high-mass bulk from data to bound contamination and tail contributions, resulting in a finite closed-form objective and tractable optimization programs. Experiments on tasks like inventory control and text classification show competitive robustness-accuracy trade-offs and efficient optimization times.
Distributionally robust optimisation (DRO) minimises the worst-case expected loss over an ambiguity set that can capture distributional shifts in out-of-sample environments. While Huber (linear-vacuous) contamination is a classical minimal-assumption model for an $\varepsilon$-fraction of arbitrary perturbations, including it in an ambiguity set can make the worst-case risk infinite and the DRO objective vacuous unless one imposes strong boundedness or support assumptions. We address these challenges by introducing bulk-calibrated credal ambiguity sets: we learn a high-mass bulk set from data while considering contamination inside the bulk and bounding the remaining tail contribution separately. This leads to a closed-form, finite $\mathrm{mean}+\sup$ robust objective and tractable linear or second-order cone programs for common losses and bulk geometries. Through this framework, we highlight and exploit the equivalence between the imprecise probability (IP) notion of upper expectation and the worst-case risk, demonstrating how IP credal sets translate into DRO objectives with interpretable tolerance levels. Experiments on heavy-tailed inventory control, geographically shifted house-price regression, and demographically shifted text classification show competitive robustness-accuracy trade-offs and efficient optimisation times, using Bayesian, frequentist, or empirical reference distributions.