Bulk-Calibrated Credal Ambiguity Sets: Fast, Tractable Decision Making under Out-of-Sample Contamination

Fuente: arXiv
Salvato in:
Dettagli Bibliografici
Autori principali: Chen, Mengqi, Berrett, Thomas B., Damoulas, Theodoros, Caprio, Michele
Natura: Preprint
Pubblicazione: 2026
Soggetti:
Accesso online:
Tags: Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
_version_ 1866918312953249792
author Chen, Mengqi
Berrett, Thomas B.
Damoulas, Theodoros
Caprio, Michele
author_facet Chen, Mengqi
Berrett, Thomas B.
Damoulas, Theodoros
Caprio, Michele
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2601_21324
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Bulk-Calibrated Credal Ambiguity Sets: Fast, Tractable Decision Making under Out-of-Sample Contamination
Chen, Mengqi
Berrett, Thomas B.
Damoulas, Theodoros
Caprio, Michele
Machine Learning
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.
title Bulk-Calibrated Credal Ambiguity Sets: Fast, Tractable Decision Making under Out-of-Sample Contamination
topic Machine Learning
url https://arxiv.org/abs/2601.21324