Contextual distributionally robust optimization: A unified paradigm bridging data science and decision making

Abstract

Decision-makers in contemporary operational settings must navigate uncertainty arising from rapidly shifting contextual factors such as volatile market dynamics and intricate supply-chain interactions. Although distributionally robust optimization offers a principled means of guarding against distributional ambiguity, conventional formulations typically ignore the contextual information that shapes uncertainty in real applications. This paper outlines the emerging framework of Contextual Distributionally Robust Optimization (CDRO), which embeds covariate information into robust decision-making. We cast CDRO as a conditional worst-case optimization problem and organize existing research into two overarching streams: (1) predict-then-robustify, where ambiguity sets are constructed around estimated conditional distributions or moments; and (2) joint contextual robustification, where robustness is imposed on the joint distribution of covariates and uncertain parameters. Illustrative studies in transportation, healthcare, and inventory systems reveal that incorporating contextual information can substantially enhance adaptability and reliability in decision policies. The paper concludes with a discussion of open challenges, including data fidelity, causal confounding, computational scalability, privacy concerns, and model interpretability, that highlight promising directions for future research.

Graphical abstract

Keywords

contextual distributionally robust optimization / predict-then-robustify / joint contextual robustification / transportation and logistics

References

[1] Alley M, Biggs M, Hariss R, Herrmann C, Li M L, Perakis G, (2023). Pricing for heterogeneous products: analytics for ticket reselling. Manufacturing & Service Operations Management, 25( 2): 409–426

[2] Ban G Y, Rudin C, (2019). The big data newsvendor: practical insights from machine learning. Operations Research, 67( 1): 90–108

[3] Bertsimas D, Kallus N, (2020). From predictive to prescriptive analytics. Management Science, 66( 3): 1025–1044

[4] Bertsimas D, O’Hair A, Relyea S, Silberholz J, (2016). An analytics approach to designing combination chemotherapy regimens for cancer. Management Science, 62( 5): 1511–1531

[5] Bravo F, Braun M, Farias V, Levi R, Lynch C, Tumolo J, Whyte R, (2021). Optimization-driven framework to understand health care network costs and resource allocation. Health Care Management Science, 24( 3): 640–660

[6] Chen Y, Zhang H, Li C, Chi B, Chen X, Wu J, (2025). Large language model empowered smart city mobility. ENGINEERING Management, 12( 1): 201–207

[7] Chung T HRostami VBastani HBastani O (2022). Decision-aware learning for optimizing health supply chains. Preprint at arXiv:2211.08507

[8] Delage E, Ye Y, (2010). Distributionally robust optimization under moment uncertainty with application to data-driven problems. Operations Research, 58( 3): 595–612

[9] Demirović E, Stuckey P J, Bailey J, Chan J, Leckie C, Ramamohanarao K, Guns T, (2020). Dynamic programming for predict + optimize. In: Proceedings of the AAAI Conference on Artificial Intelligence February. New York: AAAI Press, 34( 2): 1444–1451

[10] Esteban-Pérez A, Morales J M, (2022). Distributionally robust stochastic programs with side information based on trimmings. Mathematical Programming, 195( 1-2): 1069–1105

[11] Hu J, Chen Z, Wang S, (2025). Budget-driven multiperiod hub location: a robust time-series approach. Operations Research, 73( 2): 613–631

[12] Kannan R, Bayraksan G, Luedtke J R, (2024). Residuals-based distributionally robust optimization with covariate information. Mathematical Programming, 207( 1-2): 369–425

[13] Li Q, Wen Z, Wu Z, Hu S, Wang N, Li Y, Liu X, He B, (2023). A survey on federated learning systems: vision, hype and reality for data privacy and protection. IEEE Transactions on Knowledge and Data Engineering, 35( 4): 3347–3366

[14] Liu WZhang Z H (2023). Solving data-driven newsvendor pricing problems with decision-dependent effect. Preprint at arXiv:2304.13924

[15] Liu Y, Xiahou T, Zhang Q, Xing L, Huang H Z, (2024). Multi-state system reliability: an emerging paradigm for sophisticated engineered systems. ENGINEERING Management, 11( 3): 568–575

[16] Liu Z, Yin Y, Bai F, Grimm D K, (2023). End-to-end learning of user equilibrium with implicit neural networks. Transportation Research Part C, Emerging Technologies, 150: 104085

[17] Mohajerin Esfahani P, Kuhn D, (2018). Data-driven distributionally robust optimization using the Wasserstein metric: performance guarantees and tractable reformulations. Mathematical Programming, 171( 1-2): 115–166

[18] Nguyen V A, Zhang F, Wang S, Blanchet J, Delage E, Ye Y, (2025). Robustifying conditional portfolio decisions via optimal transport. Operations Research, 73( 5): 2801–2829

[19] Perakis G, Sim M, Tang Q, Xiong P, (2023). Robust pricing and production with information partitioning and adaptation. Management Science, 69( 3): 1398–1419

[20] Qi M, Grigas P, Shen Z J, (2026). Integrated conditional estimation-optimization. Operations Research, 74( 3): 1604–1625

[21] Sadana U, Chenreddy A, Delage E, Forel A, Frejinger E, Vidal T, (2025). A survey of contextual optimization methods for decision-making under uncertainty. European Journal of Operational Research, 320( 2): 271–289

[22] Sim M, Tang Q, Zhou M, Zhu T, (2025). The analytics of robust satisficing: predict, optimize, satisfice, then fortify. Operations Research, 73( 5): 2708–2728

[23] Smith J E, Winkler R L, (2006). The optimizer’s curse: skepticism and postdecision surprise in decision analysis. Management Science, 52( 3): 311–322

[24] Wang TChen NWang C (2021). Distributionally robust prescriptive analytics with Wasserstein distance. Preprint at arXiv: 2106.05724

[25] Wang Y, Zhang Y, Zhou M, Tang J, (2023). Feature-driven robust surgery scheduling. Production and Operations Management, 32( 6): 1921–1938

[26] . (in Chinese)

[27] Xie XLi J Y M (2025). Conditional risk minimization with side information: A tractable, universal optimal transport framework. Preprintat arXiv:2509.23128

[28] .

RIGHTS & PERMISSIONS

Higher Education Press