Decision Making with Side Information: A Causal Transport Robust Approach
Published Online:29 Apr 2026https://doi.org/10.1287/opre.2024.0997
References
- (2019) Extended mean field control problems: Stochastic maximum principle and transport perspective. SIAM J. Control Optim. 57(6):3666–3693.Crossref, Google Scholar
- (2020) Causal optimal transport and its links to enlargement of filtrations and continuous-time stochastic optimization. Stochastic Processing Appl. 130(5):2918–2953.Crossref, Google Scholar
- (2014) On distributionally robust multiperiod stochastic optimization. Comput. Management Sci. 11(3):197–220.Crossref, Google Scholar
- (2017) Causal transport in discrete time and applications. SIAM J. Optim. 27(4):2528–2562.Crossref, Google Scholar
- (2019) The big data newsvendor: Practical insights from machine learning. Oper. Res. 67(1):90–108.Link, Google Scholar
- (2019) Dynamic procurement of new products with covariate information: The residual tree method. Manufacturing Service Oper. Management 21(4):798–815.Link, Google Scholar
- (2023) Sensitivity of multiperiod optimization problems with respect to the adapted Wasserstein distance. SIAM J. Financial Math. 14(2):704–720.Crossref, Google Scholar
- (2021) Distributionally robust facility location problem under decision-dependent stochastic demand. Eur. J. Oper. Res. 292(2):548–561.Crossref, Google Scholar
- (2015) Data-driven stochastic programming using phi-divergences. Aleman DM, Thiele AC, eds. The Operations Research Revolution: INFORMS TutORials in Operations Research (INFORMS, Catonsville, MD), 1–19.Link, Google Scholar
- (2020) Generalization bounds for regularized portfolio selection with market side information. INFOR: Inform. Systems Oper. Res. 58(2):374–401.Crossref, Google Scholar
- (2015) Design of near optimal decision rules in multistage adaptive mixed-integer optimization. Oper. Res. 63(3):610–627.Link, Google Scholar
- (2012) On the power and limitations of affine policies in two-stage adaptive optimization. Math. Programming 134(2):491–531.Crossref, Google Scholar
- (2020) From predictive to prescriptive analytics. Management Sci. 66(3):1025–1044.Link, Google Scholar
- (2022) Data-driven optimization: A reproducing kernel hilbert space approach. Oper. Res. 70(1):454–471.Link, Google Scholar
- (2019) From predictions to prescriptions in multistage optimization problems. Preprint, submitted April 26, https://arxiv.org/abs/1904.11637.Google Scholar
- (2022) Bootstrap robust prescriptive analytics. Math. Programming 195:39–78.Crossref, Google Scholar
- (2010) Optimality of affine policies in multistage robust optimization. Math. Oper. Res. 35(2):363–394.Link, Google Scholar
- (2011) A hierarchy of near-optimal policies for multistage adaptive optimization. IEEE Trans. Automated Control 56(12):2809–2824.Crossref, Google Scholar
- (2023) Dynamic optimization with side information. Eur. J. Oper. Res. 304(2):634–651.Crossref, Google Scholar
- (2019) Quantifying distributional model risk via optimal transport. Math. Oper. Res. 44(2):565–600.Link, Google Scholar
- (2019) Robust Wasserstein profile inference and applications to machine learning. J. Appl. Probability 56(3):830–857.Crossref, Google Scholar
- (2009) Parametric portfolio policies: Exploiting characteristics in the cross-section of equity returns. Rev. Financial Stud. 22(9):3411–3447.Crossref, Google Scholar
- (2021) Contextual decision-making under parametric uncertainty and data-driven optimistic optimization. Optimization Online (October 16), https://optimization-online.org/wp-content/uploads/2021/10/Contextual_optimization-1.pdf.Google Scholar
- (2010) Vector valued reproducing kernel Hilbert spaces and universality. Anal. Appl. (Singapore) 8(01):19–61.Crossref, Google Scholar
- (2008) A linear decision-based approximation approach to stochastic programming. Oper. Res. 56(2):344–357.Link, Google Scholar
- (2022) Data-driven conditional robust optimization. Adv. Neural Inform. Processing Systems 35:9525–9537.Google Scholar
- (2019) Generalization bounds in the predict-then-optimize framework. Adv. Neural Inform. Processing Systems 32:14412–14421.Google Scholar
- (2021) On the optimality of affine policies for budgeted uncertainty sets. Math. Oper. Res. 46(2):674–711.Link, Google Scholar
- (2022) Smart “predict, then optimize”. Management Sci. 68(1):9–26.Link, Google Scholar
- (2020) Decision trees for decision-making under the predict-then-optimize framework. Daumé H III, Singh A, eds. Proc. 37th Internat. Conf. Machine Learn., Proceedings of Machine Learning Research, vol. 119 (ML Research Press, Cambridge, MA), 2858–2867.Google Scholar
- (2018) Data-driven distributionally robust optimization using the Wasserstein metric: Performance guarantees and tractable reformulations. Math. Programming 171(1):115–166.Crossref, Google Scholar
- (2022) Distributionally robust stochastic programs with side information based on trimmings. Math. Programming 195(1–2):1069–1105.Crossref, Google Scholar
- (2021) Slow rates of convergence in optimization with side information. Preprint, submitted March 15, https://doi.org/10.2139/ssrn.3803427.Google Scholar
- (2024) Deep nonparametric quantile regression under covariate shift. J. Machine Learn. Res. 25(385):1–50.Google Scholar
- (2023) Finite-sample guarantees for Wasserstein distributionally robust optimization: Breaking the curse of dimensionality. Oper. Res. 71(6):2291–2306.Link, Google Scholar
- (2023) Distributionally robust stochastic optimization with Wasserstein distance. Math. Oper. Res. 48(2):603–655.Link, Google Scholar
- (2024a) Data-driven multistage distributionally robust linear optimization with nested distance. Preprint, submitted July 23, https://arxiv.org/abs/2407.16346.Google Scholar
- (2024b) Wasserstein distributionally robust optimization and variation regularization. Oper. Res. 72(3):1177–1191.Link, Google Scholar
- Genpact (2019) Food demand forecasting dataset. Kaggle, https://www.kaggle.com/datasets/kannanaikkal/food-demand-forecasting.Google Scholar
- (2025) On the optimality of affine decision rules in distributionally robust optimization. Management Sci. 72(2):1456–1471.Link, Google Scholar
- (2013) Robust data-driven dynamic programming. Adv. Neural Inform. Processing Systems 26.Google Scholar
- (2015) K-adaptability in two-stage robust binary programming. Oper. Res. 63(4):877–891.Link, Google Scholar
- (2016) K-adaptability in two-stage distributionally robust binary programming. Oper. Res. Lett. 44(1):6–11.Crossref, Google Scholar
- (2010) Nonparametric density estimation for stochastic optimization with an observable state variable. Adv. Neural Inform. Processing Systems 23:820–828.Google Scholar
- (2022) Risk guarantees for end-to-end prediction and optimization processes. Management Sci. 68(12):8680–8698.Link, Google Scholar
- (2022) Fast rates for contextual linear optimization. Management Sci. 68(6):4236–4245.Link, Google Scholar
- (2024) Contextual stochastic bilevel optimization. Adv. Neural Inform. Processing Systems 36.Google Scholar
- (2013) Supermodularity and affine policies in dynamic robust optimization. Oper. Res. 61(4):941–956.Link, Google Scholar
- (1980) Weak and strong solutions of stochastic differential equations. Stochastics 3(1–4):171–191.Crossref, Google Scholar
- (2024) Duality of causal distributionally robust optimization: The discrete-time case. Preprint, submitted January 29, https://arxiv.org/abs/2401.16556.Google Scholar
- (2023) Stochastic optimization forests. Management Sci. 69(4):1975–1994.Link, Google Scholar
- (2024) Residuals-based distributionally robust optimization with covariate information. Math. Programming 207:369–425.Crossref, Google Scholar
- (2025) Data-driven sample average approximation with covariate information. Oper. Res. 73(6):3245–3259.Link, Google Scholar
- (2019) Wasserstein distributionally robust optimization: Theory and applications in machine learning. Netessine S, ed. Operations Research & Management Science in the Age of Analytics. INFORMS TutORials in Operations Research (INFORMS, Catonsville, MD), 130–166.Google Scholar
- (2014) Weak and strong solutions of general stochastic models. Electronic Comm. Probability 19:1–16.Crossref, Google Scholar
- (2018) Causal transference plans and their Monge-Kantorovich problems. Stochastic Anal. Appl. 36(3):452–484.Google Scholar
- (2021) End-to-end deep learning for inventory management with fixed ordering cost and its theoretical analysis. Preprint, submitted July 19, https://doi.org/10.2139/ssrn.3888897.Google Scholar
- (2005) A practical inventory control policy using operational statistics. Oper. Res. Lett. 33(4):341–348.Crossref, Google Scholar
- (2020) Decision-driven regularization: A blended model for predict-then-optimize. Preprint, submitted June 17, https://doi.org/10.2139/ssrn.3623006.Google Scholar
- (2022) A bilevel framework for decision-making under uncertainty with contextual information. Omega (Westport) 108:102575.Crossref, Google Scholar
- (2025) Robustifying conditional portfolio decisions via optimal transport. Oper. Res. 73(5):2801–2829.Link, Google Scholar
- (2020) Applying deep learning to the newsvendor problem. IISE Trans. 52(4):444–463.Crossref, Google Scholar
- (2023) Robust pricing and production with information partitioning and adaptation. Management Sci. 69(3):1398–1419.Link, Google Scholar
- (2010) Version-independence and nested distributions in multistage stochastic optimization. SIAM J. Optim. 20(3):1406–1420.Crossref, Google Scholar
- (2012) A distance for multistage stochastic optimization models. SIAM J. Optim. 22(1):1–23.Crossref, Google Scholar
- (2014) Multistage Stochastic Optimization (Springer, Berlin).Crossref, Google Scholar
- (2015) Dynamic generation of scenario trees. Comput. Optim. Appl. 62(3):641–668.Crossref, Google Scholar
- (2016) From empirical observations to tree models for stochastic optimization: Convergence properties. SIAM J. Optim. 26(3):1715–1740.Crossref, Google Scholar
- (2007) Ambiguity in portfolio selection. Quant. Finance 7(4):435–442.Crossref, Google Scholar
- (2021) Mathematical foundations of distributionally robust multistage optimization. SIAM J. Optim. 31(4):3044–3067.Crossref, Google Scholar
- (2016) Multistage adjustable robust mixed-integer optimization via iterative splitting of the uncertainty set. INFORMS J. Comput. 28(3):553–574.Link, Google Scholar
- (2022) Integrating prediction/estimation and optimization with applications in operations management. Chou MC, Gibson H, Staats BR, eds. Tutorials in Operations Research: Emerging and Impactful Topics in Operations (INFORMS, Catonsville, MD), 36–58.Link, Google Scholar
- (2025) Integrated conditional estimation-optimization. Oper. Res., ePub ahead of print October 28, https://doi.org/10.1287/opre.2023.0427.Link, Google Scholar
- (2024) Learning newsvendor problems with intertemporal dependence and moderate non-stationarities. Production Oper. Management 33(5):1196–1213.Crossref, Google Scholar
- (2023) A practical end-to-end inventory management model with deep learning. Management Sci. 69(2):759–773.Link, Google Scholar
- (2019) Controlling risk and demand ambiguity in newsvendor models. Eur. J. Oper. Res. 279(3):854–868.Crossref, Google Scholar
- (1985) The Wasserstein distance and approximation theorems. Probability Theory Related Fields 70(1):117–129.Crossref, Google Scholar
- (2023) End-to-end learning for stochastic optimization: A bayesian perspective. Krause A, Brunskill E, Cho K, Engelhardt B, Sabato S, Scarlett J, eds. Proc. 40th Internat. Conf. Machine Learn., Proceedings of Machine Learning Research, vol. 202 (ML Research Press, Cambridge, MA), 29455–29472.Google Scholar
- (2025) A survey of contextual optimization methods for decision-making under uncertainty. Eur. J. Oper. Res. 320(2):271–289.Crossref, Google Scholar
- (2019) Regularization via mass transportation. J. Machine Learn. Res. 20(103):1–68.Google Scholar
- (2014) Lectures on Stochastic Programming: Modeling and Theory (SIAM, Philadelphia).Crossref, Google Scholar
- (2024) Wasserstein distributionally robust policy evaluation and learning for contextual bandits. Trans. Machine Learn. Res.Google Scholar
- (2023) A nonparametric algorithm for optimal stopping based on robust optimization. Oper. Res. 71(5):1530–1557.Link, Google Scholar
- (2019) K-adaptability in two-stage mixed-integer robust optimization. Math. Programming Comput. 1–32.Google Scholar
- (2001) Analysis of a forecasting-production-inventory system with stationary demand. Management Sci. 47(9):1268–1281.Link, Google Scholar
- (2013) Machine learning with operational costs. J. Machine Learn. Res. 14:1989–2028.Google Scholar
- (2022) Robust two-stage optimization with covariate data. Optimization Online (October 24), https://optimization-online.org/wp-content/uploads/2022/10/main-3.pdf.Google Scholar
- (2021) From data to decisions: Distributionally robust optimization is optimal. Management Sci. 67(6):3387–3402.Link, Google Scholar
- (2025) Robust optimization with decision-dependent information discovery. Management Sci. 72(2):1509–1528.Link, Google Scholar
- (2026) On data-driven prescriptive analytics with side information: A regularized Nadaraya–Watson approach. Manufacturing & Service Operations Management, ePub ahead of print January 5, https://doi.org/10.1287/msom.2024.0997.Link, Google Scholar
- (2012) A framework for optimization under ambiguity. Ann. Oper. Res. 193(1):21–47.Crossref, Google Scholar
- (2020) COT-GAN: Generating sequential data via causal optimal transport. Adv. Neural Inform. Processing Systems 33:8798–8809.Google Scholar
- (1971) On the uniqueness of solutions of stochastic differential equations. J. Math. Kyoto University 11(1):155–167.Crossref, Google Scholar
- (2022) Multistage distributionally robust mixed-integer programming with decision-dependent moment-based ambiguity sets. Math. Programming 196(1):1025–1064.Crossref, Google Scholar
- (2024) Optimal robust policy for feature-based newsvendor. Management Sci. 70(4):2315–2329.Link, Google Scholar
- (2025) A short and general duality proof for Wasserstein distributionally robust optimization. Oper. Res. 73(4):2146–2155.Link, Google Scholar
- (2004) An adaptive forecasting algorithm and inventory policy for products with short life cycles. Naval Res. Logist. 51(5):633–653.Crossref, Google Scholar
- (2022) Joint estimation and robustness optimization. Management Sci. 68(3):1659–1677.Link, Google Scholar

