Help
Cart
Skip main navigation

Deep Learning for Sequential Decision Making Under Uncertainty: Foundations, Frameworks, and Frontiers

Published Online:1 Nov 2026https://doi.org/10.1287/educ.2026.0307
Acknowledgments

The author thanks the four anonymous reviewers and the three INFORMS TutORials editors for thoughtful comments and constructive guidance that improved the clarity, scope, and exposition of this tutorial. The author also gratefully acknowledges doctoral students, collaborators, and the broader scholarly community whose work helped inform the examples and perspectives discussed in this tutorial.

References

  • [1] N. Absi and W. van den Heuvel. Worst-case analysis of relax and fix heuristics for lot-sizing problems. European Journal of Operational Research 279(2):449–458, 2019.Crossref, Google Scholar
  • [2] J. Achiam, D. Held, A. Tamar, and P. Abbeel. Constrained policy optimization. Proceedings of the 34th International Conference on Machine Learning, Proceedings of Machine Learning Research, vol. 70. PMLR, New York, 22–31, 2017.Google Scholar
  • [3] A. Agrawal, B. Amos, S. Barratt, S. Boyd, S. Diamond, and J. Z. Kolter. Differentiable convex optimization layers. H. Wallach, H. Larochelle, A. Beygelzimer, F. d’Alché-Buc, E. Fox, and R. Garnett, eds. Advances in Neural Information Processing Systems, vol. 32. Curran Associates, Red Hook, NY, 9558–9570, 2019.Google Scholar
  • [4] A. Ahmaditeshnizi, W. Gao, and M. Udell. OptiMUS: Scalable optimization modeling with (MI)LP solvers and large language models. Proceedings of the 41st International Conference on Machine Learning, Proceedings of Machine Learning Research, vol. 235. PMLR, New York, 577–596, 2024.Google Scholar
  • [5] B. Amos and J. Z. Kolter. OptNet: Differentiable optimization as a layer in neural networks. Proceedings of the 34th International Conference on Machine Learning, Proceedings of Machine Learning Research, vol. 70. PMLR, New York, 136–145, 2017.Google Scholar
  • [6] R. Anderson, J. Huchette, W. Ma, C. Tjandraatmadja, and J. P. Vielma. Strong mixed-integer programming formulations for trained neural networks. Mathematical Programming 183(1):3–39, 2020.Crossref, Google Scholar
  • [7] A. N. Angelopoulos and S. Bates. Conformal prediction: A gentle introduction. Foundations and Trends in Machine Learning 16(4):494–591, 2023.Crossref, Google Scholar
  • [8] R. Ao, D. Simchi-Levi, and X. Wang. OptiRepair: Closed-loop diagnosis and repair of supply chain optimization models with LLM agents. Preprint, submitted February 23, https://arxiv.org/abs/2602.19439, 2026.Google Scholar
  • [9] D. Bahdanau, K. Cho, and Y. Bengio. Neural machine translation by jointly learning to align and translate. Proceedings of the International Conference on Learning Representations, 2015.Google Scholar
  • [10] S. Bai, J. Z. Kolter, and V. Koltun. An empirical evaluation of generic convolutional and recurrent networks for sequence modeling. Preprint, submitted March 4, https://arxiv.org/abs/1803.01271, 2018.Google Scholar
  • [11] B. Basciftci, S. Ahmed, and N. Gebraeel. Adaptive two-stage stochastic programming with an analysis on capacity expansion planning problem. Manufacturing & Service Operations Management 26(6):2121–2141, 2024.Link, Google Scholar
  • [12] A. K. Baswapuram, C. Chen, W. Cai, and İ. E. Büyüktahtakın. An interpretable ensemble heuristic for principal-agent games with machine learning. Preprint, submitted April 12, https://optimization-online.org/?p=34384, 2026.Google Scholar
  • [13] R. Bellman. Dynamic Programming, Princeton University Press, Princeton, NJ, 1957.Google Scholar
  • [14] I. Bello, H. Pham, Q. V. Le, M. Norouzi, and S. Bengio. Neural combinatorial optimization with reinforcement learning. Proceedings of the International Conference on Learning Representations, 2017.Google Scholar
  • [15] A. Ben-Tal and A. Nemirovski. Robust convex optimization. Mathematics of Operations Research 23(4):769–805, 1998.Link, Google Scholar
  • [16] J. F. Benders. Partitioning procedures for solving mixed-variables programming problems. Numerische Mathematik 4(1):238–252, 1962.Crossref, Google Scholar
  • [17] Y. Bengio, A. Lodi, and A. Prouvost. Machine learning for combinatorial optimization: A methodological tour d’horizon. European Journal of Operational Research 290(2):405–421, 2021.Crossref, Google Scholar
  • [18] Y. Bengio, P. Simard, and P. Frasconi. Learning long-term dependencies with gradient descent is difficult. IEEE Transactions on Neural Networks 5(2):157–166, 1994.Crossref, Google Scholar
  • [19] D. P. Bertsekas. Dynamic Programming and Optimal Control, vol. 1. Athena Scientific, Belmont, MA, 1995.Google Scholar
  • [20] D. P. Bertsekas and J. N. Tsitsiklis. Neuro-Dynamic Programming. Athena Scientific, Belmont, MA, 1996.Google Scholar
  • [21] D. Bertsimas and R. Demir. An approximate dynamic programming approach to multidimensional knapsack problems. Management Science 48(4):550–565, 2002.Link, Google Scholar
  • [22] D. Bertsimas and N. Kallus. From predictive to prescriptive analytics. Management Science 66(3):1025–1044, 2020.Link, Google Scholar
  • [23] D. Bertsimas, V. Gupta, and N. Kallus. Data-driven robust optimization. Mathematical Programming 167(2):235–292, 2018.Crossref, Google Scholar
  • [24] J. R. Birge and F. Louveaux. Introduction to Stochastic Programming, 2nd edition. Springer, New York, 2011.Crossref, Google Scholar
  • [25] K. Blekos, D. Brand, A. Ceschini, C. H. Chou, R. H. Li, K. Pandya, and A. Summer. A review on quantum approximate optimization algorithm and its variants. Physics Reports 1068:1–66, 2024.Crossref, Google Scholar
  • [26] N. Boland, J. Christiansen, B. Dandurand, A. Eberhard, J. Linderoth, J. Luedtke, and F. Oliveira. Combining progressive hedging with a Frank-Wolfe method to compute Lagrangian dual bounds in stochastic mixed-integer programming. SIAM Journal on Optimization 28(2):1312–1336, 2018.Crossref, Google Scholar
  • [27] T. B. Brown, B. Mann, N. Ryder, M. Subbiah, J. D. Kaplan, P. Dhariwal, A. Neelakantan, et al. Language models are few-shot learners. H. Larochelle, M. Ranzato, R. Hadsell, M. F. Balcan, and H. Lin, eds. Advances in Neural Information Processing Systems, vol. 33. Curran Associates, Red Hook, NY, 1877–1901, 2020.Google Scholar
  • [28] N. Busch, T. Crönert, S. Minner, M. Rettinger, and B. Sel. Deep learning for commodity procurement: Nonlinear data-driven optimization of hedging decisions. INFORMS Journal on Optimization 5(3):273–294, 2023.Link, Google Scholar
  • [29] S. Bushaj and İ. E. Büyüktahtakın. A K-means supported reinforcement learning framework to multi-dimensional knapsack. Journal of Global Optimization 89(3):655–685, 2024.Crossref, Google Scholar
  • [30] S. Bushaj, X. Yin, A. Beqiri, D. Andrews, and İ. E. Büyüktahtakın. A simulation-deep reinforcement learning (SiRL) approach for epidemic control optimization. Annals of Operations Research 328(1):245–277, 2023.Crossref, Google Scholar
  • [31] İ. E. Büyüktahtakın. Stage-t scenario dominance for risk-averse multi-stage stochastic mixed-integer programs. Annals of Operations Research 309:1–35, 2022.Crossref, Google Scholar
  • [32] İ. E. Büyüktahtakın, E. Des Bordes, and E. Y. Kıbış. A new epidemics–logistics model: Insights into controlling the Ebola virus disease in West Africa. European Journal of Operational Research 265(3):1046–1063, 2018.Crossref, Google Scholar
  • [33] İ. E. Büyüktahtakın, Z. Feng, G. Frisvold, F. Szidarovszky, and A. Olsson. A dynamic model of controlling invasive species. Computers & Mathematics with Applications 62(9):3326–3333, 2011.Crossref, Google Scholar
  • [34] W. N. Caballero, P. R. Jenkins, D. Banks, and M. Robbins. Bayesian graph traversal. Decision Analysis 23(1):11–27, 2025.Link, Google Scholar
  • [35] İ. O. Çetinkaya, İ. E. Büyüktahtakın, P. Shojaee, and C. K. Reddy. Discovering heuristics with large language models (LLMs) for mixed-integer programs: Single-machine scheduling. Computers & Operations Research 186:107325, 2026.Crossref, Google Scholar
  • [36] X. Chen, J. Liu, and W. Yin. Learning to optimize: A tutorial for continuous and mixed-integer optimization. Science China Mathematics 67(6):1191–1262, 2024.Crossref, Google Scholar
  • [37] L. Chen, K. Lu, A. Rajeswaran, K. Lee, A. Grover, M. Laskin, P. Abbeel, et al. Decision transformer: Reinforcement learning via sequence modeling. M. Ranzato, A. Beygelzimer, Y. Dauphin, P. S. Liang, and J. Wortman Vaughan, eds. Advances in Neural Information Processing Systems, vol. 34. Curran Associates, Red Hook, NY, 15084–15097, 2021.Google Scholar
  • [38] S. J. Choi, J. Cooper, and İ. E. Büyüktahtakın. A temporal convolutional neural network (TCNN) approach to predicting capacitated lot-sizing solutions. Proceedings of the 2024 IISE Annual Conference & Expo. Institute of Industrial and Systems Engineers, Norcross, GA, 1–6, 2024.Google Scholar
  • [39] S. J. Choi, K. Jozani, J. F. Cooper, and İ. E. Büyüktahtakın. Learning to optimize at scale: A benders decomposition-transfORmers framework for stochastic combinatorial optimization. Proceedings of the NeurIPS 2025 Workshop MLxOR: Mathematical Foundations and Operational Integration of Machine Learning for Uncertainty-Aware Decision-Making, 2025.Google Scholar
  • [40] S. J. Choi, E. Cibaku, A. Svirsko, D. Skipper, and İ. E. Büyüktahtakın. Safety-constrained reinforcement learning for naval warfare searching with an intelligent target. Refereed Proceedings of the 2026 INFORMS Optimization Society Conference, 2026.Google Scholar
  • [41] E. Cibaku and İ. E. Büyüktahtakın. An adaptive K-means and reinforcement learning (RL) algorithm to effective vaccine distribution. Computers & Operations Research 185:107275, 2026.Crossref, Google Scholar
  • [42] J. F. Cooper, S. J. Choi, and İ. E. Büyüktahtakın. Toward transfORmers: Revolutionizing the solution of mixed integer programs with transformers. Proceedings of the 2024 Industrial and Systems Engineering Research Conference. Institute of Industrial and Systems Engineers, Norcross, GA, 1178–1183, 2024.Google Scholar
  • [43] Ö. Coşgun and İ. E. Büyüktahtakın. Stochastic dynamic resource allocation for HIV prevention and treatment: An approximate dynamic programming approach. Computers & Industrial Engineering 118:423–439, 2018.Crossref, Google Scholar
  • [44] J. G. Dai and M. Gluzman. Queueing network controls via deep reinforcement learning. Stochastic Systems 12(1):30–67, 2022.Link, Google Scholar
  • [45] M. Daryalal, M. Bodur, and J. R. Luedtke. Lagrangian dual decision rules for multistage stochastic mixed-integer programming. Operations Research 72(2):717–737, 2024.Link, Google Scholar
  • [46] E. Delage and Y. Ye. Distributionally robust optimization under moment uncertainty with application to data-driven problems. Operations Research 58(3):595–612, 2010.Link, Google Scholar
  • [47] D. Dentcheva and A. Ruszczyński. Risk-Averse Optimization and Control: Theory and Methods. Springer, Cham, Switzerland, 2024.Crossref, Google Scholar
  • [48] L. Ding, S. Ahmed, and A. Shapiro. A Python package for multi-stage stochastic programming. Preprint, submitted May, https://optimization-online.org/2019/05/7199/, 2019.Google Scholar
  • [49] P. L. Donti, B. Amos, and J. Z. Kolter. Task-based end-to-end model learning in stochastic optimization. I. Guyon, U. von Luxburg, S. Bengio, H. Wallach, R. Fergus, S. V. N. Vishwanathan, and R. Garnett, eds. Advances in Neural Information Processing Systems, vol. 30. Curran Associates, Red Hook, NY, 5484–5494, 2017.Google Scholar
  • [50] J. C. Duchi and H. Namkoong. Learning models with uniform performance via distributionally robust optimization. The Annals of Statistics 49(3):1378–1406, 2021.Crossref, Google Scholar
  • [51] J. Duchi, T. Hashimoto, and H. Namkoong. Distributionally robust losses for latent covariate mixtures. Operations Research 71(2):649–664, 2023.Link, Google Scholar
  • [52] J. Dumouchelle, R. Patel, E. B. Khalil, and M. Bodur. Neur2SP: Neural two-stage stochastic programming. S. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, and A. Oh, eds. Advances in Neural Information Processing Systems, vol. 35. Curran Associates, Red Hook, NY, 23992–24005, 2022.Google Scholar
  • [53] O. El Balghiti, A. N. Elmachtoub, P. Grigas, and A. Tewari. Generalization bounds in the predict-then-optimize framework. Mathematics of Operations Research 48(4):2043–2065, 2023.Link, Google Scholar
  • [54] A. N. Elmachtoub and P. Grigas. Smart “predict, then optimize”. Management Science 68(1):9–26, 2022.Link, Google Scholar
  • [55] J. L. Elman. Finding structure in time. Cognitive Science 14(2):179–211, 1990.Crossref, Google Scholar
  • [56] M. Fan, Y. Wu, T. Liao, Z. Cao, H. Guo, G. Sartoretti, and G. Wu. Deep reinforcement learning for UAV routing in the presence of multiple charging stations. IEEE Transactions on Vehicular Technology 72(5):5732–5746, 2023.Crossref, Google Scholar
  • [57] F. Fioretto, T. W. K. Mak, and P. Van Hentenryck. Predicting AC optimal power flows: Combining deep learning and Lagrangian dual methods. Proceedings of the AAAI Conference on Artificial Intelligence, vol. 34(1). AAAI Press, Palo Alto, CA, 630–637, 2020.Google Scholar
  • [58] M. Fischetti and J. Jo. Deep neural networks and mixed integer linear optimization. Constraints 23(3):296–309, 2018.Crossref, Google Scholar
  • [59] P. I. Frazier. Bayesian optimization. Recent Advances in Optimization and Modeling of Contemporary Problems, INFORMS TutORials in Operations Research. INFORMS, Catonsville, MD, 255–278, 2018.Google Scholar
  • [60] Y. Gal and Z. Ghahramani. Dropout as a Bayesian approximation: Representing model uncertainty in deep learning. Proceedings of the 33rd International Conference on Machine Learning, Proceedings of Machine Learning Research, vol. 48. PMLR, New York, 1050–1059, 2016.Google Scholar
  • [61] N. Galande, K. M. Jozani, and İ. E. Büyüktahtakın. Artificial intelligence in supply chain optimization: A systematic review of machine learning models, methods, and applications. Preprint, submitted December 8, https://optimization-online.org/?p=32864, 2025.Google Scholar
  • [62] J. García and F. Fernández. A comprehensive survey on safe reinforcement learning. Journal of Machine Learning Research 16(1):1437–1480, 2015.Google Scholar
  • [63] M. Gasse, D. Chételat, N. Ferroni, L. Charlin, and A. Lodi. Exact combinatorial optimization with graph convolutional neural networks. H. Wallach, H. Larochelle, A. Beygelzimer, F. d’Alché-Buc, E. Fox, and R. Garnett, eds. Advances in Neural Information Processing Systems, vol. 32. Curran Associates, Red Hook, NY, 15554–15566, 2019.Google Scholar
  • [64] R. Gautron, O. A. Maillard, P. Preux, M. Corbeels, and R. Sabbadin. Reinforcement learning for crop management support: Review, prospects and challenges. Computers and Electronics in Agriculture 200:107182, 2022.Crossref, Google Scholar
  • [65] F. A. Gers, J. Schmidhuber, and F. Cummins. Learning to forget: Continual prediction with LSTM. Neural Computation 12(10):2451–2471, 2000.Crossref, Google Scholar
  • [66] J. Gijsbrechts, R. N. Boute, J. A. Van Mieghem, and D. J. Zhang. Can deep reinforcement learning improve inventory management? Performance on lost sales, dual-sourcing, and multi-echelon problems. Manufacturing & Service Operations Management 24(3):1349–1368, 2022.Link, Google Scholar
  • [67] I. Goodfellow, Y. Bengio, and A. Courville. Deep Learning. MIT Press, Cambridge, MA, 2016.Google Scholar
  • [68] W. L. Hamilton, R. Ying, and J. Leskovec. Inductive representation learning on large graphs. Advances in Neural Information Processing Systems, vol. 30. Curran Associates, Red Hook, NY, 1024–1034, 2017.Google Scholar
  • [69] P. Harsha, A. Jagmohan, J. Kalagnanam, B. Quanz, and D. Singhvi. Deep policy iteration with integer programming for inventory management. Manufacturing & Service Operations Management 27(2):369–388, 2025.Link, Google Scholar
  • [70] M. Hausknecht and P. Stone. Deep recurrent q-learning for partially observable MDPs. Proceedings of the AAAI Fall Symposium on Sequential Decision Making for Intelligent Agents. AAAI Press, Palo Alto, CA, 2015.Google Scholar
  • [71] A. Hijazi, O. Y. Özaltın, and R. Uzsoy. An improving column is all you need: Enhancing column generation for parallel machine scheduling via transformers. INFORMS Journal on Computing, ePub ahead of print June 30, https://doi.org/10.1287/ijoc.2024.1005, 2026.Crossref, Google Scholar
  • [72] S. Hochreiter and J. Schmidhuber. Long short-term memory. Neural Computation 9(8):1735–1780, 1997.Crossref, Google Scholar
  • [73] T. Homem-de-Mello and G. Bayraksan. Monte carlo sampling-based methods for stochastic optimization. Surveys in Operations Research and Management Science 19(1):56–85, 2014.Crossref, Google Scholar
  • [74] K. Hornik, M. Stinchcombe, and H. White. Multilayer feedforward networks are universal approximators. Neural Networks 2(5):359–366, 1989.Crossref, Google Scholar
  • [75] D. Ivanov. Intelligent digital twin (iDT) for supply chain stress-testing, resilience, and viability. International Journal of Production Economics 263:108938, 2023.Crossref, Google Scholar
  • [76] D. Ivanov and A. Dolgui. Viability of intertwined supply networks: Extending the supply chain resilience angles towards survivability. A position paper motivated by COVID-19 outbreak. International Journal of Production Research 58(10):2904–2915, 2020.Crossref, Google Scholar
  • [77] R. Jiang and S. Küçükyavuz. Chance-constrained optimization under limited distributional information: A review of reformulations based on sampling and distributional robustness. EURO Journal on Computational Optimization 10:100030, 2022.Crossref, Google Scholar
  • [78] D. R. Jones, M. Schonlau, and W. J. Welch. Efficient global optimization of expensive black-box functions. Journal of Global Optimization 13(4):455–492, 1998.Crossref, Google Scholar
  • [79] K. Jozani, S. Tunc, H. Eldardiry, N. A. Sageer, and İ. E. Büyüktahtakın. Adaptive multi-echelon epidemic – Supply chain optimization at national scale. IISE Transactions 1–37, 2026.Crossref, Google Scholar
  • [80] L. P. Kaelbling, M. L. Littman, and A. R. Cassandra. Planning and acting in partially observable stochastic domains. Artificial Intelligence 101(1–2):99–134, 1998.Crossref, Google Scholar
  • [81] N. Kallus and X. Mao. Stochastic optimization forests. Management Science 69(4):1975–1994, 2023.Link, Google Scholar
  • [82] A. Kendall and Y. Gal. What uncertainties do we need in Bayesian deep learning for computer vision? Advances in Neural Information Processing Systems, vol. 30. Curran Associates, Red Hook, NY, 5574–5584, 2017.Google Scholar
  • [83] C. C. Kerr, R. M. Stuart, D. Mistry, R. G. Abeysuriya, K. Rosenfeld, G. R. Hart, R. C. Nuñez, et al. Covasim: An agent-based model of COVID-19 dynamics and interventions. PLoS Computational Biology 17(7):e1009149, 2021.Crossref, Google Scholar
  • [84] E. B. Khalil, C. Morris, and A. Lodi. MIP-GNN: A data-driven framework for guiding combinatorial solvers. Proceedings of the AAAI Conference on Artificial Intelligence, vol. 36(1). AAAI Press, Palo Alto, CA,10219–10227, 2022.Google Scholar
  • [85] E. B. Khalil, H. Dai, Y. Zhang, B. Dilkina, and L. Song. Learning combinatorial optimization algorithms over graphs. Advances in Neural Information Processing Systems, vol. 30. Curran Associates, Red Hook, NY, 6348–6358, 2017.Google Scholar
  • [86] E. B. Khalil, P. Le Bodic, L. Song, G. Nemhauser, and B. Dilkina. Learning to branch in mixed integer programming. Proceedings of the AAAI Conference on Artificial Intelligence, vol. 30(1). AAAI Press, Palo Alto, CA, 724–731, 2016.Google Scholar
  • [87] E. Y. Kıbış and İ. E. Büyüktahtakın. Optimizing multi-modal cancer treatment under 3D spatio-temporal tumor growth. Mathematical Biosciences 307:53–69, 2019.Crossref, Google Scholar
  • [88] E. Y. Kıbış, İ. E. Büyüktahtakın, R. G. Haight, N. Akhundov, K. Knight, and C. E. Flower. A multistage stochastic programming approach to the optimal surveillance and control of the emerald ash borer in cities. INFORMS Journal on Computing 33(2):808–834, 2021.Abstract, Google Scholar
  • [89] T. N. Kipf and M. Welling. Semi-supervised classification with graph convolutional networks. International Conference on Learning Representations, 2017.Google Scholar
  • [90] M. Komorowski, L. A. Celi, O. Badawi, A. C. Gordon, and A. A. Faisal. The artificial intelligence clinician learns optimal treatment strategies for sepsis in intensive care. Nature Medicine 24(11):1716–1720, 2018.Crossref, Google Scholar
  • [91] V. R. Konda and J. N. Tsitsiklis. Actor-critic algorithms. S. A. Solla, T. K. Leen, and K. Müller, eds. Advances in Neural Information Processing Systems, vol. 12. MIT Press, Cambridge, MA, 1008–1014, 2000.Google Scholar
  • [92] W. Kool, H. van Hoof, and M. Welling. Attention, learn to solve routing problems! International Conference on Learning Representations, 2019.Google Scholar
  • [93] J. Kotary, F. Fioretto, P. Van Hentenryck, and B. Wilder. End-to-end constrained optimization learning: A survey. Z.-H. Zhou, ed. Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence. International Joint Conferences on Artificial Intelligence Organization, 4475–4482, 2021.Google Scholar
  • [94] B. Lakshminarayanan, A. Pritzel, and C. Blundell. Simple and scalable predictive uncertainty estimation using deep ensembles. Advances in Neural Information Processing Systems, vol. 30. Curran Associates, Red Hook, NY, 6402–6413, 2017.Google Scholar
  • [95] M. Lanctot, V. Zambaldi, A. Gruslys, A. Lazaridou, K. Tuyls, J. Perolat, D. Silver, et al. A unified game-theoretic approach to multiagent reinforcement learning. Guyon I, von Luxburg U, Bengio S, Wallach H, Fergus R, Vishwanathan SVN, Garnett R, editors, Advances in Neural Information Processing Systems, vol. 30. Curran Associates, Red Hook, NY, 4190–4203, 2017.Google Scholar
  • [96] Y. LeCun, Y. Bengio, and G. Hinton. Deep learning. Nature 521(7553):436–444, 2015.Crossref, Google Scholar
  • [97] M. Lee and İ. E. Büyüktahtakın. Mathematical formulation of transformer architecture. Proceedings of the 20th INFORMS Data Mining and Decision Analytics (DMDA) Workshop, 2025.Google Scholar
  • [98] S. Levine, A. Kumar, G. Tucker, and J. Fu. Offline reinforcement learning: Tutorial, review, and perspectives on open problems. Preprint, submitted May 4, https://arxiv.org/abs/2005.01643, 2020.Google Scholar
  • [99] C. Li, Y. Wang, F. Liu, Q. Liu, and M. Buss. Model-free incremental adaptive dynamic programming based approximate robust optimal regulation. International Journal of Robust and Nonlinear Control 32(5):2662–2682, 2022.Google Scholar
  • [100] P. Libin, A. Moonens, T. Verstraeten, F. R. Perez-Sanjines, N. Hens, P. Lemey, and A. Nowe. Deep reinforcement learning for large-scale epidemic control. Y. Dong, G. Ifrim, D. Mladenić, C. Saunders, S. Van Hoecke, eds. Machine Learning and Knowledge Discovery in Databases. Applied Data Science and Demo Track, Lecture Notes in Computer Science, vol. 12461. Springer, Cham, Switzerland, 155–170, 2021.Crossref, Google Scholar
  • [101] Z. Liu, A. Khojandi, X. Li, A. Mohammed, R. L. Davis, and R. Kamaleswaran. A machine learning–enabled partially observable Markov decision process framework for early sepsis prediction. INFORMS Journal on Computing 34(4):2039–2057, 2022.Link, Google Scholar
  • [102] A. Lodi and G. Zarpellon. On learning and branching: A survey. TOP 25(2):207–236, 2017.Crossref, Google Scholar
  • [103] G. Lulli and S. Sen. A branch-and-price algorithm for multistage stochastic integer programming with application to stochastic batch-sizing problems. Management Science 50(6):786–796, 2004.Link, Google Scholar
  • [104] S. M. Lundberg and S. I. Lee. A unified approach to interpreting model predictions. Advances in Neural Information Processing Systems, vol. 30. Curran Associates, Red Hook, NY, 4765–4774, 2017.Google Scholar
  • [105] M. T. Luong, H. Pham, and C. D. Manning. Effective approaches to attention-based neural machine translation. L. Màrquez, C. Callison-Burch, and J. Su, eds. Proceedings of the 2015 Conference on Empirical Methods in Natural Language Processing. Association for Computational Linguistics, Stroudsburg, PA, 1412–1421, 2015.Google Scholar
  • [106] J. Mandi, J. Kotary, S. Berden, M. Mulamba, V. Bucarey, T. Guns, and F. Fioretto. Decision-focused learning: Foundations, state of the art, benchmark and future opportunities. Journal of Artificial Intelligence Research 80:1623–1701, 2024.Crossref, Google Scholar
  • [107] C. Mandl and S. Minner. Data-driven optimization for commodity procurement under price uncertainty. Manufacturing & Service Operations Management 25(2):371–390, 2023.Link, Google Scholar
  • [108] N. Mazyavkina, S. Sviridov, S. Ivanov, and E. Burnaev. Reinforcement learning for combinatorial optimization: A survey. Computers & Operations Research 134:105400, 2021.Crossref, Google Scholar
  • [109] V. V. Mišić. Optimization of tree ensembles. Operations Research 68(5):1605–1624, 2020.Link, Google Scholar
  • [110] V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, et al. Human-level control through deep reinforcement learning. Nature 518(7540):529–533, 2015.Crossref, Google Scholar
  • [111] T. M. Moerland, J. Broekens, A. Plaat, and C. M. Jonker. Model-based reinforcement learning: A survey. Foundations and Trends in Machine Learning 16(1):1–118, 2023.Crossref, Google Scholar
  • [112] P. Mohajerin Esfahani and D. Kuhn. Data-driven distributionally robust optimization using the Wasserstein metric: Performance guarantees and tractable reformulations. Mathematical Programming 171(1–2):115–166, 2018.Crossref, Google Scholar
  • [113] D. P. Morton, O. Dowson, and B. K. Pagnoncelli. MDP modeling for multi-stage stochastic programs. Mathematical Programming 1–36, 2026.Google Scholar
  • [114] T. A. Nakabi and P. Toivanen. Deep reinforcement learning for energy management in a microgrid with flexible demand. Sustainable Energy, Grids and Networks 25:100413, 2021.Crossref, Google Scholar
  • [115] M. Nazari, A. Oroojlooy, L. V. Snyder, and M. Takáč. Reinforcement learning for solving the vehicle routing problem. S. Bengio, H. Wallach, H. Larochelle, K. Grauman, N. Cesa-Bianchi, and R. Garnett, eds. Advances in Neural Information Processing Systems, vol. 31. Curran Associates, Red Hook, NY, 9861–9871, 2018.Google Scholar
  • [116] L. Ntaimo, J. A. Gallego-Arrubla, J. Gan, C. Stripling, J. Young, and T. Spencer. A simulation and stochastic integer programming approach to wildfire initial attack planning. Forest Science 59(1):105–117, 2013.Crossref, Google Scholar
  • [117] A. Oroojlooyjadid, M. Nazari, L. V. Snyder, and M. Takáč. A deep Q-network for the beer game: Deep reinforcement learning for inventory optimization. Manufacturing & Service Operations Management 24(1):285–304, 2022.Link, Google Scholar
  • [118] X. Pan, T. Zhao, M. Chen, and S. Zhang. DeepOPF: A deep neural network approach for security-constrained DC optimal power flow. IEEE Transactions on Power Systems 36(3):1725–1735, 2021.Crossref, Google Scholar
  • [119] W. B. Powell. Approximate Dynamic Programming: Solving the Curses of Dimensionality, 2nd edition. John Wiley & Sons, Hoboken, NJ, 2011.Crossref, Google Scholar
  • [120] W. B. Powell. A unified framework for stochastic optimization. European Journal of Operational Research 275(3):795–821, 2019.Crossref, Google Scholar
  • [121] W. B. Powell. Reinforcement Learning and Stochastic Optimization: A Unified Framework for Sequential Decisions. Wiley, Hoboken, NJ, 2022.Crossref, Google Scholar
  • [122] M. L. Puterman. Markov Decision Processes: Discrete Stochastic Dynamic Programming. John Wiley & Sons, New York, 1994.Crossref, Google Scholar
  • [123] M. T. Ribeiro, S. Singh, and C. Guestrin. “Why should I trust you?”: Explaining the predictions of any classifier. Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. ACM, New York, 1135–1144, 2016.Google Scholar
  • [124] R. T. Rockafellar and S. Uryasev. Optimization of conditional value-at-risk. Journal of Risk 2(3):21–41, 2000.Crossref, Google Scholar
  • [125] R. T. Rockafellar and R. J. B. Wets. Variational Analysis. Springer, Berlin, 1998.Crossref, Google Scholar
  • [126] B. Romera-Paredes, M. Barekatain, A. Novikov, M. Balog, M. P. Kumar, E. Dupont, F. J. R. Ruiz, et al. Mathematical discoveries from program search with large language models. Nature 625(7995):468–475, 2024.Crossref, Google Scholar
  • [127] D. E. Rumelhart, G. E. Hinton, and R. J. Williams. Learning representations by back-propagating errors. Nature 323(6088):533–536, 1986.Crossref, Google Scholar
  • [128] U. Sadana, A. Chenreddy, E. Delage, A. Forel, E. Frejinger, and T. Vidal. A survey of contextual optimization methods for decision-making under uncertainty. European Journal of Operational Research 320(2):271–289, 2025.Crossref, Google Scholar
  • [129] S. Sagawa, P. W. Koh, T. B. Hashimoto, and P. Liang. Distributionally robust neural networks for group shifts: On the importance of regularization for worst-case generalization. Proceedings of the International Conference on Learning Representations, 2020.Google Scholar
  • [130] S. Saghafian. Ambiguous dynamic treatment regimes: A reinforcement learning approach. Management Science 70(9):5667–5690, 2024.Abstract, Google Scholar
  • [131] F. Scarselli, M. Gori, A. C. Tsoi, M. Hagenbuchner, and G. Monfardini. The graph neural network model. IEEE Transactions on Neural Networks 20(1):61–80, 2009.Crossref, Google Scholar
  • [132] A. Shapiro, D. Dentcheva, and A. Ruszczyński. Lectures on Stochastic Programming: Modeling and Theory. Society for Industrial and Applied Mathematics and Mathematical Programming Society, Philadelphia, PA, 2009.Crossref, Google Scholar
  • [133] M. Siddig and Y. Song. Multistage stochastic programming with a random number of stages: Applications in hurricane disaster relief logistics planning. European Journal of Operational Research 321(3):925–941, 2025.Crossref, Google Scholar
  • [134] D. Simchi-Levi, K. Mellou, I. Menache, and J. Pathuri. Large language models for supply chain decisions. M. C. Cohen and T. Dai, eds. AI in Supply Chains: Perspectives from Global Thought Leaders, Springer Series in Supply Chain Management, vol. 27. Springer, Cham, Switzerland, 93–104, 2026.Google Scholar
  • [135] A. Sinha, H. Namkoong, and J. Duchi. Certifying some distributional robustness with principled adversarial training. Proceedings of the International Conference on Learning Representations, 2018.Google Scholar
  • [136] I. Sutskever, O. Vinyals, and Q. V. Le. Sequence to sequence learning with neural networks. Z. Ghahramani, M. Welling, C. Cortes, N. D. Lawrence, and K. Q. Weinberger, eds. Advances in Neural Information Processing Systems, vol. 27. Curran Associates, Red Hook, NY, 3104–3112, 2014.Google Scholar
  • [137] R. S. Sutton and A. G. Barto. Reinforcement Learning: An Introduction, 2nd edition. MIT Press, Cambridge, MA, 2018.Google Scholar
  • [138] J. Tong, J. Cai, and T. Serra. Optimization over trained neural networks: Taking a relaxing walk. B. Dilkina, ed. Integration of Constraint Programming, Artificial Intelligence, and Operations Research, Lecture Notes in Computer Science. Springer, Cham, Switzerland, 221–233, 2024.Google Scholar
  • [139] M. Vaccaro, A. Almaatouq, and T. Malone. When combinations of humans and AI are useful: A systematic review and meta-analysis. Nature Human Behaviour 8(12):2293–2303, 2024.Crossref, Google Scholar
  • [140] A. van den Oord, S. Dieleman, H. Zen, K. Simonyan, O. Vinyals, A. Graves, N. Kalchbrenner, et al. WaveNet: A generative model for raw audio. Preprint, submitted September 12, https://arxiv.org/abs/1609.03499, 2016.Google Scholar
  • [141] A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, Ł. Kaiser, et al. Attention is all you need. Advances in Neural Information Processing Systems, vol. 30. Curran Associates, Red Hook, NY, 5998–6008, 2017.Google Scholar
  • [142] S. Venkatachalam. Integrating large language models with network optimization for interactive and explainable supply chain planning: A real-world case study. Preprint, submitted August 29, https://arxiv.org/abs/2508.21622, 2025.Google Scholar
  • [143] O. Vinyals, M. Fortunato, and N. Jaitly. Pointer networks. C. Cortes, N. D. Lawrence, D. D. Lee, M. Sugiyama, and R. Garnett, eds. Advances in Neural Information Processing Systems, vol. 28. Curran Associates, Red Hook, NY, 2692–2700, 2015.Google Scholar
  • [144] C. J. C. H. Watkins. Learning from delayed rewards. PhD thesis, University of Cambridge, Cambridge, UK, 1989.Google Scholar
  • [145] C. J. C. H. Watkins and P. Dayan. Q-learning. Machine Learning 8(3–4):279–292, 1992.Crossref, Google Scholar
  • [146] J. P. Watson and D. L. Woodruff. Progressive hedging innovations for a class of stochastic mixed-integer resource allocation problems. Computational Management Science 8(4):355–370, 2011.Crossref, Google Scholar
  • [147] W. Wiesemann, D. Kuhn, and M. Sim. Distributionally robust convex optimization. Operations Research 62(6):1358–1376, 2014.Link, Google Scholar
  • [148] B. Wilder, B. Dilkina, and M. Tambe. Melding the data-decisions pipeline: Decision-focused learning for combinatorial optimization. Proceedings of the AAAI Conference on Artificial Intelligence, vol. 33(1). AAAI Press, Palo Alto, CA, 1658–1665, 2019.Google Scholar
  • [149] R. J. Williams. Simple statistical gradient-following algorithms for connectionist reinforcement learning. Machine Learning 8(3–4):229–256, 1992.Crossref, Google Scholar
  • [150] G. Wu, M. Fan, J. Shi, and Y. Feng. Reinforcement learning based truck-and-drone coordinated delivery. IEEE Transactions on Artificial Intelligence 4(4):754–763, 2023.Crossref, Google Scholar
  • [151] Z. Wu, S. Pan, F. Chen, G. Long, C. Zhang, and P. S. Yu. A comprehensive survey on graph neural networks. IEEE Transactions on Neural Networks and Learning Systems 32(1):4–24, 2021.Crossref, Google Scholar
  • [152] H. Xu and S. Mannor. Distributionally robust Markov decision processes. Mathematics of Operations Research 37(2):288–300, 2012.Link, Google Scholar
  • [153] C. L. Yang, K. Bauer, X. Li, and O. Hinz. My advisor, her AI, and me: Evidence from a field experiment on human–AI collaboration and investment decisions. Management Science 72(1):242–264, 2025.Link, Google Scholar
  • [154] D. Yilmaz and İ. E. Büyüktahtakın. Learning optimal solutions via an LSTM-optimization framework. Operations Research Forum 4(2):48, 2023.Crossref, Google Scholar
  • [155] D. Yilmaz and İ. E. Büyüktahtakın. A deep reinforcement learning framework for solving two-stage stochastic programs. Optimization Letters 18(9):1993–2020, 2024.Crossref, Google Scholar
  • [156] D. Yilmaz and İ. E. Büyüktahtakın. An expandable machine learning-optimization framework for sequential decision-making. European Journal of Operational Research 314(1):280–296, 2024.Crossref, Google Scholar
  • [157] D. Yilmaz and İ. E. Büyüktahtakın. A non-anticipative learning-optimization framework for solving multi-stage stochastic programs. Annals of Operations Research 355(3):2859–2899, 2025.Crossref, Google Scholar
  • [158] X. Yin and İ. E. Büyüktahtakın. A multi-stage stochastic programming approach to epidemic resource allocation with equity considerations. Health Care Management Science 24(3):597–622, 2021.Crossref, Google Scholar
  • [159] X. Yin, İ. E. Büyüktahtakın, and B. P. Patel. COVID-19: Data-driven optimal allocation of ventilator supply under uncertainty and risk. European Journal of Operational Research 304(1):255–275, 2023.Crossref, Google Scholar
  • [160] K. Zhang, Z. Yang, and T. Başar. Multi-agent reinforcement learning: A selective overview of theories and algorithms. K. G. Vamvoudakis, Y. Wan, F. L. Lewis, D. Cansever, eds. Handbook of Reinforcement Learning and Control, Studies in Systems, Decision and Control, vol. 325. Springer, Cham, Switzerland, 321–384, 2021.Crossref, Google Scholar
  • [161] J. Zou, S. Ahmed, and X. A. Sun. Stochastic dual dynamic integer programming. Mathematical Programming 175(1):461–502, 2019.Crossref, Google Scholar
Previous
Back to Top
Next
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.
Agree