Description du cours de haut niveau

Theme of this year: Integrated learning and optimization for sustainable futures

 

Context. Many real-world decision-making problems are subject to uncertainty and are notoriously hard to solve. An important class of such decision-making problems is formulated as mathematical programs. While deterministic versions of such problems are routinely addressed in practice, incorporating uncertainty into their formulation remains challenging and is less commonly applied. However, neglecting uncertainty can result in solutions that perform poorly in practice. To address this issue, a growing body of literature focuses on integrating machine learning and operations research methodologies. These efforts can be broadly divided into two categories (i) accelerating solution algorithms by leveraging predictions from machine-learning algorithms within “traditional” operations research algorithms (surveys by Bengio et al., 2021, and Kotary et al., 2021) (ii) improving model quality by integrating machine learning models into mathematical programs and training machine learning algorithms against a task loss rather than conventional prediction loss (survey on decision-focused learning by Mandi et al., 2024, and a broader survey on contextual optimization by Sadana et al., 2025).

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Scope. The main focus of this course lies on methodologies for data-driven decision-making achieved by integrating machine learning and optimization and challenges that arise in this context. At a high level, the course covers a broad range of methods designed to address problems with single or two-stage formulations. (Note that the primary focus is not on multistage problems traditionally tackled using reinforcement learning or approximate dynamic programming). We cover applications rooted in sustainable development aligning with the 17 United Nations Sustainable Development Goals. These goals cover a wide spectrum of application domains, for example, humanitarian logistics, wildlife protection, agriculture, power systems, and transportation. The course examines the opportunities and challenges associated with solving decision-making problems aligned with these goals using integrated learning and optimization methods. We highlight gaps in the literature that are important to address such challenges.

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Language. English.

 

Format. The course mixes traditional lectures with interactive sessions and student presentations. While the primary focus is on methodologies in machine learning and operations research, their applications are examined through a holistic and interdisciplinary lens. To prepare for interactive lectures and group discussions, students will engage in activities such as information searches, reading academic papers, and viewing online seminars. This blend of approaches is designed to encourage active participation and critical thinking.

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Who is this course for? This course is designed for graduate students with a foundational understanding of operations research and machine learning who are eager to explore the potential of integrating these methodologies. It is hence necessary to have knowledge in both machine learning and operations research, for example, optimization methods for training machine learning models, consistency theory and generalization bounds, linear programming,

duality theory, integer and mixed-integer programming, and decomposition methods. Examples of graduate courses that cover related topics: IFT 6551 Integer Programming, IFT 6504  Mathematical Programming, IFT 6390 Fundamentals of Machine Learning, and IFT 6132 Advanced Structured Prediction and Optimization.

Students should be open to self-directed learning to address any gaps in foundational concepts as needed. If you enjoy engaging in discussions, collaborating with peers, and arriving well prepared for interactive lectures, this course will be a great fit for you.

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Learning objectives. By the end of this course, students should be able to:

• Describe a comprehensive taxonomy of methods integrating machine learning and optimization.

• Analyze real-world problems identifying the strengths and limitations of existing methods.

• Evaluate opportunities and potential challenges in applying machine learning and optimization to address decision-making problems aligned with sustainable development goals.

• Identify gaps in the literature and formulate meaningful research questions related to data-driven methodologies for addressing sustainability challenges.

• Implement selected existing methods to solve example problems illustrating understanding of methodologies of the class and practical application. (Python programming language and appropriate use of libraries/solvers as instructed.)

 

Evaluation. Assignments that are aligned with preparation work for interactive lectures (pass / fail) and a project (graded).

 

References (a selection serving as initial pointers to methodologies that will be covered)

 

Bengio Y., Lodi A. and Prouvost A. Machine learning for combinatorial optimization: A methodological tour d’horizon. European Journal of Operational Research 290(2):405-421, 2021.

DOI: 10.1016/j.ejor.2020.07.063

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Kotary J., Fioretto F., Van Hentenryck P., Wilder B. End-to-end constrained optimization learning: A survey. IJCAI 2021.

DOI: 10.48550/arXiv.2103.16378

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Mandi J., Kotary J., Berden S., Mulamba M., Bucarey V., Guns T., Fioretto F. Decision-focused learning: Foundations, state of the art, benchmark and future opportunities, Journal of Artificial Intelligence 81:1623-1701, 2024.

DOI: 10.48550/arXiv.2307.13565

 

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

DOI: ​10.1016/j.ejor.2024.03.020