PhD in Computer Science

Optimization algorithms for AI and learning algorithms for optimization problems

Optimization algorithms for AI and learning algorithms for optimization problems

Academic year 2025/2026

Sommario del corso

• Course objectives
• Program
• Course delivery
• Learning assessment methods
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Course objectives

This course aims at elucidating the deep links between mathematical optimisation and machine learning. The students will be introduced to the following themes and abilities: understand the properties of different kinds of non-linear continuous optimisation algorithms to tune the (hyper-)parameters of machine learning models and how to apply them; understand how to model some advanced machine learning models as bi-level optimisation models; identify situations where machine learning and process mining can be used as a sub-module for combinatorial optimisation problems.

Program

Non-linear optimisation for the tuning of Machine Learning models (10h)

• Why do we need optimisation for Machine Learning (ML) models?
• First-order methods: principles of Gradient Descent and Stochastic Gradient Descent, convergence analysis.
• Second-order methods: Newton’s method, Hessian-free methods, Stochastic Quasi-Newton methods, Gauss-Newton ⇒ possible improvements and drawbacks of second-order algorithms for ML optimisation.
• Intermediate methods: Gradient methods with acceleration and momentum.
• Landscape analysis: avoiding bad local minima, geometry of the loss function for Deep Neural Networks.
• Bi-Level Optimisation (BLO): advanced ML models tuning as BLO problems (optimisation of hyper-parameters).

Machine Learning for combinatorial optimisation (10h)

This part will focus on several successful applications of Machine Learning (ML) methods in the context of classical Operations Research (OR) problems.

• Learning Combinatorial Optimization Algorithms over Graphs — A greedy procedure, guided by Reinforcement Learning, to solve various graph optimization problems.
• Learning when to use a decomposition — Comparison of binary classifiers employed to decide whether a model possesses a structure suited for the application of Dantzig-Wolfe decomposition.
• What makes a VRP solution good? The generation of problem-specific knowledge for heuristics — Application of binary classifiers to the Vehicle Routing Problem for the learning of instance and solution structure, in order to distinguish between optimal and non-optimal heuristic solutions.
• Machine learning meets mathematical optimization to predict the optimal production of offshore wind parks — Comparison of different Machine Learning approaches in the prediction of the optimal solution value for the offshore wind farm layout problem.
• A reinforcement learning iterated local search for makespan minimization in additive manufacturing machine scheduling problems — A meta-heuristic procedure, based upon Iterated Local Search guided by Reinforcement Learning, for the minimization of Makespan in the context of Additive Manufacturing problems.

A paper will be presented in each of the lessons, then a discussion upon obtained results and strengths/weaknesses of each paper will take place. Students are strongly encouraged to take part, actively, to these discussions.

Analytics in Healthcare delivery (4h)

• Introduction to Healthcare and the processes behind the delivery of healthcare services.
• Predictive and Prescriptive analytics in Healthcare: basics of process mining and online optimisation.
• The Emergency Care Pathway: analysis and solutions.

Course delivery

The lectures consist of 24 hours divided between the three themes previously described (respectively 10h/10h/4h) and will take place on Friday mornings between 8:30am and 12:30am on the following dates: 17/04/2026, 24/04/2026, 08/05/2026, 15/05/2026, 22/05/2026 and 29/05/2026 in streaming.

Learning assessment methods

The candidates can choose between different possible forms of exam for this course, to be agreed upon with the teachers.

• Explanation/discussion around a scientific paper of the literature pertinent to the themes of the lectures.
• Implementation and comparison of some of the methods presented during the lectures (e.g., first-order vs second-order method for training a neural network).
• Discussion on how the presented methods could be applied to the students’ research lines.
• Other proposal from the student, after agreement with the teachers

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