EURO Online Seminar Series on Operational Research and Machine Learning

Large language models alternate multilayer perceptrons and self-attention to process token sequences. Gabriel Peyré compares the proof methods and approximation capabilities of these components. Whereas perceptron approximation is well understood, attention presents less explored mathematical questions. The talk connects their expressive power to approximation theory in infinite-dimensional spaces representing distributions of input tokens and identifies open problems at that interface.

Tito Homem-de-Mello presents decision-focused learning for two-stage stochastic optimization conditioned on contextual data. Recent theory shows that some two-stage stochastic linear programs can be solved using a single, initially unknown scenario. The talk establishes when learned scenario generators induce optimal policies and why one scenario component outside the observed support can suffice. A log-barrier smoothing operator makes that learning possible. The resulting method draws on interior-point optimization and is evaluated on standard contextual stochastic-programming benchmarks.

Shadi Sharif Azadeh examines how artificial intelligence is turning operations research into a learning-enabled approach to decisions in dynamic, uncertain and data-rich systems. The talk develops two directions: integrating prediction, optimization and learning sequentially, and embedding AI within optimization algorithms. Applications address demand and supply in multimodal mobility with uncertain resources, train scheduling and modular autonomous vehicle operations. Rather than replacing optimization, AI can predict changing states, learn from operational feedback, improve computational efficiency and support adaptation where static models are inadequate.

Three talks examine machine learning within optimization. J. Carlos Castro partitions distributed networks into connected regions sharing an interpretable predictor, contrasting selection of existing models with training on pooled data. A variable-neighbourhood search enforces connectivity; dynamic programming provides exact solutions for particular spatial configurations and a comparison for general networks. Ilaria Ciocci studies nonlinear support-vector machines with hard feature cardinality limits. An exact convex mixed-integer quadratic reformulation uses auxiliary variables for polynomial-kernel interactions, removes redundant terms through symmetry, and aggregates dual variables for compactness. It extends to arbitrary polynomial degree and obtains certified global solutions on benchmarks where the nonconvex formulation is intractable. Jiaxiao (Frances) Fang presents practical constraint learning with trained neural networks embedded in optimization models. Learned constraints or objective approximations can capture complex relationships, but their size and computational demands require careful design for efficient solution.