IX YOUNG Session: Optimization Approaches for Explainable Models in Distributed Settings; Hard Feature Selection in Nonlinear SVMs; Constraint Learning with Neural Networks

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.