7 papers
Long-time Stability and Convergence of Particle Swarm Optimization
Giacomo Borghi, Hui Huang, Dohyeon Kim
Particle Swarm Optimization (PSO) is a global optimization algorithm defined by an interacting set of particles evolving over the search space. Heuristically motivated, its theoret…
Variational inference via Gaussian interacting particles in the Bures-Wasserstein geometry
Giacomo Borghi, José A. Carrillo
Motivated by variational inference methods, we propose a zeroth-order algorithm for solving optimization problems in the space of Gaussian probability measures. The algorithm is ba…
Two-Time-Scale Learning Dynamics: A Population View of Neural Network Training
Giacomo Borghi, Hyesung Im, Lorenzo Pareschi
Population-based learning paradigms, including evolutionary strategies, Population-Based Training (PBT), and recent model-merging methods, combine fast within-model optimisation wi…
Chaos propagation in genetic algorithms: An optimal transport approach
Giacomo Borghi
Genetic algorithms are high-level heuristic optimization methods which enjoy great popularity thanks to their intuitive description, flexibility, and, of course, effectiveness. The…
Swarm-based optimization with jumps: a kinetic BGK framework and convergence analysis
Giacomo Borghi, Hyesung Im, Lorenzo Pareschi
Metaheuristic algorithms are powerful tools for global optimization, particularly for non-convex and non-differentiable problems where exact methods are often impractical. Particle…
Wasserstein convergence rates for stochastic particle approximation of Boltzmann models
Giacomo Borghi, Lorenzo Pareschi
We establish quantitative convergence rates for stochastic particle approximation based on Nanbu-type Monte Carlo schemes applied to a broad class of collisional kinetic models. Us…