H.B. Keller Colloquium

Optimization methods based on stochastic particle systems have a long history and play a pivotal role today in many applications, ranging from machine learning to optimal control. Many of these methods rely on metaheuristic algorithms, which often lack a rigorous mathematical foundation. Recently, the use of tools inspired by statistical physics has allowed for the description of these gradient-free algorithms from the perspective of kinetic and mean-field PDEs, which enable convergence guarantees to the global minimum under mild assumptions on the objective function. In this talk, we will illustrate these ideas using some of the most popular algorithms, such as particle swarm optimization, simulated annealing, and genetic algorithms.