688	RWTH Publication No: 1005610        2025
TITLE	Kinetic variable-sample methods for stochastic optimization problems
AUTHORS	Sabrina Bonandin, Michael Herty
ABSTRACT	We discuss variable-sample strategies and consensus- and kinetic-based particle optimization methods for problems where the cost function represents the expected value of a random mapping. Variable-sample strategies replace the expected value by an approximation at each iteration of the optimization algorithm. We introduce a novel variable-sample inspired time-discrete consensus-type algorithm and demonstrate its computational efficiency. Subsequently, we present an alternative time-continuous kinetic-based description of the algorithm, which allows us to exploit tools of kinetic theory to conduct a comprehensive theoretical analysis. Finally, we test the consistency of the proposed modelling approaches through several numerical experiments.
KEYWORDS	global optimization, stochastic optimization problems, particle-based methods, consensus-based optimization, Boltzmann equation, kinetic equations