Abstract

Particle methods provide a powerful paradigm for solving complex global optimization problems leading to highly parallelizable algorithms. Despite widespread and growing adoption, theory underpinning their behavior has been mainly based on meta-heuristics. In application settings involving black-box procedures, or where gradients are too costly to obtain, one relies on derivative-free approaches instead. This talk will focus on two recent techniques, consensus-based optimization and consensus-based sampling. We explain how these methods can be used for the following two goals: (i) generating approximate samples from a given target distribution, and (ii) optimizing a given objective function. They circumvent the need for gradients via Laplace’s principle. We investigate the properties of this family of methods in terms of various parameter choices and present an overview of recent advances in the field.