MAE Seminar: Consensus Based Optimization and Sampling

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. 

Bio: Franca Hoffmann is an assistant professor at Caltech and AIMS-Carnegie Research chair in data science at Quantum Leap Africa, AIMS Rwanda. She was previously a Bonn Junior Fellow at University of Bonn (Germany). After completing her Ph.D. at the Cambridge Centre for Analysis at University of Cambridge (UK) in 2017, she held the position of von Karman instructor at California Institute of Technology (US) from 2017 to 2020. Her research is focused on the applied mathematics/data analysis interface, driven by the need to provide rigorous mathematical foundations for modeling tools used in applications.