FRE Special Seminar: Robert Crowell and Qi Feng
This event is free, but registration is required.
4 PM
Robert Crowell
Title
McKean-Vlasov SDEs: New Results on Existence of Weak Solutions and on Propagation of Chaos
Abstract
We consider the existence of weak solutions of McKean-Vlasov SDEs with common noise and the propagation of chaos for the associated weakly interacting finite particle systems. Our strategy consists of two main components allowing us to analyze settings with general nonlinear but uniformly elliptic coefficients possessing only low regularity through a marriage of probabilistic and analytic techniques. First, we explore the emergence of regularity in limit points of McKean-Vlasov particle systems, leading to a priori regularity estimates for large-system limits of the empirical measure flows from finite particle systems. Second, we leverage this regularity to establish the existence of weak solutions for McKean-Vlasov SDEs and to identify more nuanced conditions under which chaos propagates, i.e. under which an asymptotic decoupling of the particles takes place and the dynamics in large systems become conditionally independent in law. Next to its applicability to low-regularity regimes, including the case of singular drifts that are discontinuous with respect to narrow convergence, the approach we take to obtain weak solutions and the propagation of chaos may also be useful for future applications to mean-field games and controlled problems.
Bio
Robert Crowell holds a doctoral degree in mathematics from ETH Zürich. He is now a postdoctoral researcher in the Finance and Risk Engineering Department (FRE), New York University Tandon School of Engineering. Robert's research focuses on stochastic calculus, control, and financial mathematics. He also takes an interest in interdisciplinary interactions between mathematics and economics, both theoretical and applied.
5 PM
Qi Feng
Title
Continuous Policy and Value Iteration for Stochastic Control Problems and Its Convergence
Abstract
We introduce a continuous policy-value iteration algorithm where the ap proximations of the value function of a stochastic control problem and the optimal control are simultaneously updated through Langevin-type dynamics. This framework applies to both the entropy-regularized relaxed control problems and the classical control problems, with infinite horizon. We establish policy improvement and demonstrate convergence to the optimal control un der the monotonicity condition of the Hamiltonian. By utilizing Langevin-type stochastic differential equations for continuous updates along the policy iteration direction, our approach enables the use of distribution sampling and non-convex learning techniques in machine learning to optimize the value function and identify the optimal control simultaneously. Numerical examples will be presented for both concave and non-concave examples. This talk is based on a joint work with Gu Wang from WPI.
Bio
Qi Feng is an Assistant Professor in the Department of Mathematics at Florida State University. His recent research focuses on machine learning theory and algorithm design, reinforcement learning in stochastic control, conditional McKean–Vlasov SDEs, data-driven modeling, and the signature method. He is also interested in stochastic analysis, rough path theory, and sub-Riemannian geometry.
Before joining Florida State University, Qi Feng was a Huntington Research Assistant Professor in the Department of Mathematics at the University of Michigan (2021–2023). From 2018 to 2021, he served as a RTPC Assistant Professor in the Department of Mathematics at the University of Southern California. He received his Ph.D. in Mathematics from the University of Connecticut in 2018 and an M.S. in Computational Finance from Purdue University in 2017.
