We organize a two-day meeting the 10th and 11th of April 2025 on following topics:
stochastic optimal control, reinforcement learning and model uncertainty
Marie-Amélie Morlais and Alexandre Popier
Thursday
14h — 14h45: Adrien Richou
14h50 — 15h35: Wissal Sabbagh
Coffee Break
16h00 — 16h45: Nicolas Baradel
16h50 — 17h35: William Hammersley
Friday
9h — 9h45: Idris Kharroubi
9h50 — 10h35: Guillaume Broux-Quemerais
Coffee Break
11h — 11h45: Jean-François Chassagneux
Laboratoire Manceau de Mathématiques - Le Mans Université
Title: Optimal control under unknown intensity with Bayesian learning
Title: Deep learning schemes for forward utilities using ergodic BSDEs and their extension to a regime-switching setting
Title: Computing the stationary measure of McKean-Vlasov SDEs
Abstract: Under some confluence assumption, it is known that the stationary distribution of a McKean-Vlasov SDE is the limit of the empirical measure of its associated self-interacting diffusion. Our numerical method consists in introducing the Euler scheme with decreasing step size of this self-interacting diffusion and seeing its empirical measure as the approximation of the stationary distribution of the original McKean-Vlasov SDEs. This simple approach is successful (under some raisonnable assumptions...) as we are able to prove convergence with a rate for the Wasserstein distance between the two measures both in the L2 and almost sure sense. In this talk, I will first explain the rationale behind this approach and then I will discuss the various convergence results we have obtained so far.
This is a joint work with G. Pagès (Sorbonne Université)
Title: Stochastic Impulse Control: Ergodic Formulation
Abstract: This talk presents a forthcoming study of the stochastic optimal switching problem faced by an agent having access to a finite number of operational modes yet must pay a cost to transition amongst them. This work combines several advances in the literature regarding ergodic backwards stochastic differential equations and provides technical groundwork to consider problems with unknown environments. Extensions allowing for unbounded driver and state-dependent switching costs are considered. Starting from a finite horizon discounted obliquely reflected system of backwards stochastic differential equations, the time horizon is sent to infinity to recover an infinite horizon system. These systems, parametrised by the discounting rate, possess uniformly Lipschitz continuous Markovian representations, permitting subsequential passage to zero of the discount parameter. One recovers in the limit the solution to an ergodic obliquely reflected BSDE system providing the optimal strategy for an appropriately defined ergodic control problem. Asymptotic relations of finite and ergodic switching problems are demonstrated.
Title: Optimal Stopping for Branching Diffusion Processes
Title: Numerical approximation of Ergodic BSDEs