Date: Wednesday, April 13, 2022
Location: 1360 East Hall (4:00 PM to 5:00 PM)
Title: Second Van Eenam Lecture: MeanField Markov Decision Processes With Common Noise And OpenLoop Controls
Abstract: We develop an exhaustive study of Markov decision process (MDP) under mean field interaction both on states and actions in the presence of common noise, and when optimization is performed over openloop controls on infinite horizon. Such model, called CMKVMDP for conditional McKeanVlasov MDP, arises and is obtained here rigorously with a rate of convergence as the asymptotic problem of Ncooperative agents controlled by a social planner/influencer that observes the environment noises but not necessarily the individual states of the agents. We highlight the crucial role of relaxed controls and randomization hypothesis for this class of models with respect to classical MDP theory. We prove the correspondence between CMKVMDP and a general lifted MDP on the space of probability measures, and establish the dynamic programming Bellman fixed point equation satisfied by the value function, as well as the existence of epsilonoptimal randomized feedback controls. The arguments of proof involve an original measurable optimal coupling for the Wasserstein distance. This provides a procedure for learning strategies in a large population of interacting collaborative agents
Files: 7635_VanEenamLect2.pdf
Speaker: Huyen Pham
Institution: Universite de Paris
Event Organizer:
