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SUMMARY:Mean-field Markov Decision process with common noise and randomize
 d controls: convergence rate and applications to targeted advertising - Hu
 yen Pham (Université de Paris)
DTSTART:20220420T080000Z
DTEND:20220420T090000Z
UID:TALK171440@talks.cam.ac.uk
DESCRIPTION: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 open-loop contro
 ls on infinite horizon.&nbsp\; We highlight the crucial role of relaxed co
 ntrols for this class of models\, called CMKV-MDP for conditional McKean-V
 lasov MDP\, with respect to classical MDP theory. We prove the corresponde
 nce between CMKV-MDP and a general lifted MDP on the space of probability 
 measures\, and establish the dynamic programming Bellman fixed point equat
 ion satisfied by the value function\, as well as the existence of &epsilon
 \;-optimal randomized feedback controls.&nbsp\; We obtain the propagation 
 of chaos of the optimal value functions of the N-agent MDP to the CMKVMDP 
 when N &rarr\; +&infin\;\, with some convergence rate\, denoted by O(MN&ga
 mma\; ).&nbsp\; We finally provide examples of application of the propagat
 ion of chaos result\, by approximately solving several toy models for N-ag
 ent targeted advertising problem with social influence via the resolution 
 of the associated CMKV-MDP.\nBased on joint work with M&eacute\;d&eacute\;
 ric Motte (LPSM).&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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