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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Mean-field Markov Decision process with common noi
se and randomized controls: convergence rate and a
pplications to targeted advertising - Huyen Pham (
Université de Paris)
DTSTART;TZID=Europe/London:20220420T090000
DTEND;TZID=Europe/London:20220420T100000
UID:TALK171440AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/171440
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 nois
e\, and when optimization is performed over open-l
oop controls on infinite horizon. \; We highli
ght the crucial role of relaxed controls for this
class of models\, called CMKV-MDP for conditional
McKean-Vlasov MDP\, with respect to classical MDP
theory. We prove the correspondence between CMKV-M
DP and a general lifted MDP on the space of probab
ility measures\, and establish the dynamic program
ming Bellman fixed point equation satisfied by the
value function\, as well as the existence of &eps
ilon\;-optimal randomized feedback controls. \
; We obtain the propagation of chaos of the optima
l value functions of the N-agent MDP to the CMKVMD
P when N &rarr\; +&infin\;\, with some convergence
rate\, denoted by O(MN&gamma\; ). \; We final
ly provide examples of application of the propagat
ion of chaos result\, by approximately solving sev
eral toy models for N-agent targeted advertising p
roblem with social influence via the resolution of
the associated CMKV-MDP.\nBased on joint work wit
h Mé\;dé\;ric Motte (LPSM). \;
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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