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DTSTART:20070311T020000
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DTSTAMP:20260807T120756
DTSTART;TZID=America/Detroit:20270217T160000
DTEND;TZID=America/Detroit:20270217T170000
SUMMARY:Workshop / Seminar:The optimal rate of convergence in mean field control
DESCRIPTION:I will discuss the sharp rate of convergence of the value functions of N-particle stochastic control problems to their mean field limit\, for merely Lipschitz mean field costs. For d ≥ 2\, the optimal rate is that of the empirical measures of i.i.d. samples in the 1-Wasserstein distance\, as conjectured by Daudin\, Delarue\, and Jackson\, and it persists with additive common noise. In dimension one\, this benchmark can surprisingly be beaten: cooperating particles outperform independent samples\, and the optimal exponent is 4/7\, strictly between the accuracy of independent sampling (N^{-1/2}) and that of quantization (N^{-1}). The proofs rely on a new control-theoretic technique of recoupled shadow flows and\, in dimension one\, on a Gibbs law implementing the cooperation and a Schrödinger ground-state estimate.
UID:149994-21907791@events.umich.edu
URL:https://events.umich.edu/event/149994
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 1360
CONTACT:
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