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DTSTART:20070311T020000
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DTSTAMP:20260810T083123
DTSTART;TZID=America/Detroit:20261014T160000
DTEND;TZID=America/Detroit:20261014T170000
SUMMARY:Workshop / Seminar:Kullback–Leibler Mirror-Prox for Measure-Valued Variational Inequalities and Mean-Field Equilibria
DESCRIPTION:We study the computation of static mean-field equilibria on a compact state space by formu-\nlating the equilibrium condition as a variational inequality over probability measures. We propose\nan entropic variant of Korpelevich’s extragradient algorithm—the Kullback–Leibler Mirror-Prox\nmethod—in which Euclidean projections are replaced by relative-entropy proximal steps. Each\nhalf-step is therefore an explicit exponential reweighting of the current measure\, implemented on a\nfinite state-space discretization. Under Lasry–Lions monotonicity and continuity assumptions\, we\nprove convergence of mesh-refined ergodic averages and obtain finite-iteration Minty-residual and\napproximate-equilibrium bounds that jointly quantify iteration and discretization errors. Under\nstrong monotonicity\, we derive metric convergence rates for the last\, best\, and averaged iterates.\nWe also develop a KL-type Tikhonov regularization that selects the equilibrium minimizing relative\nentropy with respect to a reference measure. The framework applies to potential and nonpotential\ncost operators and does not require differentiability or convexity of the cost in the individual state.\n\nJoint work with Erhan Bayraktar\, Ibrahim Ekren and Lu Vy.
UID:150040-21907900@events.umich.edu
URL:https://events.umich.edu/event/150040
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 1360
CONTACT:
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