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SUMMARY:Élise Devey - A Frank–Wolfe-Type Algorithm for High-Dimensional
  Stochastic Control Problems with Non-Exchangeable Agents
DTSTART:20261106T150000Z
DTEND:20261106T160000Z
DTSTAMP:20261030T044400Z
UID:indico-event-16986@indico.math.cnrs.fr
DESCRIPTION:Abstract : This paper presents a Frank--Wolfe type algorithm f
 or computing approximately optimal distributed stochastic controls in a la
 rge population of $N$ agents cooperating to minimize a convex cost functio
 nal. The cost includes a heterogeneous pairwise interaction term between t
 he agents' controls\, which rules out a direct treatment by the classical 
 Mean Field Control framework. Working directly at finite $N$ rather than t
 hrough a mean-field limit\, we prove that the distributed controls returne
 d by our algorithm are $N^{-1/2}$-optimal for the original problem\, with 
 an explicit rate in the number of iterations $K$ and in a measure of inter
 action heterogeneity\, $\\Delta_{\\mathrm{spread}}$\, that we introduce. T
 he algorithm avoids the curse of dimensionality: at each iteration\, the c
 oupled $N$-agent problem is linearized and decomposed into $N$ independent
 \, low-dimensional subproblems. We illustrate the approach on a linear-qua
 dratic benchmark\, for which we derive a closed-form Riccati-type characte
 rization of the optimal control\, and validate the predicted convergence r
 ate numerically. Interaction structures of this heterogeneous\, pairwise-p
 enalized type arise naturally in applications such as electricity grid fle
 xibility management\, where local storage units are coupled through shared
  transmission-line capacity constraints.\n\nhttps://indico.math.cnrs.fr/ev
 ent/16986/
LOCATION:Salle Maurice Fréchet  (IHP - Bâtiment Borel)
URL:https://indico.math.cnrs.fr/event/16986/
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