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Pré-Publication, Document De Travail Année : 2023

A Mirror Descent Approach for Mean Field Control applied to Demande-Side Management

Résumé

We consider a finite-horizon Mean Field Control problem for Markovian models. The objective function is composed of a sum of convex and Lipschitz functions taking their values on a space of state-action distributions. We introduce an iterative algorithm which we prove to be a Mirror Descent associated with a non-standard Bregman divergence, having a convergence rate of order 1/ √ K. It requires the solution of a simple dynamic programming problem at each iteration. We compare this algorithm with learning methods for Mean Field Games after providing a reformulation of our control problem as a game problem. These theoretical contributions are illustrated with numerical examples applied to a demand-side management problem for power systems aimed at controlling the average power consumption profile of a population of flexible devices contributing to the power system balance.
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Dates et versions

hal-03972660 , version 1 (15-02-2023)
hal-03972660 , version 2 (24-05-2023)

Identifiants

Citer

Bianca Marin Moreno, Margaux Brégère, Pierre Gaillard, Nadia Oudjane. A Mirror Descent Approach for Mean Field Control applied to Demande-Side Management. 2023. ⟨hal-03972660v1⟩
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