Stochastic Programming with Primal-Dual Dynamics: A Mean-Field Game Approach
Abstract
This study addresses primal-dual dynamics for a stochastic programming problem for capacity network design. It is proven that consensus can be achieved on the \textit{here and now} variables which represent the capacity of the network. The main contribution is a heuristic approach which involves the formulation of the problem as a mean-field game. Every agent in the mean-field game has control over its own primal-dual dynamics and seeks consensus with neighboring agents according to a communication topology. We obtain theoretical results concerning the existence of a mean-field equilibrium. Moreover, we prove that the consensus dynamics converge such that the agents agree on the capacity of their respective micro-networks. Lastly, we emphasize how penalties on control and state influence the dynamics of agents in the mean-field game.
Cite
@article{arxiv.2009.04766,
title = {Stochastic Programming with Primal-Dual Dynamics: A Mean-Field Game Approach},
author = {Casper T. Röling and Dario Bauso and Hamidou Tembine},
journal= {arXiv preprint arXiv:2009.04766},
year = {2020}
}