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arXiv · 2009.04766

Stochastic Programming with Primal-Dual Dynamics: A Mean-Field Game Approach

Casper T. Röling·Dario Bauso·Hamidou Tembine
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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.

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BibTeXRIS

Casper T. Röling, Dario Bauso, Hamidou Tembine. 2020-09-10. Stochastic Programming with Primal-Dual Dynamics: A Mean-Field Game Approach. https://arxiv.org/abs/2009.04766

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