Optimal control in large stochastic multi-agent systems

Authors:
Bart Van Den Broek;Wim Wiegerinck;Bert Kappen
Affiliations:
SNN, Radboud University Nijmegen, Nijmegen, The Netherlands;SNN, Radboud University Nijmegen, Nijmegen, The Netherlands;SNN, Radboud University Nijmegen, Nijmegen, The Netherlands
Venue:
ALAMAS'05/ALAMAS'06/ALAMAS'07 Proceedings of the 5th , 6th and 7th European conference on Adaptive and learning agents and multi-agent systems: adaptation and multi-agent learning
Year:
2005

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Abstract

We study optimal control in large stochastic multi-agent systems in continuous space and time. We consider multi-agent systems where agents have independent dynamics with additive noise and control. The goal is to minimize the joint cost, which consists of a state dependent term and a term quadratic in the control. The system is described by a mathematical model, and an explicit solution is given. We focus on large systems where agents have to distribute themselves over a number of targets with minimal cost. In such a setting the optimal control problem is equivalent to a graphical model inference problem. Exact inference will be intractable, and we use the mean field approximation to compute accurate approximations of the optimal controls. We conclude that near to optimal control in large stochastic multi-agent systems is possible with this approach.