PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Stochastic optimal control in continuous space-time multi-agent systems
Wim Wiegerinck, Bart Broek and Bert Kappen
In: UAI 2006, 22nd Conference on Uncertainty in Artificial Intelligence, 13-16 July 2006, Cambridge, MA, USA.


Recently, a theory for stochastic optimal control in non-linear dynamical systems in continuous space-time has been developed (Kappen, 2005). We apply this theory to collaborative multi-agent systems. The agents evolve according to a given non-linear dynamics with additive Wiener noise. Each agent can control its own dynamics. The goal is to minimize the accumulated joint cost, which consists of a state dependent term and a term that is quadratic in the control. We focus on systems of non-interacting agents that have to distribute themselves optimally over a number of targets, given a set of end-costs for the different possible agent-target combinations. We show that optimal control is the combinatorial sum of independent singleagent single-target optimal controls weighted by a factor proportional to the end-costs of the different combinations. Thus, multiagent control is related to a standard graphical model inference problem. The additional computational cost compared to single-agent control is exponential in the tree-width of the graph specifying the combinatorial sum times the number of targets. We illustrate the result by simulations of systems with up to 42 agents.

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EPrint Type:Conference or Workshop Item (Paper)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:2753
Deposited By:Wim Wiegerinck
Deposited On:22 November 2006