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. We propose to use Belief Propatation or Mean Field theory to approximate this infererence computation. We illustrate the result by simulations a system of N agents in two spatial dimensions, where each agent is modelled as a second order system. Their task is to coordinate their motions such as to each reach one of N target locations. Exact computation is limited to about N=10 and approximate inference is shown to be effective with polynomial complexity up to N=80.

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