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, 13 - 16 July 2006, Cambridge, USA.

Abstract

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 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 single-agent single-target optimal controls weighted by a factor proportional to the end-costs of the different combinations. Thus, multi-agent 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.

EPrint Type:Conference or Workshop Item (Poster)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:2734
Deposited By:Bart Broek
Deposited On:22 November 2006