In this article we describe a set of scalable techniques for learning the behavior of a group of agents in a collaborative multiagent setting. As a basis we use the framework of coordination graphs of Guestrin, Koller, and Parr (2002a) which exploits the dependencies between agents to decompose the global payoff function into a sum of local terms. First, we deal with the single-state case and describe a payoff propagation algorithm that computes the individual actions that approximately maximize the global payoff function. The method can be viewed as the decision-making analogue of belief propagation in Bayesian networks. Second, we focus on learning the behavior of the agents in sequential decision-making tasks. We introduce different model-free reinforcement-learning techniques, unitedly called Sparse Cooperative Q-learning, which approximate the global action-value function based on the topology of a coordination graph, and perform updates using the contribution of the individual agents to the maximal global action value. The combined use of an edge-based decomposition of the action-value function and the payoff propagation algorithm for efficient action selection, result in an approach that scales only linearly in the problem size. We provide experimental evidence that our method outperforms related multiagent reinforcement-learning methods based on temporal differences.

Learning in multiagent systems suffers from the fact that both the state and the action space scale exponentially with the number of agents. In this paper we are interested in using Q-learning to learn the coordinated actions of a group of cooperative agents, using a sparse representation of the joint state-action space of the agents. We first examine a compact representation in which the agents need to explicitly coordinate their actions only in a predefined set of states. Next, we use a coordination-graph approach in which we represent the Q-values by value rules that specify the coordination dependencies of the agents at particular states. We show how Q-learning can be efficiently applied to learn a coordinated policy for the agents in the above framework. We demonstrate the proposed method on the predator-prey domain, and we compare it with other related multiagent Q-learning methods.