Multiagent allocation of Markov decision process tasks

Producing task assignments for multiagent teams often leads to an exponential growth in the decision space as the number of agents and objectives increases. One approach to finding a task assignment is to model the agents and the environment as a single Markov decision process, and solve the planning problem using standard MDP techniques. However, both exact and approximate MDP solvers in this environment struggle to produce assignments even for problems involving few agents and objectives. Conversely, problem formulations based upon mathematical programming typically scale well with the problem size at the expense of requiring comparatively simple agent and task models. This paper combines these two formulations by modeling task and agent dynamics using MDPs, and then using optimization techniques to solve the combinatorial problem of assigning tasks to agents. The computational complexity of the resulting algorithm is polynomial in the number of tasks and is constant in the number of agents. Simulation results are provided which highlight the performance of the algorithm in a grid world mobile target surveillance scenario, while demonstrating that these techniques can be extended to even larger tasking domains.