No-regret learning and a mechanism for distributed multiagent planning

We develop a novel mechanism for coordinated, distributed multiagent planning. We consider problems stated as a collection of single-agent planning problems coupled by common soft constraints on resource consumption. (Resources may be real or fictitious, the latter introduced as a tool for factoring the problem). A key idea is to recast the distributed planning problem as learning in a repeated game between the original agents and a newly introduced group of adversarial agents who influence prices for the resources. The adversarial agents benefit from arbitrage: that is, their incentive is to uncover violations of the resource usage constraints and, by selfishly adjusting prices, encourage the original agents to avoid plans that cause such violations. If all agents employ no-regret learning algorithms in the course of this repeated interaction, we are able to show that our mechanism can achieve design goals such as social optimality (efficiency), budget balance, and Nash-equilibrium convergence to within an error which approaches zero as the agents gain experience. In particular, the agents' average plans converge to a socially optimal solution for the original planning task. We present experiments in a simulated network routing domain demonstrating our method's ability to reliably generate sound plans.