Risk Allocation for Multi-agent Systems using Tatonnement

Abstract

This paper proposes a new market-based distributed planning algorithm for multi-agent systems under uncertainty, called MIRA (Market-based Iterative Risk Allocation). In large coordination problems, from power grid management to multi-vehicle missions, multiple agents act collectively in order to optimize the performance of the system, while satisfying mission constraints. These optimal plans are particularly susceptible to risk when uncertainty is introduced. We present a distributed planning algorithm that minimizes the system cost while ensuring that the probability of violating mission constraints is below a user-specified level. We build upon the paradigm of risk allocation (Ono and Williams, AAAI-08), in which the planner optimizes not only the sequence of actions, but also its allocation of risk among each constraint at each time step. We extend the concept of risk allocation to multi-agent systems by highlighting risk as a good that is traded in a computational market. The equilibrium price of risk that balances the supply and demand is found by an iterative price adjustment process called tatonnement (also known as Walrasian auction). The simulation results demonstrate the efficiency and optimality of the proposed distributed planner.