| Summary: | This paper proposes Market-based Iterative Risk Allocation (MIRA), a new market-based distributed planning algorithm for multi-agent systems under uncertainty. 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 & Williams 2008), 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 commodity 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 tˆatonnement (also known as Walrasian auction). Our work is distinct from the classical tˆatonnement approach in that we use Brent's method to provide fast guaranteed convergence to the equilibrium price. The simulation results demonstrate the efficiency of the proposed distributed planner.
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