Market-based Risk Allocation Optimization

This paper proposes Market-based Iterative Risk Allocation (MIRA), a new market-based decentralized optimization algorithm for multiagent systems under stochastic uncertainty, with a focus on problems with continuous action and state space. In large coordination problems, from power grid management to multi-vehicle missions, multiple agents act collectively in order to maximize the performance of the system, while satisfying mission constraints. These optimal action plans are particularly susceptible to risk when uncertainty is introduced. We present a decentralized optimization algorithm that minimizes the system cost while ensuring that the probability of violating mission constraints is below a user-specified upper bound. We build upon the paradigm of risk allocation [13], in which the planner optimizes not only the sequence of actions, but also its allocation of risk among state constraints. We extend the concept of risk allocation to multi-agent systems by highlighting risk as a resource 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 tâtonnement (also known as Walrasian auction). Our work is distinct from the classical tâtonnement approach in that we use Brent’s method to provide fast guaranteed convergence to the equilibrium price. The simulation results demonstrate the efficiency and optimality of the proposed decentralized optimization algorithm.