On Risk Evaluation and Control of Distributed Multi-agent Systems
提出一套公理和双重表示法来评估分布式系统的总风险，并构建风险度量族，用于风险规避的分布式决策，在通信网络问题中验证了方法的有效性。
Abstract In this paper, we deal with risk evaluation and risk-averse optimization of complex distributed systems with general risk functionals. We postulate a novel set of axioms for the functionals evaluating the total risk of the system. We derive a dual representation for the systemic risk measures and propose new ways to construct families of systemic risk measures using either a collection of linear scalarizations or non-linear risk aggregation. The proposed framework facilitates risk-averse sequential decision-making by distributed methods. The new approach is compared theoretically and numerically to other systemic risk measurements from the existing literature. We formulate a two-stage decision problem for a distributed system using a systemic measure of risk. The structure accommodates distributed systems arising in energy networks, robotics, and other practical situations. A distributed decomposition method for solving the two-stage problem is proposed and applied to a problem arising in communication networks. We have used this problem to compare the methods of systemic risk evaluation. We show that the risk evaluation via linear scalarizations of outcomes leads to less conservative risk evaluation and results in a substantially better solution to the problem at hand than aggregating the risk of individual agents.