Distributed Subgradient Method in Open Multiagent Systems

This article considers a distributed method for constrained convex optimization over open multiagent networks. In open multiagent systems, each agent freely joins or leaves the network at its timing. The active agents, which participate in the network, have time-varying local cost functions and attempt to find an optimal strategy that minimizes the cumulative local cost functions in a finite-time horizon. Each active agent updates its estimation by a distributed subgradient-based algorithm with information exchange of the estimation with neighboring active agents. The performance of the algorithm is analyzed by a regret, which represents the error of the costs between the estimations of the agents and the optimal strategy. To this end, the recursive relation of the error between the sum of the estimations of the active agents and the optimal strategy is considered. This article shows that the upper bound of the regret is sublinear for an appropriate step-size rule.