Performance Evaluation of Multi-Agent Distributed Collaborative Optimizationunder Random Communication Topologies

We investigate collaborative optimization in a multi-agent setting, when the agents execute in a distributed manner using local information, while the communication topology used to exchange messages and information is modeled by a graph-valued random process, independent of other time instances. Specifically, we study the performance of the consensus-based multi-agent subgradient method, for the case of a constant stepsize, as measured by two metrics: rate of convergence and guaranteed region of convergence, evaluated via their expected values. Under a strong convexity type of assumption, we provide upper bounds on the performance metrics, which explicitly depend on the probability distribution of the random graph and on the agents’ estimates of the optimal solution. This provides a guide for tuning the parameters of the communication protocol such that good performance of the multi-agent subgradient method is ensured.