Graph-Hierarchical Approaches for Distributed Learning Over Nonuniform Durations of Agents

The design and analysis of distributed learning for multi-agent networks generally resort to the graph-theoretical methods in the leader-follower framework, but how to exploit new graph-theoretical methods in distributed learning is not clear. This paper is targeted at developing novel graph-theoretical methods to address a novel class of nonuniform distributed learning (NUDL) problems for networks consisting of nonlinear agents subject to nonuniform durations that are agent- and iteration-dependent. An NUDL algorithm is proposed by making full use of the available interaction information among agents in spite of the limitation of the network topology and the nonuniform durations. Furthermore, a graph-hierarchical method is presented to obtain feasible design conditions for NUDL such that the nonuniform cooperative tracking objectives of the agents can be accomplished in the presence of any specified trajectory, despite whether the unknown nonlinear dynamics of agents are globally or locally Lipschitz. In particular, an inherent relation is disclosed between the changing of agent- and iteration-dependent durations and the switching of network topologies in distributed learning. Simulations performed on a network of four nonlinear agents are used to demonstrate the effectiveness of the given NUDL results.