Cooperative learning in multi-agent systems from intermittent measurements

Motivated by the problem of decentralized direction-tracking, we consider the general problem of cooperative learning in multi-agent systems with time-varying connectivity and intermittent measurements. We propose a distributed learning protocol capable of learning an unknown vector $\mu$ from noisy measurements made independently by autonomous nodes. Our protocol is completely distributed and able to cope with the time-varying, unpredictable nature of inter-agent connectivity, repeated failures of nodes, and intermittent noisy measurements of $\mu$. Our main results bound the learning speed of our protocol in terms of a novel measure of graph connectivity we call the sieve constant of a graph.