Distributed Learning With Time Correlated Information

We consider learning an environment by a team of spatially distributed agents, each agent with ongoing local measurements and the team of agents linked by a sparse directed communication network. Agents exploit their local measurements and exchange messages with neighbors in the communication network to quickly learn which environment-from a given finite set of presumed ones-is active. Works on such distributed learning setup assumed that the local measurements taken by the agents are uncorrelated over time, a convenient assumption that leaves, however, many practical setups excluded. In this letter, via modifying a recent distributed learning algorithm, we expand distributed learning to environments in which the time correlation of the local measurements is arbitrary. Since correlated measurements invalidate the previous proofs, we need a new proof guaranteeing that the modified distributed learning algorithm succeeds. Our new proof technique is simple, relies only on basic tools such as the Perron-Frobenius and the ergodic Markov chain theorems, and even covers the case of mismatched assumptions-the active environment is not in the finite set of presumed ones. A numerical example confirms the novel theoretical findings.