Distributed gradient temporal difference off-policy learning with eligibility traces: Weak convergence

In this paper we propose two novel distributed algorithms for multi-agent off-policy learning of linear approximation of the value function in Markov decision processes. The algorithms differ in the way of how distributed consensus iterations are incorporated in a basic, recently proposed, single agent scheme. The proposed completely decentralized off-policy learning schemes subsume local eligibility traces, and allow applications in which all the agents may have different behavior policies while evaluating a single target policy. Under nonrestrictive assumptions on the time-varying network topology and the individual state-visiting distributions of the agents, we prove that the parameter estimates of the algorithms weakly converge to a consensus. The variance reduction properties of the proposed algorithms are demonstrated. We also formulate specific guidelines on how to design the network weights and topology. The results are illustrated using simulations.