Distributed Value Function Approximation for Collaborative Multi-Agent Reinforcement Learning

In this paper we propose novel distributed gradient-based temporal difference algorithms for multi-agent off-policy learning of linear approximation of the value function in Markov decision processes. The algorithms are composed of: 1) local parameter updates based on the single-agent off-policy gradient temporal difference learning algorithms, including eligibility traces with state dependent parameters, and 2) linear dynamic consensus scheme over the underlying, typically sparsely connected, inter-agent communication network. The proposed algorithms differ in the way of how the time-scales are selected, how local recursions are performed and how consensus iterations are incorporated. The algorithms are completely decentralized, allowing applications in which all the agents may have completely different behavior policies while evaluating a single target policy. In this sense, the algorithms may be considered as a tool for either parallelization or multi-agent collaborative learning under given constraints. We provide weak convergence results, taking rigorously into account properties of the underlying Feller-Markov processes. We prove that, under nonrestrictive assumptions on the time-varying network topology and the individual state-visiting distributions of the agents, the parameter estimates of the algorithms weakly converge to a consensus point. The variance reduction effect of the proposed algorithms is demonstrated by analyzing a limiting stochastic differential equation. Specific guidelines for network design, providing the desired convergence points, are given. The algorithms' properties are illustrated by characteristic simulation results.