  This work develops a fully decentralized multi-agent algorithm for policy
evaluation. The proposed scheme can be applied to two distinct scenarios. In
the first scenario, a collection of agents have distinct datasets gathered
following different behavior policies (none of which is required to explore the
full state space) in different instances of the same environment and they all
collaborate to evaluate a common target policy. The network approach allows for
efficient exploration of the state space and allows all agents to converge to
the optimal solution even in situations where neither agent can converge on its
own without cooperation. The second scenario is that of multi-agent games, in
which the state is global and rewards are local. In this scenario, agents
collaborate to estimate the value function of a target team policy. The
proposed algorithm combines off-policy learning, eligibility traces and linear
function approximation. The proposed algorithm is of the variance-reduced kind
and achieves linear convergence with $O(1)$ memory requirements. The linear
convergence of the algorithm is established analytically, and simulations are
used to illustrate the effectiveness of the method.
