AbstractThis paper proposes a gradient-based multi-agent actor-critic algorithm for off-policy reinforcement learning using importance sampling. Our algorithm is incremental with full gradients, and its complexity per iteration scales linearly with the size of approximation features. Previous multi-agent actor-critic algorithms are limited to the on-policy setting or off-policy emphatic temporal difference (TD) learning and they do not take advantage of the advances in off-policy gradient temporal difference learning (GTD). As a theoretical contribution, we establish that the critic step of the proposed algorithm converges to the TD solution of the projected Bellman equation and the actor step converges to the set of asymptotically stable fixed points. Numerical experiments on the multi-agent generalization of the Boyan’s chain problem show that the proposed approach provides improved performances in terms of stability and convergence rate as compared with the state-of-the-art baseline algorithm.