  We present a framework to integrate tensor network (TN) methods with
reinforcement learning (RL) for solving dynamical optimisation tasks. We
consider the RL actor-critic method, a model-free approach for solving RL
problems, and introduce TNs as the approximators for its policy and value
functions. Our "actor-critic with tensor networks" (ACTeN) method is especially
well suited to problems with large and factorisable state and action spaces. As
an illustration of the applicability of ACTeN we solve the exponentially hard
task of sampling rare trajectories in two paradigmatic stochastic models, the
East model of glasses and the asymmetric simple exclusion process (ASEP), the
latter being particularly challenging to other methods due to the absence of
detailed balance. With substantial potential for further integration with the
vast array of existing RL methods, the approach introduced here is promising
both for applications in physics and to multi-agent RL problems more generally.
