  Reinforcement learning (RL) is an important field of research in machine
learning that is increasingly being applied to complex optimization problems in
physics. In parallel, concepts from physics have contributed to important
advances in RL with developments such as entropy-regularized RL. While these
developments have led to advances in both fields, obtaining analytical
solutions for optimization in entropy-regularized RL is currently an open
problem. In this paper, we establish a mapping between entropy-regularized RL
and research in non-equilibrium statistical mechanics focusing on Markovian
processes conditioned on rare events. In the long-time limit, we apply
approaches from large deviation theory to derive exact analytical results for
the optimal policy and optimal dynamics in Markov Decision Process (MDP) models
of reinforcement learning. The results obtained lead to a novel analytical and
computational framework for entropy-regularized RL which is validated by
simulations. The mapping established in this work connects current research in
reinforcement learning and non-equilibrium statistical mechanics, thereby
opening new avenues for the application of analytical and computational
approaches from one field to cutting-edge problems in the other.
