Gradient dynamics in reinforcement learning

Despite the success achieved by the analysis of supervised learning algorithms in the framework of statistical mechanics, reinforcement learning has remained largely untouched. Here we move towards closing the gap by analyzing the dynamics of the policy gradient algorithm. For a convex problem, we show that it obeys a drift-diffusion motion with coeffcients tuned by learning rate. Furthermore, we propose a mapping between a non-convex reinforcement learning problem and a disordered system. This mapping enables us to show how the learning rate acts as an effective temperature and thus is capable of smoothing rough landscapes, corroborating what is displayed by the drift-diffusive description and paving the way for physics-inspired algorithmic optimization based on annealing procedures in disordered systems.