A Large Deviations Perspective on Policy Gradient Algorithms

We derive the first large deviation rate function for the stochastic iterates generated by policy gradient methods with a softmax parametrization and an entropy regularized objective. Leveraging the contraction principle from large deviations theory, we also develop a general recipe for deriving exponential convergence rates for a wide spectrum of other policy parametrizations. This approach unifies several results from the literature and simplifies existing proof techniques.