Finite-Sample Bounds for Adaptive Inverse Reinforcement Learning using Passive Langevin Dynamics

Stochastic gradient Langevin dynamics (SGLD) are a useful methodology for sampling from probability distributions. This paper provides a finite sample analysis of a passive stochastic gradient Langevin dynamics algorithm (PSGLD) designed to achieve inverse reinforcement learning. By "passive", we mean that the noisy gradients available to the PSGLD algorithm (inverse learning process) are evaluated at randomly chosen points by an external stochastic gradient algorithm (forward learner). The PSGLD algorithm thus acts as a randomized sampler which recovers the cost function being optimized by this external process. Previous work has analyzed the asymptotic performance of this passive algorithm using stochastic approximation techniques; in this work we analyze the non-asymptotic performance. Specifically, we provide finite-time bounds on the 2-Wasserstein distance between the passive algorithm and its stationary measure, from which the reconstructed cost function is obtained.