A Study of Policy Gradient on a Class of Exactly Solvable Models
Abstract
Policy gradient methods are extensively used in reinforcement learning as a way to optimize expected return. In this paper, we explore the evolution of the policy parameters, for a special class of exactly solvable POMDPs, as a continuousstate Markov chain, whose transition probabilities are determined by the gradient of the distribution of the policy's value. Our approach relies heavily on random walk theory, specifically on affine Weyl groups. We construct a class of novel partially observable environments with controllable exploration difficulty, in which the value distribution, and hence the policy parameter evolution, can be derived analytically. Using these environments, we analyze the probabilistic convergence of policy gradient to different local maxima of the value function. To our knowledge, this is the first approach developed to analytically compute the landscape of policy gradient in POMDPs for a class of such environments, leading to interesting insights into the difficulty of this problem.
 Publication:

arXiv eprints
 Pub Date:
 November 2020
 arXiv:
 arXiv:2011.01859
 Bibcode:
 2020arXiv201101859M
 Keywords:

 Computer Science  Machine Learning;
 Mathematics  Probability