Entropy Regularization with Discounted Future State Distribution in Policy Gradient Methods
Abstract
The policy gradient theorem is defined based on an objective with respect to the initial distribution over states. In the discounted case, this results in policies that are optimal for one distribution over initial states, but may not be uniformly optimal for others, no matter where the agent starts from. Furthermore, to obtain unbiased gradient estimates, the starting point of the policy gradient estimator requires sampling states from a normalized discounted weighting of states. However, the difficulty of estimating the normalized discounted weighting of states, or the stationary state distribution, is quite wellknown. Additionally, the large sample complexity of policy gradient methods is often attributed to insufficient exploration, and to remedy this, it is often assumed that the restart distribution provides sufficient exploration in these algorithms. In this work, we propose exploration in policy gradient methods based on maximizing entropy of the discounted future state distribution. The key contribution of our work includes providing a practically feasible algorithm to estimate the normalized discounted weighting of states, i.e, the \textit{discounted future state distribution}. We propose that exploration can be achieved by entropy regularization with the discounted state distribution in policy gradients, where a metric for maximal coverage of the state space can be based on the entropy of the induced state distribution. The proposed approach can be considered as a three timescale algorithm and under some mild technical conditions, we prove its convergence to a locally optimal policy. Experimentally, we demonstrate usefulness of regularization with the discounted future state distribution in terms of increased state space coverage and faster learning on a range of complex tasks.
 Publication:

arXiv eprints
 Pub Date:
 December 2019
 DOI:
 10.48550/arXiv.1912.05104
 arXiv:
 arXiv:1912.05104
 Bibcode:
 2019arXiv191205104I
 Keywords:

 Computer Science  Machine Learning;
 Computer Science  Artificial Intelligence;
 Statistics  Machine Learning
 EPrint:
 In Submission