Derivatives of logarithmic stationary distributions for policy gradient reinforcement learning

Tetsuro Morimura, Eiji Uchibe, Junichiro Yoshimoto, Jan Peters, Kenji Doya

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)

Abstract

Most conventional policy gradient reinforcement learning (PGRL) algorithms neglect (or do not explicitly make use of) a term in the average reward gradient with respect to the policy parameter. That term involves the derivative of the stationary state distribution that corresponds to the sensitivity of its distribution to changes in the policy parameter. Although the bias introduced by this omission can be reduced by setting the forgetting rate γ for the value functions close to 1, these algorithms do not permit γ to be set exactly at γ = 1. In this article, we propose a method for estimating the log stationary state distribution derivative (LSD) as a useful form of the derivative of the stationary state distribution through backward Markov chain formulation and a temporal difference learning framework. A new policy gradient (PG) framework with an LSD is also proposed, in which the average reward gradient can be estimated by setting γ = 0, so it becomes unnecessary to learn the value functions. We also test the performance of the proposed algorithms using simple benchmark tasks and show that these can improve the performances of existing PG methods.

Original languageEnglish
Pages (from-to)342-376
Number of pages35
JournalNeural Computation
Volume22
Issue number2
DOIs
Publication statusPublished - 02-2010
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Arts and Humanities (miscellaneous)
  • Cognitive Neuroscience

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