{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,19]],"date-time":"2025-11-19T14:49:00Z","timestamp":1763563740796},"reference-count":40,"publisher":"MIT Press","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neural Computation"],"published-print":{"date-parts":[[2010,2]]},"abstract":"<jats:p> 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 \u03b3 for the value functions close to 1, these algorithms do not permit \u03b3 to be set exactly at \u03b3 = 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 \u03b3 = 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. <\/jats:p>","DOI":"10.1162\/neco.2009.12-08-922","type":"journal-article","created":{"date-parts":[[2009,10,20]],"date-time":"2009-10-20T19:41:07Z","timestamp":1256067667000},"page":"342-376","source":"Crossref","is-referenced-by-count":6,"title":["Derivatives of Logarithmic Stationary Distributions for Policy Gradient Reinforcement Learning"],"prefix":"10.1162","volume":"22","author":[{"given":"Tetsuro","family":"Morimura","sequence":"first","affiliation":[{"name":"IBM Research \u2013 Tokyo, Yamato, Kanagawa 242-8502, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eiji","family":"Uchibe","sequence":"additional","affiliation":[{"name":"Okinawa Institute of Science and Technology, Uruma, Okinawa 904-2234, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Junichiro","family":"Yoshimoto","sequence":"additional","affiliation":[{"name":"Okinawa Institute of Science and Technology, Uruma, Okinawa 904-2234, Japan, and Nara Institute of Science and Technology, Ikoma, Nara 630-0192, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jan","family":"Peters","sequence":"additional","affiliation":[{"name":"Max Planck Institute for Biological Cybernetics, 72076, T\u00fcbingen, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kenji","family":"Doya","sequence":"additional","affiliation":[{"name":"Okinawa Institute of Science and Technology, Uruma, Okinawa 904-2234, Japan; Nara Institute of Science and Technology, Ikoma, Nara 630-0192, Japan; and ATR Computational Neuroscience Laboratories, Soraku, Kyoto 619-0288, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"281","reference":[{"key":"B2","volume-title":"Advances in neural information processing systems","volume":"11","author":"Baird L.","year":"1999"},{"key":"B3","doi-asserted-by":"publisher","DOI":"10.1613\/jair.806"},{"key":"B4","doi-asserted-by":"publisher","DOI":"10.1613\/jair.807"},{"volume-title":"Dynamic programming and optimal control","year":"1995","author":"Bertsekas D. 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