KL-learning: Online solution of Kullback-Leibler control problems

Joris Bierkens; Bert Kappen

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arXiv · 1112.1996

KL-learning: Online solution of Kullback-Leibler control problems

Joris Bierkens·Bert Kappen

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Abstract

We introduce a stochastic approximation method for the solution of an ergodic Kullback-Leibler control problem. A Kullback-Leibler control problem is a Markov decision process on a finite state space in which the control cost is proportional to a Kullback-Leibler divergence of the controlled transition probabilities with respect to the uncontrolled transition probabilities. The algorithm discussed in this work allows for a sound theoretical analysis using the ODE method. In a numerical experiment the algorithm is shown to be comparable to the power method and the related Z-learning algorithm in terms of convergence speed. It may be used as the basis of a reinforcement learning style algorithm for Markov decision problems.

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BibTeX RIS

Joris Bierkens, Bert Kappen. 2012-02-16. KL-learning: Online solution of Kullback-Leibler control problems. https://arxiv.org/abs/1112.1996

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