Natural gradient works efficiently in learning
Neural Computation
Dynamic Programming and Optimal Control, Two Volume Set
Dynamic Programming and Optimal Control, Two Volume Set
Introduction to Reinforcement Learning
Introduction to Reinforcement Learning
Reinforcement Learning in POMDPs with Function Approximation
ICML '97 Proceedings of the Fourteenth International Conference on Machine Learning
Infinite-horizon policy-gradient estimation
Journal of Artificial Intelligence Research
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
ECML'05 Proceedings of the 16th European conference on Machine Learning
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The parameter space of a statistical learning machine has a Riemannian metric structure in terms of its objective function. [1] Amari proposed the concept of "natural gradient" that takes the Riemannian metric of the parameter space into account. Kakade [2] applied it to policy gradient reinforcement learning, called a natural policy gradient (NPG). Although NPGs evidently depend on the underlying Riemannian metrics, careful attention was not paid to the alternative choice of the metric in previous studies. In this paper, we propose a Riemannian metric for the joint distribution of the state-action, which is directly linked with the average reward, and derive a new NPG named "Natural State-action Gradient"(NSG). Then, we prove that NSG can be computed by fitting a certain linear model into the immediate reward function. In numerical experiments, we verify that the NSG learning can handle MDPs with a large number of states, for which the performances of the existing (N)PG methods degrade.