L. Busoniu, D. Ernst, B. De Schutter, and R. Babuska, "Policy search with cross-entropy optimization of basis functions," Proceedings of the 2009 IEEE Symposium on Adaptive Dynamic Programming and Reinforcement Learning (ADPRL 2009), Nashville, Tennessee, pp. 153-160, Mar.-Apr. 2009.
This paper introduces a novel algorithm for approximate policy search in continuous-state, discrete-action Markov Decision Process (MDP). Previous policy search approaches have typically used ad-hoc parameterizations developed for specific MDPs. In contrast, the novel algorithm employs a flexible policy parameterization, suitable for solving general discrete-action MDPs. The algorithm looks for the best closed-loop policy that can be represented using a given number of basis functions, where a discrete action is assigned to each basis function. The locations and shapes of the basis functions are optimized, together with the action assignments. This allows a large class of policies to be represented. The optimization is carried out with the cross-entropy method and evaluates the policies by their empirical return from a representative set of initial states. We report simulation experiments in which the algorithm reliably obtains good policies with only a small number of basis functions, albeit at sizable computational costs.