Abstract
The adaptability of resolution to the complexity of approximated function has a great influence on the performance of learning in the function approximation for reinforcement learning. We propose applying the reaction-diffusion equation on a graph to function approximation for reinforcement learning.The function approximator expressed by nodes can change its resolution adaptively by distributing them densely in the complex region of the state space with the proposed algorithm. A function is expressed in a plane. The successive least square method is adopted to approximate the function from the data. Each plane corresponds to a node, which is an element of the graph. Each node moves to diffuse the complexity of the approximated function in the neighborhood based on the reaction-diffusion equation. The complexity of the function is defined by the change of gradient. The simulation shows the two points: 1) The proposed algorithm provides the adaptability for function approximation. 2) The function approximation improves the efficiency of the reinforcement learning.
