Basis Function Construction in Reinforcement Learning Using Cascade-Correlation Learning Architecture

In reinforcement learning, it is a common practice to map the state(-action) space to a different one using basis functions. This transformation aims to represent the input data in a more informative form that facilitates and improves subsequent steps. As a "good'' set of basis functions result in better solutions and defining such functions becomes a challenge with increasing problem complexity, it is beneficial to be able to generate them automatically. In this paper, we propose a new approach based on Bellman residual for constructing basis functions using cascade-correlation learning architecture. We show how this approach can be applied to Least Squares Policy Iteration algorithm in order to obtain a better approximation of the value function, and consequently improve the performance of the resulting policies. We also present the effectiveness of the method empirically on some benchmark problems.