Basis function adaptation in temporal difference reinforcement learning

Reinforcement Learning (RL) is an approach for solving complex multi-stage decision problems that fall under the general framework of Markov Decision Problems (MDPs), with possibly unknown parameters. Function approximation is essential for problems with a large state space, as it facilitates compact representation and enables generalization. Linear approximation architectures (where the adjustable parameters are the weights of pre-fixed basis functions) have recently gained prominence due to efficient algorithms and convergence guarantees. Nonetheless, an appropriate choice of basis function is important for the success of the algorithm. In the present paper we examine methods for adapting the basis function during the learning process in the context of evaluating the value function under a fixed control policy. Using the Bellman approximation error as an optimization criterion, we optimize the weights of the basis function while simultaneously adapting the (non-linear) basis function parameters. We present two algorithms for this problem. The first uses a gradient-based approach and the second applies the Cross Entropy method. The performance of the proposed algorithms is evaluated and compared in simulations.