Kernelized value function approximation for reinforcement learning

A recent surge in research in kernelized approaches to reinforcement learning has sought to bring the benefits of kernelized machine learning techniques to reinforcement learning. Kernelized reinforcement learning techniques are fairly new and different authors have approached the topic with different assumptions and goals. Neither a unifying view nor an understanding of the pros and cons of different approaches has yet emerged. In this paper, we offer a unifying view of the different approaches to kernelized value function approximation for reinforcement learning. We show that, except for different approaches to regularization, Kernelized LSTD (KLSTD) is equivalent to a modelbased approach that uses kernelized regression to find an approximate reward and transition model, and that Gaussian Process Temporal Difference learning (GPTD) returns a mean value function that is equivalent to these other approaches. We also discuss the relationship between our modelbased approach and the earlier Gaussian Processes in Reinforcement Learning (GPRL). Finally, we decompose the Bellman error into the sum of transition error and reward error terms, and demonstrate through experiments that this decomposition can be helpful in choosing regularization parameters.