Regularized Fitted Q-Iteration for planning in continuous-space Markovian decision problems

Reinforcement learning with linear and non-linear function approximation has been studied extensively in the last decade. However, as opposed to other fields of machine learning such as supervised learning, the effect of finite sample has not been thoroughly addressed within the reinforcement learning framework. In this paper we propose to use L² regularization to control the complexity of the value function in reinforcement learning and planning problems. We consider the Regularized Fitted Q-Iteration algorithm and provide generalization bounds that account for small sample sizes. Finally, a realistic visual-servoing problem is used to illustrate the benefits of using the regularization procedure.