Kalman Temporal Differences: The deterministic case

This paper deals with value function and Q-function approximation in deterministic Markovian decision processes. A general statistical framework based on the Kalman filtering paradigm is introduced. Its principle is to adopt a parametric representation of the value function, to model the associated parameter vector as a random variable and to minimize the mean-squared error of the parameters conditioned on past observed transitions. From this general framework, which will be called Kalman Temporal Differences (KTD), and using an approximation scheme called the unscented transform, a family of algorithms is derived, namely KTD-V, KTD-SARSA and KTD-Q, which aim respectively at estimating the value function of a given policy, the Q-function of a given policy and the optimal Q-function. The proposed approach holds for linear and nonlinear parameterization. This framework is discussed and potential advantages and shortcomings are highlighted.