Statistically linearized least-squares temporal differences

A common drawback of standard reinforcement learning algorithms is their inability to scale-up to real-world problems. For this reason, a current important trend of research is (state-action) value function approximation. A prominent value function approximator is the least-squares temporal differences (LSTD) algorithm. However, for technical reasons, linearity is mandatory: the parameterization of the value function must be linear (compact nonlinear representations are not allowed) and only the Bellman evaluation operator can be considered (imposing policy-iteration-like schemes). In this paper, this restriction of LSTD is lifted thanks to a derivative-free statistical linearization approach. This way, nonlinear parameterizations and the Bellman optimality operator can be taken into account (this last point allows taking into account value-iteration-like schemes). The efficiency of the resulting algorithms are demonstrated using a linear parametrization and neural networks as well as on a Q-learning-like problem. A theoretical analysis is also provided.