  This paper presents four different ways of looking at the well-known Least
Squares Temporal Differences (LSTD) algorithm for computing the value function
of a Markov Reward Process, each of them leading to different insights: the
operator-theory approach via the Galerkin method, the statistical approach via
instrumental variables, the linear dynamical system view as well as the limit
of the TD iteration. We also give a geometric view of the algorithm as an
oblique projection. Furthermore, there is an extensive comparison of the
optimization problem solved by LSTD as compared to Bellman Residual
Minimization (BRM). We then review several schemes for the regularization of
the LSTD solution. We then proceed to treat the modification of LSTD for the
case of episodic Markov Reward Processes.
