  Using insight from numerical approximation of ODEs and the problem
formulation and solution methodology of TD learning through a Galerkin
relaxation, I propose a new class of TD learning algorithms. After applying the
improved numerical methods, the parameter being approximated has a guaranteed
order of magnitude reduction in the Taylor Series error of the solution to the
ODE for the parameter $\theta(t)$ that is used in constructing the linearly
parameterized value function. Predictor-Corrector Temporal Difference (PCTD) is
what I call the translated discrete time Reinforcement Learning(RL) algorithm
from the continuous time ODE using the theory of Stochastic Approximation(SA).
Both causal and non-causal implementations of the algorithm are provided, and
simulation results are listed for an infinite horizon task to compare the
original TD(0) algorithm against both versions of PCTD(0).
