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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 θ(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).

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