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Using insight from numerical approximation of ODEs and the problemformulation and solution methodology of TD learning through a Galerkinrelaxation, I propose a new class of TD learning algorithms. After applying theimproved numerical methods, the parameter being approximated has a guaranteedorder of magnitude reduction in the Taylor Series error of the solution to theODE for the parameter $\theta(t)$ that is used in constructing the linearlyparameterized value function. Predictor-Corrector Temporal Difference (PCTD) iswhat I call the translated discrete time Reinforcement Learning(RL) algorithmfrom the continuous time ODE using the theory of Stochastic Approximation(SA).Both causal and non-causal implementations of the algorithm are provided, andsimulation results are listed for an infinite horizon task to compare theoriginal TD(0) algorithm against both versions of PCTD(0).

Predictor-Corrector(PC) Temporal Difference(TD) Learning (PCTD)