This paper explores the relationship between numerical integrators and optimal control algorithms. Specifically, the performance of the differential dynamical programming (DDP) algorithm is examined when a variational integrator and a newly proposed surrogate variational integrator are used to propagate and linearize system dynamics. Surrogate variational integrators, derived from backward error analysis, achieve higher levels of accuracy while maintaining the same integration complexity as nominal variational integrators. The increase in the integration accuracy is shown to have a large effect on the performance of the DDP algorithm. In particular, significantly more optimized inputs are computed when the surrogate variational integrator is utilized.