Neural network approaches that parameterize the value function have shown success in high-dimensional optimal control problems when the maximization of the Hamiltonian yields a closed-form solution for the optimal control. However, many problems of practical importance including space shuttle reentry, aircraft landing, and constrained vehicle control involve Hamiltonians that do not admit such an explicit formulas (implicit Hamiltonians). We propose an end-to-end implicit deep learning approach based on Jacobian-Free Backpropagation that allows for efficient training of value functions for high-dimensional optimal problems when the Hamiltonian is implicitly defined.