  In this paper, we propose novel learning frameworks to tackle optimal control
problems by applying the Pontryagin maximum principle and then solving for a
Hamiltonian dynamical system. Applying the Pontryagin maximum principle to the
original optimal control problem shifts the learning focus to reduced
Hamiltonian dynamics and corresponding adjoint variables. Then, the reduced
Hamiltonian networks can be learned by going backwards in time and then
minimizing loss function deduced from the Pontryagin maximum principle's
conditions. The learning process is further improved by progressively learning
a posterior distribution of the reduced Hamiltonians. This is achieved through
utilizing a variational autoencoder which leads to more effective path
exploration process. We apply our learning frameworks called NeuralPMP to
various control tasks and obtain competitive results.
