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Optimal control problems can be solved by first applying the Pontryaginmaximum principle, followed by computing a solution of the correspondingunconstrained Hamiltonian dynamical system. In this paper, and to achieve abalance between robustness and efficiency, we learn a reduced Hamiltonian ofthe unconstrained Hamiltonian. This reduced Hamiltonian is learned by goingbackward in time and by minimizing the loss function resulting from applicationof the Pontryagin maximum principle conditions. The robustness of our learningprocess is then further improved by progressively learning a posteriordistribution of reduced Hamiltonians. This leads to a more efficient samplingof the generalized coordinates (position, velocity) of our phase space. Oursolution framework applies to not only optimal control problems withfinite-dimensional phase (state) spaces but also the infinite dimensional case.

Learning Optimal Control with Stochastic Models of Hamiltonian Dynamics