  This paper proposes a discontinuity-sensitive approach to learn the solutions
of parametric optimal control problems with high accuracy. Many tasks, ranging
from model predictive control to reinforcement learning, may be solved by
learning optimal solutions as a function of problem parameters. However,
nonconvexity, discrete homotopy classes, and control switching cause
discontinuity in the parameter-solution mapping, thus making learning difficult
for traditional continuous function approximators. A mixture of experts (MoE)
model composed of a classifier and several regressors is proposed to address
such an issue. The optimal trajectories of different parameters are clustered
such that in each cluster the trajectories are continuous function of problem
parameters. Numerical examples on benchmark problems show that training the
classifier and regressors individually outperforms joint training of MoE. With
suitably chosen clusters, this approach not only achieves lower prediction
error with less training data and fewer model parameters, but also leads to
dramatic improvements in the reliability of trajectory tracking compared to
traditional universal function approximation models (e.g., neural networks).
