  Interpretation of Deep Neural Networks (DNNs) training as an optimal control
problem with nonlinear dynamical systems has received considerable attention
recently, yet the algorithmic development remains relatively limited. In this
work, we make an attempt along this line by reformulating the training
procedure from the trajectory optimization perspective. We first show that most
widely-used algorithms for training DNNs can be linked to the Differential
Dynamic Programming (DDP), a celebrated second-order method rooted in the
Approximate Dynamic Programming. In this vein, we propose a new class of
optimizer, DDP Neural Optimizer (DDPNOpt), for training feedforward and
convolution networks. DDPNOpt features layer-wise feedback policies which
improve convergence and reduce sensitivity to hyper-parameter over existing
methods. It outperforms other optimal-control inspired training methods in both
convergence and complexity, and is competitive against state-of-the-art first
and second order methods. We also observe DDPNOpt has surprising benefit in
preventing gradient vanishing. Our work opens up new avenues for principled
algorithmic design built upon the optimal control theory.
