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.

本研究旨在将深度神经网络的训练过程从轨迹优化的角度重新制定，提出了一种基于差分动态规划的优化器，DDP Neural Optimizer（DDPNOpt），其具有层间反馈策略、收敛性高等优点，且在避免梯度消失方面表现出惊人的优越性，展示了基于最优控制理论的算法设计的新思路。