  Connections between Deep Neural Networks (DNNs) training and optimal control
theory has attracted considerable attention as a principled tool of algorithmic
design. Differential Dynamic Programming (DDP) neural optimizer is a recently
proposed method along this line. Despite its empirical success, the
applicability has been limited to feedforward networks and whether such a
trajectory-optimization inspired framework can be extended to modern
architectures remains unclear. In this work, we derive a generalized DDP
optimizer that accepts both residual connections and convolution layers. The
resulting optimal control representation admits a game theoretic perspective,
in which training residual networks can be interpreted as cooperative
trajectory optimization on state-augmented dynamical systems. This Game
Theoretic DDP (GT-DDP) optimizer enjoys the same theoretic connection in
previous work, yet generates a much complex update rule that better leverages
available information during network propagation. Evaluation on image
classification datasets (e.g. MNIST and CIFAR100) shows an improvement in
training convergence and variance reduction over existing methods. Our approach
highlights the benefit gained from architecture-aware optimization.
