  Alternating Direction Method of Multipliers (ADMM) has been used successfully
in many conventional machine learning applications and is considered to be a
useful alternative to Stochastic Gradient Descent (SGD) as a deep learning
optimizer. However, as an emerging domain, several challenges remain, including
1) The lack of global convergence guarantees, 2) Slow convergence towards
solutions, and 3) Cubic time complexity with regard to feature dimensions. In
this paper, we propose a novel optimization framework for deep learning via
ADMM (dlADMM) to address these challenges simultaneously. The parameters in
each layer are updated backward and then forward so that the parameter
information in each layer is exchanged efficiently. The time complexity is
reduced from cubic to quadratic in (latent) feature dimensions via a dedicated
algorithm design for subproblems that enhances them utilizing iterative
quadratic approximations and backtracking. Finally, we provide the first proof
of global convergence for an ADMM-based method (dlADMM) in a deep neural
network problem under mild conditions. Experiments on benchmark datasets
demonstrated that our proposed dlADMM algorithm outperforms most of the
comparison methods.
