  We present ADMM-Softmax, an alternating direction method of multipliers
(ADMM) for solving multinomial logistic regression (MLR) problems. Our method
is geared toward supervised classification tasks with many examples and
features. It decouples the nonlinear optimization problem in MLR into three
steps that can be solved efficiently. In particular, each iteration of
ADMM-Softmax consists of a linear least-squares problem, a set of independent
small-scale smooth, convex problems, and a trivial dual variable update.
Solution of the least-squares problem can be be accelerated by pre-computing a
factorization or preconditioner, and the separability in the smooth, convex
problem can be easily parallelized across examples. For two image
classification problems, we demonstrate that ADMM-Softmax leads to improved
generalization compared to a Newton-Krylov, a quasi Newton, and a stochastic
gradient descent method.
