ADMM-SOFTMAX : An ADMM Approach for Multinomial Logistic Regression
This work addresses optimization efficiency in multinomial logistic regression for classification tasks, but it is incremental as it adapts an existing ADMM framework to a specific problem.
The paper tackles multinomial logistic regression for supervised classification with many examples and features by proposing ADMM-Softmax, an ADMM-based method that decouples the problem into efficient steps, leading to improved generalization in image classification tasks compared to Newton-Krylov, quasi-Newton, and stochastic gradient descent methods.
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.