Stochastic Alternating Direction Method of Multipliers with Conjugate Gradient

Abstract

The Alternating Direction Method of Multipliers(ADMM) is an important method for machine learning. A large number of stochastic versions of ADMM continue to emerge. But almost all the algorithm focused on the Steepest Descent, which cause slow convergence rate. In our work, we propose a new stochastic alternative direction method of multipliers with conjugate gradient(SCG-ADMM), and prove its convergence rate in ergodic sense. Conjugate gradient descent has a better performance in traditional cases. Experiments on LASSO and Logistics Regression show that our proposed algorithm can achieve state-of-the-art performance in real applications. And we use the linear search method to replace the manual setting of the step length.