Although deep learning models are highly effective for various learning tasks, their high computational costs prohibit the deployment to scenarios where either memory or computational resources are limited. In this paper, we focus on compressing and accelerating deep models with network weights represented by very small numbers of bits, referred to as extremely low bit neural network. We model this problem as a discretely constrained optimization problem. Borrowing the idea from Alternating Direction Method of Multipliers (ADMM), we decouple the continuous parameters from the discrete constraints of network, and cast the original hard problem into several subproblems. We propose to solve these subproblems using extragradient and iterative quantization algorithms that lead to considerably faster convergency compared to conventional optimization methods. Extensive experiments on image recognition and object detection verify that the proposed algorithm is more effective than state-of-the-art approaches when coming to extremely low bit neural network.
Many problems of recent interest in statistics and machine learning can be posed in the framework of convex optimization. Due to the explosion in size and complexity of modern datasets, it is increasingly important to be able to solve problems with a very large number of features or training examples. As a result, both the decentralized collection or storage of these datasets as well as accompanying distributed solution methods are either necessary or at least highly desirable. In this review, we argue that the alternating direction method of multipliers is well suited to distributed convex optimization, and in particular to large-scale problems arising in statistics, machine learning, and related areas. The method was developed in the 1970s, with roots in the 1950s, and is equivalent or closely related to many other algorithms, such as dual decomposition, the method of multipliers, Douglas–Rachford splitting, Spingarn's method of partial inverses, Dykstra's alternating projections, Bregman iterative algorithms for l1 problems, proximal methods, and others. After briefly surveying the theory and history of the algorithm, we discuss applications to a wide variety of statistical and machine learning problems of recent interest, including the lasso, sparse logistic regression, basis pursuit, covariance selection, support vector machines, and many others. We also discuss general distributed optimization, extensions to the nonconvex setting, and efficient implementation, including some details on distributed MPI and Hadoop MapReduce implementations.