TASK DEFINITION: In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
PROBLEM: The alternating direction method of multipliers (ADMM) has been recognized as a versatile approach for solving modern large-scale machine learning and signal processing problems efficiently. When the data size and/or the problem dimension is large, a distributed version of ADMM can be used, which is capable of distributing the computation load and the data set to a network of computing nodes. Unfortunately, a direct synchronous implementation of such algorithm does not scale well with the problem size, as the algorithm speed is limited by the slowest computing nodes. To address this issue, in a companion paper, we have proposed an asynchronous distributed ADMM (AD-ADMM) and studied its worst-case convergence conditions. In this paper, we further the study by characterizing the conditions under which the AD-ADMM achieves linear convergence. Our conditions as well as the resulting linear rates reveal the impact that various algorithm parameters, network delay and network size have on the algorithm performance. To demonstrate the superior time efficiency of the proposed AD-ADMM, we test the ADADMM on a high-performance computer cluster by solving a large-scale logistic regression problem. Keywords Distributed optimization, ADMM, Asynchronous, Consensus optimization Tsung-Hui Chang is the corresponding author. Address: School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, China 518172, E-mail: tsunghui.chang@ieee.org. Wei-Cheng Liao is with Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN 55455, USA, E-mail: mhong@umn.edu Mingyi Hong is with Department of Industrial and Manufacturing Systems Engineering, Iowa State University, Ames, 50011, USA, E-mail: mingyi@iastate.edu Xiangfeng Wang is with Shanghai Key Lab for Trustworthy Computing, Software Engineering Institute, East China Normal University, Shanghai, 200062, China, E-mail: xfwang@sei.ecnu.edu.cn September 10, 2015 DRAFT

SOLUTION: Asynchronous Distributed ADMM for Large-Scale Optimization- Part II: Linear Convergence Analysis and Numerical Performance

PROBLEM: This paper presents a theoretical, idealized model of the thinking process with the following characteristics: 1) the model can produce complex thought sequences and can be generalized to new inputs, 2) it can receive and maintain input information indefinitely for the generation of thoughts and later use, and 3) it supports learning while executing. The crux of the model lies within the concept of internal consistency, or the generated thoughts should always be consistent with the inputs from which they are created. Its merit, apart from the capability to generate new creative thoughts from an internal mechanism, depends on the potential to help training to generalize better. This is consequently enabled by separating input information into several parts to be handled by different processing components with a focus mechanism to fetch information for each. This modularized view with the focus binds the model with the computationally capable Turing machines. And as a final remark, this paper constructively shows that the computational complexity of the model is at least, if not surpass, that of a universal Turing machine.

SOLUTION: (Yet) Another Theoretical Model of Thinking

PROBLEM: The goal of minimizing misclassification error on a training set is often just one of several real-world goals that might be defined on different datasets. For example, one may require a classifier to also make positive predictions at some specified rate for some subpopulation (fairness), or to achieve a specified empirical recall. Other real-world goals include reducing churn with respect to a previously deployed model, or stabilizing online training. In this paper we propose handling multiple goals on multiple datasets by training with dataset constraints, using the ramp penalty to accurately quantify costs, and present an efficient algorithm to approximately optimize the resulting non-convex constrained optimization problem. Experiments on both benchmark and real-world industry datasets demonstrate the effectiveness of our approach.

SOLUTION:
Satisfying Real-world Goals with Dataset Constraints