Multi-agent distributed consensus optimization problems arise in many signal processing applications. Recently, the alternating direction method of multipliers (ADMM) has been used for solving this family of problems. ADMM based distributed optimization method is shown to have faster convergence rate compared with classic methods based on consensus subgradient, but can be computationally expensive, especially for problems with complicated structures or large dimensions. In this paper, we propose lowcomplexity algorithms that can reduce the overall computational cost of consensus ADMM by an order of magnitude for certain large-scale problems. Central to the proposed algorithms is the use of an inexact step for each ADMM update, which enables the agents to perform cheap computation at each iteration. Our convergence analyses show that the proposed methods converge well under some convexity assumptions. Numerical results show that the proposed algorithms offer considerably lower computational complexity than the standard ADMM based distributed optimization methods.

Aiming at solving large-scale optimization problems, this paper studies distributed optimization methods based on the alternating direction method of multipliers (ADMM). By formulating the optimization problem as a consensus problem, the ADMM can be used to solve the consensus problem in a fully parallel fashion over a computer network with a star topology. However, traditional synchronized computation does not scale well with the problem size, as the speed of the algorithm is limited by the slowest workers. This is particularly true in a heterogeneous network where the computing nodes experience different computation and communication delays. In this paper, we propose an asynchronous distributed ADMM (AD-ADMM) which can effectively improve the time efficiency of distributed optimization. Our main interest lies in analyzing the convergence conditions of the AD-ADMM, under the popular partially asynchronous model, which is defined based on a maximum tolerable delay of the network. Specifically, by considering general and possibly non-convex cost functions, we show that the AD-ADMM is guaranteed to converge to the set of Karush-Kuhn-Tucker (KKT) points as long as the algorithm parameters are chosen appropriately according to the network delay. We further illustrate that the asynchrony of the ADMM has to be handled with care, as slightly modifying the implementation of the AD-ADMM can jeopardize the algorithm convergence, even under the standard convex setting.

Extreme multi-label learning (XML) or classification has been a practical and important problem since the boom of big data. The main challenge lies in the exponential label space which involves 2 L possible label sets especially when the label dimension L is huge, e.g., in millions for Wikipedia labels. This paper is motivated to better explore the label space by originally establishing an explicit label graph. In the meanwhile, deep learning has been widely studied and used in various classification problems including multi-label classification, however it has not been properly introduced to XML, where the label space can be as large as in millions. In this paper, we propose a practical deep embedding method for extreme multi-label classification, which harvests the ideas of non-linear embedding and graph priors-based label space modeling simultaneously. Extensive experiments on public datasets for XML show that our method performs competitive against state-of-the-art result.

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Consider the problem of minimizing the sum of a smooth convex function and a separable nonsmooth convex function subject to linear coupling constraints. Problems of this form arise in many contemporary applications including signal processing, wireless networking and smart grid provisioning. Motivated by the huge size of these applications, we propose a new class of first order primal-dual algorithms called the block successive upper-bound minimization method of multipliers (BSUM-M) to solve this family of problems. The BSUM-M updates the primal variable blocks successively by minimizing locally tight upper-bounds of the augmented Lagrangian of the original problem, followed by a gradient type update for the dual variable in closed form. We show that under certain regularity conditions, and when the primal block variables are updated in either a deterministic or a random fashion, the BSUM-M converges to the set of optimal solutions. Moreover, in the absence of linear constraints, we show that the BSUM-M, which reduces to the block successive upper-bound minimization (BSUM [1]) method, is capable of linear convergence without strong convexity.

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Consider the problem of minimizing the sum of a smooth convex function and a separable nonsmooth convex function subject to linear coupling constraints. Problems of this form arise in many contemporary applications, including signal processing, wireless networking, and smart grid provisioning. Motivated by the huge size of these applications, we propose a new class of first-order primal–dual algorithms called the block successive upper-bound minimization method of multipliers (BSUM-M) to solve this family of problems. The BSUM-M updates the primal variable blocks successively by minimizing locally tight upper bounds of the augmented Lagrangian of the original problem, followed by a gradient-type update for the dual variable in closed form. We show that under certain regularity conditions, and when the primal block variables are updated in either a deterministic or a random fashion, the BSUM-M converges to a point in the set of optimal solutions. Moreover, in the absence of linear constraints and under similar conditions as in the previous result, we show that the randomized BSUM-M (which reduces to the randomized block successive upper-bound minimization method) converges at an asymptotically linear rate without relying on strong convexity.

Along with the proliferation of Artificial Intelligence (AI) and Internet of Things (IoT) techniques, various kinds of adversarial attacks are increasingly emerging to fool Deep Neural Networks (DNNs) used by Industrial IoT (IIoT) applications. Due to biased training data or vulnerable underlying models, imperceptible modifications on inputs made by adversarial attacks may result in devastating consequences. Although existing methods are promising in defending such malicious attacks, most of them can only deal with limited existing attack types, which makes the deployment of large-scale IIoT devices a great challenge. To address this problem, we present an effective federated defense approach named FDA 3 that can aggregate defense knowledge against adversarial examples from different sources. Inspired by federated learning, our proposed cloudbased architecture enables the sharing of defense capabilities against different attacks among IIoT devices. Comprehensive experimental results show that the generated DNNs by our approach can not only resist more malicious attacks than existing attack-specific adversarial training methods, but also can prevent IIoT applications from new attacks.