A Screening Strategy for Structured Optimization Involving Nonconvex $\ell_{q,p}$ Regularization

In this paper, we develop a simple yet effective screening rule strategy to improve the computational efficiency in solving structured optimization involving nonconvex $\ell_{q,p}$ regularization. Based on an iteratively reweighted $\ell_1$ (IRL1) framework, the proposed screening rule works like a preprocessing module that potentially removes the inactive groups before starting the subproblem solver, thereby reducing the computational time in total. This is mainly achieved by heuristically exploiting the dual subproblem information during each iteration.Moreover, we prove that our screening rule can remove all inactive variables in a finite number of iterations of the IRL1 method. Numerical experiments illustrate the efficiency of our screening rule strategy compared with several state-of-the-art algorithms.

Traffic Event Detection as a Slot Filling Problem

In this paper, we introduce the new problem of extracting fine-grained traffic information from Twitter streams by also making publicly available the two (constructed) traffic-related datasets from Belgium and the Brussels capital region. In particular, we experiment with several models to identify (i) whether a tweet is traffic-related or not, and (ii) in the case that the tweet is traffic-related to identify more fine-grained information regarding the event (e.g., the type of the event, where the event happened). To do so, we frame (i) the problem of identifying whether a tweet is a traffic-related event or not as a text classification subtask, and (ii) the problem of identifying more fine-grained traffic-related information as a slot filling subtask, where fine-grained information (e.g., where an event has happened) is represented as a slot/entity of a particular type. We propose the use of several methods that process the two subtasks either separately or in a joint setting, and we evaluate the effectiveness of the proposed methods for solving the traffic event detection problem. Experimental results indicate that the proposed architectures achieve high performance scores (i.e., more than 95% in terms of F$_{1}$ score) on the constructed datasets for both of the subtasks (i.e., text classification and slot filling) even in a transfer learning scenario. In addition, by incorporating tweet-level information in each of the tokens comprising the tweet (for the BERT-based model) can lead to a performance improvement for the joint setting.

An Iteratively Reweighted Method for Sparse Optimization on Nonconvex $\ell_{p}$ Ball

This paper is intended to solve the nonconvex $\ell_{p}$-ball constrained nonlinear optimization problems. An iteratively reweighted method is proposed, which solves a sequence of weighted $\ell_{1}$-ball projection subproblems. At each iteration, the next iterate is obtained by moving along the negative gradient with a stepsize and then projecting the resulted point onto the weighted $\ell_{1}$ ball to approximate the $\ell_{p}$ ball. Specifically, if the current iterate is in the interior of the feasible set, then the weighted $\ell_{1}$ ball is formed by linearizing the $\ell_{p}$ norm at the current iterate. If the current iterate is on the boundary of the feasible set, then the weighted $\ell_{1}$ ball is formed differently by keeping those zero components in the current iterate still zero. In our analysis, we prove that the generated iterates converge to a first-order stationary point. Numerical experiments demonstrate the effectiveness of the proposed method.

Effcient Projection Onto the Nonconvex $\ell_p$-ball

This paper primarily focuses on computing the Euclidean projection of a vector onto the $\ell_{p}$-ball with $p\in(0,1)$. Such a problem emerges as the core building block in many signal processing and machine learning applications because of its ability to promote sparsity, yet it is challenging to solve due to its nonconvex and nonsmooth nature. First-order necessary optimality conditions of this problem are derived using Fr\'echet normal cone. We develop a novel numerical approach for computing the stationary point through solving a sequence of projections onto the reweighted $\ell_{1}$-balls. This method is shown to converge uniquely under mild conditions and has a worst-case $O(1/\sqrt{k})$ convergence rate. Numerical experiments demonstrate the efficiency of our proposed algorithm.

Sparse Optimization for Green Edge AI Inference

With the rapid upsurge of deep learning tasks at the network edge, effective edge artificial intelligence (AI) inference becomes critical to provide low-latency intelligent services for mobile users via leveraging the edge computing capability. In such scenarios, energy efficiency becomes a primary concern. In this paper, we present a joint inference task selection and downlink beamforming strategy to achieve energy-efficient edge AI inference through minimizing the overall power consumption consisting of both computation and transmission power consumption, yielding a mixed combinatorial optimization problem. By exploiting the inherent connections between the set of task selection and group sparsity structural transmit beamforming vector, we reformulate the optimization as a group sparse beamforming problem. To solve this challenging problem, we propose a log-sum function based three-stage approach. By adopting the log-sum function to enhance the group sparsity, a proximal iteratively reweighted algorithm is developed. Furthermore, we establish the global convergence analysis and provide the ergodic worst-case convergence rate for this algorithm. Simulation results will demonstrate the effectiveness of the proposed approach for improving energy efficiency in edge AI inference systems.