SPM Article

Zeroth-order (ZO) optimization is a subset of gradient-free optimization that emerges in many signal processing and machine learning (ML) applications. It is used for solving optimization problems similarly to gradient-based methods. However, it does not require the gradient, using only function evaluations. Specifically, ZO optimization iteratively performs three major steps: gradient estimation, descent direction computation, and the solution update. In this article, we provide a comprehensive review of ZO optimization, with an emphasis on showing the underlying intuition, optimization principles, and recent advances in convergence analysis.

Optimization lies at the heart of machine learning (ML) and signal processing (SP). Contemporary approaches based on the stochastic gradient (SG) method are nonadaptive in the sense that their implementation employs prescribed parameter values that need to be tuned for each application. This article summarizes recent research and motivates future work on adaptive stochastic optimization methods, which have the potential to offer significant computational savings when training largescale systems.

Many contemporary applications in signal processing and machine learning give rise to structured nonconvex nonsmooth optimization problems that can often be tackled by simple iterative methods quite effectively. One of the keys to understanding such a phenomenon-and, in fact, a very difficult conundrum even for experts-lies in the study of "stationary points" of the problem in question. Unlike smooth optimization, for which the definition of a stationary point is rather standard, there are myriad definitions of stationarity in nonsmooth optimization.

The articles in this special section focus on nonconvex optimization for signal processing and machine learning. Optimization is now widely recognized as an indispensable tool in signal processing (SP) and machine learning (ML). Indeed, many of the advances in these fields rely crucially on the formulation of suitable optimization models and deployment of efficient numerical optimization algorithms. In the early 2000s, there was a heavy focus on the use of convex optimization techniques to tackle SP and ML applications.

We continue to live through a unique experience in history. Out of concern for each other, we have voluntarily participated in essentially shutting down economic activities across the globe. We have discovered the interdependencies and precariousness of our lives and livelihoods. We have learned who and what is essential or important and have simplified our lives. We have realized the virtue of patience and self-kindness as we navigate the tremendous challenges of working from home and balancing our work obligations and family needs.

The safety and success of autonomous vehicles (AVs) depend on their ability to accurately map and respond to their surroundings in real time. One of the most promising recent technologies for depth mapping is single-photon lidar (SPL), which measures the time of flight of individual photons. The long-range capabilities (kilometers), excellent depth resolution (centimeters), and use of low-power (eye-safe) laser sources renders this modality a strong candidate for use in AVs. 

The articles in this special section were focused on the current state of the art as well as emerging trends in the design, development, and deployment of sensing and perception technologies for autonomous and automated driving. Such technologies include camera, ultrasound, Global Navigation Satellite System-, lidar-, and radar-based platforms integrat ing signa l processing components to process the acquired data and extract information to be used for recognition, navigation, and situational awareness.