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A Primer on Zeroth-Order Optimization in Signal Processing and Machine Learning (2006.06224v2)

Published 11 Jun 2020 in cs.LG, eess.SP, and stat.ML

Abstract: Zeroth-order (ZO) optimization is a subset of gradient-free optimization that emerges in many signal processing and machine learning 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 solution update. In this paper, we provide a comprehensive review of ZO optimization, with an emphasis on showing the underlying intuition, optimization principles and recent advances in convergence analysis. Moreover, we demonstrate promising applications of ZO optimization, such as evaluating robustness and generating explanations from black-box deep learning models, and efficient online sensor management.

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Authors (6)
  1. Sijia Liu (204 papers)
  2. Pin-Yu Chen (311 papers)
  3. Bhavya Kailkhura (108 papers)
  4. Gaoyuan Zhang (18 papers)
  5. Alfred Hero (67 papers)
  6. Pramod K. Varshney (135 papers)
Citations (191)

Summary

  • The paper presents a comprehensive review of gradient-free techniques that approximate gradients via finite differences for black-box optimization challenges.
  • It details a systematic framework involving gradient estimation, descent direction computation, and solution updates to handle both unconstrained and constrained problems.
  • The work highlights applications in adversarial machine learning and sensor management, discussing convergence rates and query complexities to guide practical implementations.

Overview of Zeroth-Order Optimization in Signal Processing and Machine Learning

The paper "A Primer on Zeroth-Order Optimization in Signal Processing and Machine Learning" provides an extensive review of Zeroth-Order (ZO) optimization, a class of gradient-free optimization techniques pertinent to a wide array of applications in signal processing and machine learning. Unlike traditional optimization methods that rely on gradient information, ZO optimization leverages function evaluations to approximate gradients. This approach is especially useful in scenarios involving black-box models where direct gradient computation is infeasible or computationally prohibitive.

Key Concepts and Methodologies

The authors categorize ZO optimization into three primary steps: gradient estimation, descent direction computation, and solution update. Gradient estimation is achieved through techniques such as finite difference approximations, which have evolved over decades since their introduction in the mid-20th century. The paper elaborates on various types of gradient estimators, including $1$-point and multi-point estimators, highlighting their statistical properties and approximation errors. These estimators form the basis of ZO algorithms that can mirror first-order methods, allowing adaptation to different optimization scenarios without explicit gradient information.

The paper also presents a generic ZO optimization framework applicable to stochastic optimization problems. This framework serves as a blueprint for developing specific ZO algorithms suited to both unconstrained and constrained optimization. It further discusses the convergence rates and function query complexities associated with these methods, offering insights into their practical applications.

Applications of ZO Optimization

ZO optimization has been applied successfully in areas such as adversarial machine learning and sensor management. In black-box adversarial attack scenarios, ZO optimization reveals vulnerabilities in deep learning models without accessing internal gradient information, thus simulating realistic attack conditions. These methods have demonstrated substantial efficacy in generating adversarial examples while maintaining query efficiency, a significant concern in practical deployments.

In sensor management, ZO optimization aids in resource allocation across sensor networks by minimizing computational overhead and circumventing gradient-related bottlenecks. By optimizing the tradeoff between sensor activation and estimation accuracy, ZO methods facilitate efficient parameter estimation in dynamic networks.

Implications and Future Directions

The advancement and application of ZO optimization methods pose significant implications for both theoretical exploration and practical implementation in AI and signal processing domains. These techniques offer researchers tools for effectively addressing complex optimization challenges without the need for gradient information, thereby expanding the scope of feasible problems to tackle.

Despite the progress, the paper identifies several challenges and open questions in ZO optimization research, such as extending the approach to non-smooth and black-box constrained problems, enhancing privacy in distributed learning, and reducing function query complexity. Addressing these challenges could unlock further potential applications and improve the efficiency and robustness of ZO methods, providing a critical component of future AI development.