Zeroth-order optimization algorithms are an attractive alternative for stochastic optimization problems, when gradient computations are expensive or when closed-form loss functions are not available. Recently, there has been a surge of activity in utilizing zeroth-order optimization algorithms in myriads of applications including black-box adversarial attacks on machine learning frameworks, reinforcement learning, and simulation-based optimization, to name a few. In addition to utilizing the simplicity of a typical zeroth-order optimization scheme, distributed implementations of zeroth-order schemes so as to exploit data parallelizability are getting significant attention recently. This article presents an overview of recent work in the area of distributed zeroth-order optimization, focusing on constrained optimization settings and algorithms built around the Frank–Wolfe framework. In particular, we review different types of architectures, from master–worker-based decentralized to fully distributed, and describe appropriate zeroth-order projection-free schemes for solving constrained stochastic optimization problems catered to these architectures. We discuss performance issues including convergence rates and dimension dependence. In addition, we also focus on more refined extensions such as by employing variance reduction and describe and quantify convergence rates for a variance-reduced decentralized zeroth-order optimization method inspired by martingale difference sequences. We discuss limitations of zeroth-order optimization frameworks in terms of dimension dependence. Finally, we illustrate the use of distributed zeroth-order algorithms in the context of adversarial attacks on deep learning models.

中文翻译：

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去中心化零阶约束随机优化算法：Frank-Wolfe 及其变体应用于黑盒对抗攻击

当梯度计算成本高昂或闭式损失函数不可用时，零阶优化算法是随机优化问题的一种有吸引力的替代方法。最近，在无数应用中使用零阶优化算法的活动激增，包括对机器学习框架的黑盒对抗攻击、强化学习和基于模拟的优化，仅举几例。除了利用典型零阶优化方案的简单性之外，零阶方案的分布式实现以利用数据可并行性最近得到了极大的关注。本文概述了分布式零阶优化领域的最新工作，专注于围绕 Frank-Wolfe 框架构建的约束优化设置和算法。特别是，我们回顾了不同类型的架构，从基于 master-worker 的分散到完全分布式，并描述了适当的零阶无投影方案，用于解决满足这些架构的约束随机优化问题。我们讨论性能问题，包括收敛速度和维度相关性。此外，我们还专注于更精细的扩展，例如通过采用方差减少并描述和量化方差减少的分散零阶优化方法的收敛率，该方法受鞅差分序列的启发。我们讨论了零阶优化框架在维度依赖方面的局限性。最后，