一阶光滑Optimization解黑箱非光滑问题的幂
The Power of First-Order Smooth Optimization for Black-Box Non-Smooth Problems
摘要：
在过去的十年中，黑盒凸优化的无约束/零阶方法得到了广泛的研究，主要集中在Oracle调用复杂性上。在本文中，除了预言的复杂性，我们还专注于迭代的复杂性，并提出了一个通用的方法，最佳的一阶方法的基础上，允许在一个黑盒时尚获得新的零阶算法的非光滑凸优化问题。我们的方法不仅导致最佳的预言复杂性，但也允许获得类似的一阶方法，这反过来又允许利用并行计算，以加速我们的算法的收敛迭代复杂性。我们还详细介绍了随机最优化问题，鞍点问题和分布式优化的扩展。
英文摘要：
Gradient-free/zeroth-order methods for black-box convex optimization have been extensively studied in the last decade with the main focus on oracle calls complexity. In this paper, besides the oracle complexity, we focus also on iteration complexity, and propose a generic approach that, based on optimal first-order methods, allows to obtain in a black-box fashion new zeroth-order algorithms for non-smooth convex optimization problems. Our approach not only leads to optimal oracle complexity, but also allows to obtain iteration complexity similar to first-order methods, which, in turn, allows to exploit parallel computations to accelerate the convergence of our algorithms. We also elaborate on extensions for stochastic optimization problems, saddle-point problems, and distributed optimization.
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