In many optimization problems arising from scientific, engineering and artificial intelligence applications, objective and constraint functions are available only as the output of a black-box or simulation oracle that does not provide derivative information. Such settings necessitate the use of methods for derivative-free, or zeroth-order, optimization. We provide a review and perspectives on developments in these methods, with an emphasis on highlighting recent developments and on unifying treatment of such problems in the non-linear optimization and machine learning literature. We categorize methods based on assumed properties of the black-box functions, as well as features of the methods. We first overview the primary setting of deterministic methods applied to unconstrained, non-convex optimization problems where the objective function is defined by a deterministic black-box oracle. We then discuss developments in randomized methods, methods that assume some additional structure about the objective (including convexity, separability and general non-smooth compositions), methods for problems where the output of the black-box oracle is stochastic, and methods for handling different types of constraints.

中文翻译：

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无导数优化方法

在科学、工程和人工智能应用产生的许多优化问题中，目标和约束函数仅作为不提供衍生信息的黑盒或模拟预言机的输出可用。这样的设置需要使用无导数或零阶优化的方法。我们对这些方法的发展进行了回顾和展望，重点是强调最近的发展以及在非线性优化和机器学习文献中统一处理这些问题。我们根据黑盒函数的假定属性以及方法的特征对方法进行分类。我们首先概述了应用于无约束的确定性方法的主要设置，目标函数由确定性黑盒预言机定义的非凸优化问题。然后，我们讨论了随机方法的发展，假设一些关于目标的附加结构的方法（包括凸性、可分离性和一般非光滑组合），黑盒预言机的输出是随机的问题的方法，以及处理不同的方法的方法。约束类型。