在目标函数嘈杂、不规则或两者时，一类无梯度优化方案的收敛性
Convergence of a class of gradient-free optimisation schemes when the objective function is noisy, irregular, or both
AI总结：
本文研究了在目标函数嘈杂或不规则时，一类无梯度优化算法的收敛性，通过分析和实验展示了其在机器学习中的应用。
摘要：
我们研究了一类迭代算法的收敛性质，这些算法旨在最小化一个可能非光滑且嘈杂的目标函数，该函数可能在代数上难以处理，其值可能作为黑箱的输出获得。考虑的算法可以归入广义梯度下降递归的框架下，其中梯度是目标函数的光滑近似梯度。我们开发的框架包括模型基于和 mollification 方法作为特殊情况，这两种方法是零阶优化的两种经典方法。收敛结果是在非常弱的正则性假设下获得的，并涉及平滑程度和参数更新中步长大小之间的权衡。正如预期的那样，随机情况需要额外的假设。我们通过机器学习中的一个具有挑战性的分类示例来说明这些算法和收敛结果的相关性。
英文摘要：
We investigate the convergence properties of a class of iterative algorithms designed to minimize a potentially non-smooth and noisy objective function, which may be algebraically intractable and whose values may be obtained as the output of a black box. The algorithms considered can be cast under the umbrella of a generalised gradient descent recursion, where the gradient is that of a smooth approximation of the objective function. The framework we develop includes as special cases model-based and mollification methods, two classical approaches to zero-th order optimisation. The convergence results are obtained under very weak assumptions on the regularity of the objective function and involve a trade-off between the degree of smoothing and size of the steps taken in the parameter updates. As expected, additional assumptions are required in the stochastic case. We illustrate the relevance of these algorithms and our convergence results through a challenging classification example from machine learning.
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