Derivative-free optimization algorithms play an important role in scientific and engineering design optimization problems, especially when derivative information is not accessible. In this paper, we study the framework of classification-based derivative-free optimization algorithms. By introducing a concept called hypothesis-target shattering rate, we revisit the computational complexity upper bound of this type of algorithms. Inspired by the revisited upper bound, we propose an algorithm named "RACE-CARS", which adds a random region-shrinking step compared with "SRACOS" (Hu et al., 2017).. We further establish a theorem showing the acceleration of region-shrinking. Experiments on the synthetic functions as well as black-box tuning for language-model-as-a-service demonstrate empirically the efficiency of "RACE-CARS". An ablation experiment on the introduced hyperparameters is also conducted, revealing the mechanism of "RACE-CARS" and putting forward an empirical hyperparameter-tuning guidance.

翻译：无导数优化算法在科学与工程设计优化问题中发挥着重要作用，尤其在导数信息不可获取时。本文研究了基于分类的无导数优化算法框架。通过引入一个称为“假设-目标破碎率”的概念，我们重新审视了此类算法的计算复杂度上界。受该上界的启发，我们提出了一种名为“RACE-CARS”的算法，该算法在“SRACOS”（Hu等人，2017）的基础上增加了一个随机区域收缩步骤。我们进一步建立了一个定理，证明了区域收缩的加速效果。在合成函数以及语言模型即服务的黑箱调优实验上，实证了“RACE-CARS”的效率。同时，对所引入的超参数进行了消融实验，揭示了“RACE-CARS”的机制，并提出了经验性的超参数调优指导。