随机搜索在噪声函数优化中更高效，且可加速收敛。
Stochastic Optimization with Random Search
- 利用平移不变性平衡噪声与方差，提升稳定性。
- 弱光滑性假设下仍有效，强假设下收敛更快。
- 适合噪声大、无梯度的优化场景，如强化学习。
我们重新审视仅依赖噪声函数评估的随机优化中的随机搜索方法。研究表明，该方法在比以往更弱的光滑性假设下依然有效，更强的假设可带来更优的收敛保证。在有限求和设置中，我们设计了一种方差缩减变体，通过利用多个样本加速收敛。分析基于一个简单的平移不变性性质，为噪声平衡与方差降低提供了理论依据。
原文摘要 · Abstract (English)
We revisit random search for stochastic optimization, where only noisy function evaluations are available. We show that the method works under weaker smoothness assumptions than previously considered, and that stronger assumptions enable improved guarantees. In the finite-sum setting, we design a variance-reduced variant that leverages multiple samples to accelerate convergence. Our analysis relies on a simple translation invariance property, which provides a principled way to balance noise and reduce variance.
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