无需知道平滑性，也能高效优化带噪函数。
Black-box optimization of noisy functions with unknown smoothness
- 自适应算法POO自动处理未知平滑性问题。
- 在n次评估后误差仅比已知平滑性的最优算法高√(ln n)倍。
- 适用于难优化函数，适合噪声环境下黑箱优化场景。
我们研究了任意维度函数f的黑箱优化问题，函数值受噪声干扰。假设函数在某个全局最优点附近局部光滑，但该光滑性未知。本文提出自适应优化算法POO（并行乐观优化），可有效应对这一情形。POO的表现几乎等同于已知光滑性时的最佳算法。此外，POO适用的函数类别比以往更广，尤其适用于难以优化的函数。我们提供了POO的有限时间性能分析，表明经过n次评估后，其误差最多比已知光滑性的最优算法高√(ln n)倍。
原文摘要 · Abstract (English)
We study the problem of black-box optimization of a function f of any dimension, given function evaluations perturbed by noise. The function is assumed to be locally smooth around one of its global optima, but this smoothness is unknown. Our contribution is an adaptive optimization algorithm, POO or parallel optimistic optimization, that is able to deal with this setting. POO performs almost as well as the best known algorithms requiring the knowledge of the smoothness. Furthermore, POO works for a larger class of functions than what was previously considered, especially for functions that are difficult to optimize, in a very precise sense. We provide a finite-time analysis of POO's performance, which shows that its error after n evaluations is at most a factor of sqrt(ln n) away from the error of the best known optimization algorithms using the knowledge of the smoothness.
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