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.

翻译：我们研究在存在噪声干扰的函数评估条件下，对任意维函数f进行黑箱优化的问题。该函数假设在其某个全局最优点附近具有局部光滑性，但这种光滑性未知。我们的贡献在于提出一种自适应优化算法——POO（即并行乐观优化），该算法能够处理此类设置。POO的性能几乎与需要已知光滑性的最佳算法相当。此外，POO适用于比先前考虑的更广泛的函数类别，特别是对于那些在非常精确的意义上难以优化的函数。我们提供了POO性能的有限时间分析，表明其经过n次评估后的误差，至多与利用光滑性知识的最佳已知优化算法的误差相差一个sqrt(ln n)因子。