Black-box optimization of noisy functions with unknown smoothness

TL;DR

This paper introduces POO, an adaptive black-box optimization algorithm for noisy functions with unknown smoothness, achieving near-optimal performance without prior smoothness knowledge.

Contribution

The paper presents POO, an adaptive algorithm that handles unknown smoothness in noisy black-box optimization, extending applicability to more complex functions.

Findings

POO performs nearly as well as algorithms with known smoothness.

Error after n evaluations is within a sqrt(ln n) factor of the best algorithms.

POO works for a broader class of functions, including difficult-to-optimize ones.

Abstract

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.