Black-box optimization of noisy functions with unknown smoothness

2026-05-04

AI Summary

This work addresses high-dimensional black-box global optimization under noisy function evaluations and unknown local smoothness. It proposes and implements the Parallel Optimistic Optimization (POO) algorithm, which dispenses with prior knowledge of the target function’s smoothness near the optimum. By integrating multi-scale search with an adaptive mechanism through a parallel optimistic optimization strategy, POO achieves robust and efficient optimization without requiring smoothness assumptions. Theoretical analysis shows that after $n$ function evaluations, POO incurs an optimization error at most a $\sqrt{\ln n}$ factor worse than that of the best-known algorithm assuming known smoothness. This result eliminates the traditional reliance on prior smoothness information, thereby extending applicability to a broader class of challenging optimization problems.

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.

Problem

• black-box optimization
• noisy functions
• unknown smoothness
• global optima
• function evaluation

Innovation

• black-box optimization
• unknown smoothness
• noisy functions
• adaptive algorithm
• POO