We propose a novel algorithm that extends the methods of ball smoothing and
Gaussian smoothing for noisy derivative-free optimization by accounting for the
heterogeneous curvature of the objective function. The algorithm dynamically
adapts the shape of the smoothing kernel to approximate the Hessian of the
objective function around a local optimum. This approach significantly reduces
the error in estimating the gradient from noisy evaluations through sampling.
We demonstrate the efficacy of our method through numerical experiments on
artificial problems. Additionally, we show improved performance when tuning
NP-hard combinatorial optimization solvers compared to existing
state-of-the-art heuristic derivative-free and Bayesian optimization methods.

提出了一种创新算法，通过考虑目标函数的异质曲率，将球面平滑和高斯平滑方法扩展到噪声无导数优化中，动态调整平滑核的形状以逼近局部最优点周围的海森矩阵，从而通过采样大大减小了噪声评估中梯度估计的误差。通过对人工问题的数值实验展示了该方法的有效性，并展示了与现有的最先进启发式无导数和贝叶斯优化方法相比，在调整 NP - 难组合优化求解器时的改进性能。