  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.
