Dynamic Anisotropic Smoothing for Noisy Derivative-Free Optimization

TL;DR

This paper introduces a dynamic anisotropic smoothing algorithm for noisy derivative-free optimization that adapts to the local curvature, improving gradient estimation and optimization performance.

Contribution

It extends existing smoothing methods by dynamically shaping the kernel to better approximate the Hessian, enhancing accuracy in noisy settings.

Findings

Reduces gradient estimation error in noisy evaluations

Improves tuning of NP-hard combinatorial solvers

Outperforms existing heuristic and Bayesian methods

Abstract

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.