Dynamic Anisotropic Smoothing for Noisy Derivative-Free Optimization

arXiv:2405.01731v1 Announce Type: new
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 …

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