Dynamic Anisotropic Smoothing for Noisy Derivative-Free Optimization
This work addresses optimization problems where derivatives are unavailable and noise is present, offering incremental improvements for applications like heuristic solver tuning.
The paper tackles noisy derivative-free optimization by proposing a dynamic anisotropic smoothing algorithm that adapts the smoothing kernel shape to approximate the Hessian, reducing gradient estimation error; it demonstrates improved performance in tuning NP-hard combinatorial optimization solvers compared to state-of-the-art methods.
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.