Improved maximum noise level estimation in black-box optimization problems

In black-box optimization, accurately estimating the maximum noise level is crucial for robust performance. In this work, we propose a novel approach for improving maximum noise level estimation, focusing on scenarios where only function values (possibly with bounded adversarial noise) are available. Leveraging gradient-free optimization algorithms, we introduce a new noise constraint based on the Lipschitz assumption, enhancing the noise level estimate (or improving error floor) for non-smooth and convex functions. Theoretical analysis and numerical experiments demonstrate the effectiveness of our approach, even for smooth and convex functions. This advancement contributes to enhancing the robustness and efficiency of black-box optimization algorithms in diverse domains such as machine learning and engineering design, where adversarial noise presents a significant challenge.