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Life sciences · Preprint
arXiv · September 8, 2026
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This preprint presents CV-ZOD, a new zeroth-order optimization framework designed to adaptively incorporate directional hints while maintaining robustness to their quality. The authors prove theoretical convergence guarantees that interpolate between first-order O(1/T) and zeroth-order O(d/T) rates depending on hint quality, and demonstrate empirical performance on simulation-based optimization tasks where the method outperforms zeroth-order descent and guided methods as guidance degrades.
Methods paper with theoretical analysis and simulation-based empirical validation. Intervention: Control-Variate Zeroth-Order Descent (CV-ZOD) framework incorporating directional hints via adaptive control variate. Compared with: Classical zeroth-order gradient descent and existing guided optimization methods.
Oracle algorithm achieves convergence rate interpolating between first-order O(1/T) and zeroth-order O(d/T) depending on hint quality Practical CV-ZOD variant achieves oracle guarantee up to logarithmic factors without prior knowledge of hint quality Method demonstrates sustained progress on non-convex landscapes where zeroth-order descent is slower and existing guided methods stall
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This is a theoretical and computational methods paper presenting a novel algorithm with mathematical analysis and empirical validation on simulation tasks, but no clinical or real-world application data to support practice change.
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We study zeroth-order optimization of non-convex functions with the aid of directional hints, which are cheap but potentially inaccurate approximations of the true gradient direction, given by linear subspaces at each iteration. To leverage these hints adaptively while maintaining robustness to their quality, we introduce Control-Variate Zeroth-Order Descent (CV-ZOD), a new framework that refines the classical zeroth-order gradient estimator with a control variate that can be set based on the directional hints. We first show that the oracle algorithm that optimally sets the reference vector and step size at each iteration achieves a convergence rate that interpolates between the first-order $O(1/T)$ rate and the zeroth-order $O(d/T)$ rate, depending on the quality of the hints along the trajectory. We then develop a practical variant of CV-ZOD that achieves the same oracle guarantee up to logarithmic factors, without any prior knowledge of the hint quality. We validate the method empirically on simulation-based scientific optimization tasks, demonstrating sustained progress on non-convex landscapes where zeroth-order descent is slower and existing guided methods stall as guidance deteriorates.
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