arXiv Machine Learning By El Mahdi Chayti, Alireza Mirrokni, Martin Jaggi

Partially Informed Stochastic Optimization via Zeroth-Order Residual Tracking

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The paper introduces Partially Informed Stochastic Optimization (PISO), a method that blends an available gradient component with a running estimate of the missing residual. By centering zeroth‑order observations on this estimate, PISO reduces variance to depend on tracking error, yielding a contraction‑based iteration with a clear momentum interpretation. For smooth nonconvex objectives, the authors prove convergence rates that rely only on the residual’s variation and initial magnitude, achieving state‑of‑the‑art function‑evaluation complexities with minimal probe directions and samples, and demonstrating empirical improvements across five benchmark settings.

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