arXiv:2605.30960v1 Announce Type: new Abstract: Accurate Zeroth-Order (ZO) Hessian estimation is a cornerstone of derivative-free methods, essential for tasks such as bilevel optimization, Bayesian inference, and uncertainty quantification. However, obtaining a complete suite of low-variance estimators for the Hessian and its inverse in high-dimensional settings remains a significant challenge. To address this, we propose a unified framework that reinterprets ZO Hessian approximation through the lens of single-step Policy Optimization (PO). This perspective establishes a theoretical equivalenc
The continuous growth in AI model complexity and the increasing demand for efficient, derivative-free optimization methods in diverse high-dimensional applications necessitate more robust Hessian estimation techniques.
Improved zeroth-order Hessian approximation can significantly enhance the performance and applicability of AI models in scenarios where traditional gradient information is unavailable or computationally expensive, such as complex real-world systems.
This research provides a theoretical framework that could lead to more accurate and low-variance Hessian estimators, potentially making AI optimization more efficient and reliable, especially in settings like bilevel optimization and uncertainty quantification.
- · AI researchers
- · Developers of derivative-free optimization algorithms
- · Industries relying on complex AIin high-dimensional spaces
More efficient and robust AI model training and deployment for specific, challenging tasks.
Accelerated development of new AI applications in fields currently limited by optimization difficulties.
Potentially democratized access to advanced AI for users without deep mathematical expertise, as optimization becomes more automated and reliable.
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Read at arXiv cs.LG