arXiv:2405.11454v3 Announce Type: replace Abstract: We study gradient testing and gradient estimation of smooth functions using only a comparison oracle that, given two points, indicates which one has the larger function value. For any smooth $f\colon\mathbb R^n\to\mathbb R$, $\mathbf{x}\in\mathbb R^n$, and $\varepsilon>0$, we design a gradient testing algorithm that determines whether the normalized gradient $\nabla f(\mathbf{x})/\|\nabla f(\mathbf{x})\|$ is $\varepsilon$-close or $2\varepsilon$-far from a given unit vector $\mathbf{v}$ using $O(1)$ queries, as well as a gradient estimation a
The continuous research in machine learning and AI foundational concepts drives constant innovation in optimization techniques, seeking more efficient and robust methods for complex models.
This research addresses fundamental challenges in machine learning optimization, potentially leading to more efficient and less data-intensive ways to train and deploy AI, especially in scenarios with limited information.
New methods for gradient-free optimization could accelerate the development and deployment of AI models by reducing the computational cost and data requirements for certain tasks.
- · AI researchers
- · AI developers
- · Robotics
- · Autonomous systems
- · Inefficient gradient-based optimization techniques
More robust and efficient AI training algorithms become available.
Reduced computational barriers could enable AI development in resource-constrained environments or for novel applications.
This could accelerate the deployment of AI in physical systems where direct gradient information is difficult to obtain, fostering advancements in areas like AI agents and robotics.
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