arXiv:2606.27082v1 Announce Type: new Abstract: We study the problem of finding stationary points of non-convex functions when access to the objective is provided only through a comparison oracle that, given two points, outputs which has the larger function value. For a twice differentiable $f\colon\mathbb R^n\to\mathbb R$ with Lipschitz gradient and Hessian, we develop an algorithm that visits an $\epsilon$-stationary point using $\widetilde O(n^2/\epsilon^{1.5})$ queries. Our approach uses a subroutine that estimates the normalized Hessian to accuracy $\delta$ using $\widetilde O(n^2\log(1/\
The continuous push for more efficient and robust machine learning algorithms, especially for non-convex optimization, is driven by the increasing complexity of AI models and the need to reduce computational overhead.
This research provides a more efficient comparison-based optimization method for non-convex functions, which could improve the performance and reduce the resource demands of various AI applications, particularly those with opaque objective functions.
Traditional gradient-based optimization methods are supplemented or potentially surpassed in scenarios where gradient information is unavailable or costly, opening new avenues for algorithm design and AI system capabilities.
- · AI/ML researchers
- · Developers of 'black-box' optimization systems
- · Sectors using complex, non-convex machine learning models
- · Cloud computing providers (due to potential efficiency gains)
- · Inefficient gradient-based optimization approaches
- · Computational resources consumed by current methods
More efficient training and deployment of complex AI models, especially in areas with limited data or indirect feedback.
Acceleration of AI research and application development as optimization barriers are lowered.
Potential for new types of AI agents or systems that learn from comparisons rather than explicit objective functions, expanding the scope of 'ai-agents' capabilities.
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Read at arXiv cs.LG