arXiv:2502.00753v4 Announce Type: replace-cross Abstract: Smoothness is crucial for attaining fast rates in first-order optimization. However, many optimization problems in modern machine learning involve non-smooth objectives. Recent studies relax the smoothness assumption by allowing the Lipschitz constant of the gradient to grow with respect to the gradient norm, which accommodates a broad range of objectives in practice. Despite this progress, existing generalizations of smoothness are restricted to Euclidean geometry with $\ell_2$-norm and only have theoretical guarantees for optimization
This research addresses fundamental limitations in optimization theory, pushing the boundaries of AI capabilities by improving the efficiency and applicability of machine learning algorithms for non-smooth problems.
Improved optimization techniques could lead to more robust and versatile AI models, particularly in complex, real-world applications where non-smooth objectives are common.
The theoretical understanding and practical application of optimization algorithms are enhanced, potentially enabling faster training and more effective deployment of AI systems in diverse environments.
- · AI researchers
- · Machine learning developers
- · Companies using complex AI for non-Euclidean data
More efficient and effective development of advanced AI models.
Expansion of AI applicability to new problem domains previously hampered by optimization challenges.
Potentially, accelerated progress in various scientific and industrial fields leveraging these improved AI capabilities.
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Read at arXiv cs.LG