New algorithms for learning and testing convex functions over Gaussian space

Researchers have developed new algorithms for learning and testing convex functions in high-dimensional Gaussian spaces. The proposed agnostic proper learning algorithm for Lipschitz convex functions achieves an error of \(\\varepsilon\) with a sample complexity of \(n^{O(1/\\varepsilon^2)}\). Complementary to this, a lower bound of \(n^{\\mathrm{poly}(1/\\varepsilon)}\) samples is established within the correlational statistical query (CSQ) model. The work also presents a tolerant tester for convexity with similar sample complexity and a one-sided tester requiring \(O(\\sqrt{n}/\\varepsilon)^n\) samples. AI

RANK_REASON The cluster contains a research paper detailing new algorithms and theoretical bounds for learning and testing convex functions. [lever_c_demoted from research: ic=1 ai=0.7]

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• arXiv
• CSQ model
• Gaussian space
• Hugging Face
• Lipschitzness
• Renato Ferreira Pinto Jr.

• paper
• other

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