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[2602.22300] Testable Learning of General Halfspaces under Massart Noise
Summary
This paper presents a novel algorithm for testably learning general Massart halfspaces under Gaussian noise, achieving near-optimal error rates and advancing the field of machine learning.
Why It Matters
The research addresses a critical challenge in machine learning: developing algorithms that can learn effectively in the presence of noise. This work not only introduces a new algorithm but also provides insights into the complexity of learning tasks, which is essential for both theoretical understanding and practical applications in data science.
Key Takeaways
- Introduces the first testable learning algorithm for Massart halfspaces with Gaussian noise.
- Achieves a complexity of d^polylog(1/γ, 1/ε), aligning with existing theoretical bounds.
- Utilizes a novel sandwiching polynomial approximation to enhance algorithm performance.
Computer Science > Data Structures and Algorithms arXiv:2602.22300 (cs) [Submitted on 25 Feb 2026] Title:Testable Learning of General Halfspaces under Massart Noise Authors:Ilias Diakonikolas, Giannis Iakovidis, Daniel M. Kane, Sihan Liu View a PDF of the paper titled Testable Learning of General Halfspaces under Massart Noise, by Ilias Diakonikolas and 3 other authors View PDF HTML (experimental) Abstract:We study the algorithmic task of testably learning general Massart halfspaces under the Gaussian distribution. In the testable learning setting, the aim is the design of a tester-learner pair satisfying the following properties: (1) if the tester accepts, the learner outputs a hypothesis and a certificate that it achieves near-optimal error, and (2) it is highly unlikely that the tester rejects if the data satisfies the underlying assumptions. Our main result is the first testable learning algorithm for general halfspaces with Massart noise and Gaussian marginals. The complexity of our algorithm is $d^{\mathrm{polylog}(\min\{1/\gamma, 1/\epsilon \})}$, where $\epsilon$ is the excess error and $\gamma$ is the bias of the target halfspace, which qualitatively matches the known quasi-polynomial Statistical Query lower bound for the non-testable setting. The analysis of our algorithm hinges on a novel sandwiching polynomial approximation to the sign function with multiplicative error that may be of broader interest. Subjects: Data Structures and Algorithms (cs.DS); Machine L...
