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[2602.21039] Is Multi-Distribution Learning as Easy as PAC Learning: Sharp Rates with Bounded Label Noise
Summary
This paper investigates the complexities of multi-distribution learning, revealing that achieving fast learning rates is inherently more challenging than in single-task learning, particularly under bounded label noise conditions.
Why It Matters
Understanding the limitations of multi-distribution learning is crucial for developing more effective machine learning models that can generalize across various data sources. This research highlights the statistical barriers faced when learning from heterogeneous data, which is increasingly relevant in today's data-rich environments.
Key Takeaways
- Multi-distribution learning incurs slower rates than single-task learning, scaling with the number of distributions.
- Bounded label noise presents unique challenges that complicate learning across multiple sources.
- A structured hypothesis-testing framework is essential for understanding the statistical costs involved.
- Learning each distribution separately may be necessary to achieve optimal performance.
- The study establishes a statistical separation between random classification noise and Massart noise.
Statistics > Machine Learning arXiv:2602.21039 (stat) [Submitted on 24 Feb 2026] Title:Is Multi-Distribution Learning as Easy as PAC Learning: Sharp Rates with Bounded Label Noise Authors:Rafael Hanashiro, Abhishek Shetty, Patrick Jaillet View a PDF of the paper titled Is Multi-Distribution Learning as Easy as PAC Learning: Sharp Rates with Bounded Label Noise, by Rafael Hanashiro and 2 other authors View PDF HTML (experimental) Abstract:Towards understanding the statistical complexity of learning from heterogeneous sources, we study the problem of multi-distribution learning. Given $k$ data sources, the goal is to output a classifier for each source by exploiting shared structure to reduce sample complexity. We focus on the bounded label noise setting to determine whether the fast $1/\epsilon$ rates achievable in single-task learning extend to this regime with minimal dependence on $k$. Surprisingly, we show that this is not the case. We demonstrate that learning across $k$ distributions inherently incurs slow rates scaling with $k/\epsilon^2$, even under constant noise levels, unless each distribution is learned separately. A key technical contribution is a structured hypothesis-testing framework that captures the statistical cost of certifying near-optimality under bounded noise-a cost we show is unavoidable in the multi-distribution setting. Finally, we prove that when competing with the stronger benchmark of each distribution's optimal Bayes error, the sample complexi...
