Paper
Is Multi-Distribution Learning as Easy as PAC Learning: Sharp Rates with Bounded Label Noise
Authors
Rafael Hanashiro, Abhishek Shetty, Patrick Jaillet
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 $1/ε$ 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 $k/ε^2$, 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 complexity incurs a \textit{multiplicative} penalty in $k$. This establishes a \textit{statistical} separation between random classification noise and Massart noise, highlighting a fundamental barrier unique to learning from multiple sources.
Metadata
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Raw Data (Debug)
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"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2602.21039v1</id>\n <title>Is Multi-Distribution Learning as Easy as PAC Learning: Sharp Rates with Bounded Label Noise</title>\n <updated>2026-02-24T16:00:15Z</updated>\n <link href='https://arxiv.org/abs/2602.21039v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2602.21039v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>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 $1/ε$ 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 $k/ε^2$, 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.\n Finally, we prove that when competing with the stronger benchmark of each distribution's optimal Bayes error, the sample complexity incurs a \\textit{multiplicative} penalty in $k$. This establishes a \\textit{statistical} separation between random classification noise and Massart noise, highlighting a fundamental barrier unique to learning from multiple sources.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='stat.ML'/>\n <category scheme='http://arxiv.org/schemas/atom' term='cs.LG'/>\n <published>2026-02-24T16:00:15Z</published>\n <arxiv:primary_category term='stat.ML'/>\n <author>\n <name>Rafael Hanashiro</name>\n </author>\n <author>\n <name>Abhishek Shetty</name>\n </author>\n <author>\n <name>Patrick Jaillet</name>\n </author>\n </entry>"
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