A Distributional-Lifting Theorem for PAC Learning
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912442207961088 |
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| author | Blanc, Guy Lange, Jane Strassle, Carmen Tan, Li-Yang |
| author_facet | Blanc, Guy Lange, Jane Strassle, Carmen Tan, Li-Yang |
| contents | The apparent difficulty of efficient distribution-free PAC learning has led to a large body of work on distribution-specific learning. Distributional assumptions facilitate the design of efficient algorithms but also limit their reach and relevance. Towards addressing this, we prove a distributional-lifting theorem: This upgrades a learner that succeeds with respect to a limited distribution family $\mathcal{D}$ to one that succeeds with respect to any distribution $D^\star$, with an efficiency overhead that scales with the complexity of expressing $D^\star$ as a mixture of distributions in $\mathcal{D}$.
Recent work of Blanc, Lange, Malik, and Tan considered the special case of lifting uniform-distribution learners and designed a lifter that uses a conditional sample oracle for $D^\star$, a strong form of access not afforded by the standard PAC model. Their approach, which draws on ideas from semi-supervised learning, first learns $D^\star$ and then uses this information to lift.
We show that their approach is information-theoretically intractable with access only to random examples, thereby giving formal justification for their use of the conditional sample oracle. We then take a different approach that sidesteps the need to learn $D^\star$, yielding a lifter that works in the standard PAC model and enjoys additional advantages: it works for all base distribution families, preserves the noise tolerance of learners, has better sample complexity, and is simpler. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_16651 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Distributional-Lifting Theorem for PAC Learning Blanc, Guy Lange, Jane Strassle, Carmen Tan, Li-Yang Machine Learning Computational Complexity Data Structures and Algorithms The apparent difficulty of efficient distribution-free PAC learning has led to a large body of work on distribution-specific learning. Distributional assumptions facilitate the design of efficient algorithms but also limit their reach and relevance. Towards addressing this, we prove a distributional-lifting theorem: This upgrades a learner that succeeds with respect to a limited distribution family $\mathcal{D}$ to one that succeeds with respect to any distribution $D^\star$, with an efficiency overhead that scales with the complexity of expressing $D^\star$ as a mixture of distributions in $\mathcal{D}$. Recent work of Blanc, Lange, Malik, and Tan considered the special case of lifting uniform-distribution learners and designed a lifter that uses a conditional sample oracle for $D^\star$, a strong form of access not afforded by the standard PAC model. Their approach, which draws on ideas from semi-supervised learning, first learns $D^\star$ and then uses this information to lift. We show that their approach is information-theoretically intractable with access only to random examples, thereby giving formal justification for their use of the conditional sample oracle. We then take a different approach that sidesteps the need to learn $D^\star$, yielding a lifter that works in the standard PAC model and enjoys additional advantages: it works for all base distribution families, preserves the noise tolerance of learners, has better sample complexity, and is simpler. |
| title | A Distributional-Lifting Theorem for PAC Learning |
| topic | Machine Learning Computational Complexity Data Structures and Algorithms |
| url | https://arxiv.org/abs/2506.16651 |