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arXiv · 2307.12135

The Sample Complexity of Multi-Distribution Learning for VC Classes

Pranjal Awasthi·Nika Haghtalab·Eric Zhao
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Abstract

Multi-distribution learning is a natural generalization of PAC learning to settings with multiple data distributions. There remains a significant gap between the known upper and lower bounds for PAC-learnable classes. In particular, though we understand the sample complexity of learning a VC dimension d class on $k$ distributions to be $O(\epsilon^{-2} \ln(k)(d + k) + \min\{\epsilon^{-1} dk, \epsilon^{-4} \ln(k) d\})$, the best lower bound is $\Omega(\epsilon^{-2}(d + k \ln(k)))$. We discuss recent progress on this problem and some hurdles that are fundamental to the use of game dynamics in statistical learning.

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Pranjal Awasthi, Nika Haghtalab, Eric Zhao. 2023-07-22. The Sample Complexity of Multi-Distribution Learning for VC Classes. https://arxiv.org/abs/2307.12135

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