The sample complexity of multi-distribution learning

• URL: http://arxiv.org/abs/2312.04027v2
• Date: Mon, 29 Jan 2024 02:17:38 GMT
• Title: The sample complexity of multi-distribution learning
• Authors: Binghui Peng
• Abstract summary: We show that an algorithm of sample complexity $widetildeO((d+k)epsilon-2) cdot (k/epsilon)o(1)$ resolves the COLT 2023 open problem of Awasthi, Haghtalab and Zhao.
• Score: 17.45683822446751
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Multi-distribution learning generalizes the classic PAC learning to handle data coming from multiple distributions. Given a set of $k$ data distributions and a hypothesis class of VC dimension $d$, the goal is to learn a hypothesis that minimizes the maximum population loss over $k$ distributions, up to $\epsilon$ additive error. In this paper, we settle the sample complexity of multi-distribution learning by giving an algorithm of sample complexity $\widetilde{O}((d+k)\epsilon^{-2}) \cdot (k/\epsilon)^{o(1)}$. This matches the lower bound up to sub-polynomial factor and resolves the COLT 2023 open problem of Awasthi, Haghtalab and Zhao [AHZ23].

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