Sample-Adaptivity Tradeoff in On-Demand Sampling
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914164396523520 |
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| author | Haghtalab, Nika Montasser, Omar Qiao, Mingda |
| author_facet | Haghtalab, Nika Montasser, Omar Qiao, Mingda |
| contents | We study the tradeoff between sample complexity and round complexity in on-demand sampling, where the learning algorithm adaptively samples from $k$ distributions over a limited number of rounds. In the realizable setting of Multi-Distribution Learning (MDL), we show that the optimal sample complexity of an $r$-round algorithm scales approximately as $dk^{Θ(1/r)} / ε$. For the general agnostic case, we present an algorithm that achieves near-optimal sample complexity of $\widetilde O((d + k) / ε^2)$ within $\widetilde O(\sqrt{k})$ rounds. Of independent interest, we introduce a new framework, Optimization via On-Demand Sampling (OODS), which abstracts the sample-adaptivity tradeoff and captures most existing MDL algorithms. We establish nearly tight bounds on the round complexity in the OODS setting. The upper bounds directly yield the $\widetilde O(\sqrt{k})$-round algorithm for agnostic MDL, while the lower bounds imply that achieving sub-polynomial round complexity would require fundamentally new techniques that bypass the inherent hardness of OODS. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_15507 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sample-Adaptivity Tradeoff in On-Demand Sampling Haghtalab, Nika Montasser, Omar Qiao, Mingda Machine Learning Data Structures and Algorithms We study the tradeoff between sample complexity and round complexity in on-demand sampling, where the learning algorithm adaptively samples from $k$ distributions over a limited number of rounds. In the realizable setting of Multi-Distribution Learning (MDL), we show that the optimal sample complexity of an $r$-round algorithm scales approximately as $dk^{Θ(1/r)} / ε$. For the general agnostic case, we present an algorithm that achieves near-optimal sample complexity of $\widetilde O((d + k) / ε^2)$ within $\widetilde O(\sqrt{k})$ rounds. Of independent interest, we introduce a new framework, Optimization via On-Demand Sampling (OODS), which abstracts the sample-adaptivity tradeoff and captures most existing MDL algorithms. We establish nearly tight bounds on the round complexity in the OODS setting. The upper bounds directly yield the $\widetilde O(\sqrt{k})$-round algorithm for agnostic MDL, while the lower bounds imply that achieving sub-polynomial round complexity would require fundamentally new techniques that bypass the inherent hardness of OODS. |
| title | Sample-Adaptivity Tradeoff in On-Demand Sampling |
| topic | Machine Learning Data Structures and Algorithms |
| url | https://arxiv.org/abs/2511.15507 |