Sample-Adaptivity Tradeoff in On-Demand Sampling

Fuente: arXiv
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Main Authors: Haghtalab, Nika, Montasser, Omar, Qiao, Mingda
Format: Preprint
Published: 2025
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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
id 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