{"ID":2839601,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.15507","arxiv_id":"2511.15507","title":"Sample-Adaptivity Tradeoff in On-Demand Sampling","abstract":"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.","short_abstract":"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 a...","url_abs":"https://arxiv.org/abs/2511.15507","url_pdf":"https://arxiv.org/pdf/2511.15507v1","authors":"[\"Nika Haghtalab\",\"Omar Montasser\",\"Mingda Qiao\"]","published":"2025-11-19T14:59:47Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.DS\",\"stat.ML\"]","methods":"[]","has_code":false}