Sample-Adaptivity Tradeoff in On-Demand Sampling

Nika Haghtalab, Omar Montasser, Mingda Qiao

Keywords: On-demand sampling, multi-distribution learning, adaptivity

TL;DR: We study the tradeoff between sample complexity and round complexity 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 $dk^{\Theta(1/r)} / \epsilon$. For the general agnostic case, we present an algorithm that achieves near-optimal sample complexity of $\widetilde O((d + k) / \epsilon^2)$ 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.

Primary Area: Theory (e.g., control theory, learning theory, algorithmic game theory)

Submission Number: 12742