Sample-Adaptivity Tradeoff in On-Demand Sampling

2025-11-19

AI Summary

This paper investigates the trade-off between sample complexity and round complexity in multi-distribution learning under on-demand sampling. We propose a novel framework—On-Demand Distribution Sampling (OODS)—that unifies modeling for both realizable and universally adversarial settings. Leveraging adaptive sampling, statistical learning theory, and complexity analysis, we design near-optimal algorithms and establish tight upper and lower bounds. In the realizable setting, our algorithm achieves optimal sample complexity $ ilde{O}(d k^{Theta(1/r)} / varepsilon)$; in the adversarial setting, it attains sample complexity $ ilde{O}((d + k)/varepsilon^2)$ within $ ilde{O}(sqrt{k})$ rounds. Crucially, we identify that achieving subpolynomial round complexity necessitates fundamentally new techniques—thereby exposing and overcoming inherent limitations of existing approaches. Our work provides the first rigorous characterization of this trade-off and advances the theoretical foundations of interactive multi-distribution learning.

Technology Category

• Machine Learning: Online Learning & Bandits
• Game Theory and Economic Paradigms: Adversarial Learning
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments

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.

Problem

• Studies tradeoff between sample complexity and round complexity in on-demand sampling
• Develops algorithms for Multi-Distribution Learning in realizable and agnostic settings
• Introduces Optimization via On-Demand Sampling framework to capture adaptivity tradeoffs

Innovation

• Multi-round adaptive sampling from k distributions
• OODS framework abstracts sample-adaptivity tradeoffs
• Near-optimal sample complexity with sublinear round complexity