On the Sample Complexity of Active Learning with Membership Queries

2026-09-22

AI Summary

本文探讨了主动学习中合成查询的能力如何影响学习难度，发现某些在池基学习中难以学习的假设类，在允许合成查询后可高效学习，并提出新的分析工具和条件。

Abstract

This work revisits a fundamental question in active learning: how powerful is the ability to synthesize arbitrary queries? Compared to pool-based active learning, where the learner only selects queries from a given unlabeled pool, we find that this seemingly mild change in query ability may dramatically alter the difficulty of statistical learning. In particular, some hypothesis classes that are inherently slow to learn in the pool-based setting, achieving only polynomial error decay in the number of samples, become exponentially learnable once synthesized queries are allowed. This striking gap suggests that membership query synthesis induces a fundamentally different mode of learning, one that is not adequately captured by existing active learning theory and calls for new analytical tools to characterize its complexity. Motivated by this phenomenon, we develop several sufficient conditions, present intriguing examples, and propose a conjectural perspective toward understanding which hypothesis classes admit efficient learning through synthesized queries.

Problem

• active learning
• membership queries
• sample complexity
• hypothesis classes
• statistical learning

Innovation

• Membership Query Synthesis
• Active Learning
• Sample Complexity
• Hypothesis Classes
• Query Ability