# Nuances in Margin Conditions Determine Gains in Active Learning

arXiv: https://arxiv.org/abs/2110.08418 · HTML: https://mlsanity.com/paper/2110.08418/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 14 references that are in the map.
- First posted on arXiv 16 Oct 2021.

## Builds on (most cited first, 4 of 4)

- [Minimax Analysis of Active Learning](https://mlsanity.com/paper/1410.0996/) (2014)
- [Active Learning from Imperfect Labelers](https://mlsanity.com/paper/1610.09730/) (2016)
- [Adaptivity to Noise Parameters in Nonparametric Active Learning](https://mlsanity.com/paper/1703.05841/) (2017)
- [An Adaptive Strategy for Active Learning with Smooth Decision Boundary](https://mlsanity.com/paper/1711.09294/) (2017)

## Built on by (most cited first, 9 of 9)

- [Efficient Active Learning with Abstention](https://mlsanity.com/paper/2204.00043/) (2022)
- [Active Learning with Neural Networks: Insights from Nonparametric Statistics](https://mlsanity.com/paper/2210.08367/) (2022)
- [Querying Easily Flip-flopped Samples for Deep Active Learning](https://mlsanity.com/paper/2401.09787/) (2024)
- [Nonparametric active learning for cost-sensitive classification](https://mlsanity.com/paper/2310.00511/) (2023)
- [Accounting for Missing Covariates in Heterogeneous Treatment Estimation](https://mlsanity.com/paper/2410.15655/) (2024)
- [Active Learning via Regression Beyond Realizability](https://mlsanity.com/paper/2506.00316/) (2025)
- [Sample Complexity Analysis for Constrained Bilevel Reinforcement Learning](https://mlsanity.com/paper/2602.00282/) (2026)
- [Active learning from positive and unlabeled examples](https://mlsanity.com/paper/2602.02081/) (2026)
- [The Evidence Ladder for Reinforcement Learning in Healthcare: From Retrospective Policies to Trusted Interventions](https://mlsanity.com/paper/2609.23374/) (2026)

## Abstract (arXiv)

We consider nonparametric classification with smooth regression functions, where it is well known that notions of margin in E[Y|X] determine fast or slow rates in both active and passive learning. Here we elucidate a striking distinction between the two settings. Namely, we show that some seemingly benign nuances in notions of margin -- involving the uniqueness of the Bayes classifier, and which have no apparent effect on rates in passive learning -- determine whether or not any active learner can outperform passive learning rates. In particular, for Audibert-Tsybakov's margin condition (allowing general situations with non-unique Bayes classifiers), no active learner can gain over passive learning in commonly studied settings where the marginal on X is near uniform. Our results thus negate the usual intuition from past literature that active rates should improve over passive rates in nonparametric settings.