# An Adaptive Strategy for Active Learning with Smooth Decision Boundary

arXiv: https://arxiv.org/abs/1711.09294 · HTML: https://mlsanity.com/paper/1711.09294/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Nov 2017.

## Built on by (most cited first, 6 of 6)

- [SplineCam: Exact Visualization and Characterization of Deep Network Geometry and Decision Boundaries](https://mlsanity.com/paper/2302.12828/) (2023)
- [Exponential Savings in Agnostic Active Learning through Abstention](https://mlsanity.com/paper/2102.00451/) (2021)
- [Active Learning in Bayesian Neural Networks with Balanced Entropy Learning Principle](https://mlsanity.com/paper/2105.14559/) (2021)
- [Active Learning with Neural Networks: Insights from Nonparametric Statistics](https://mlsanity.com/paper/2210.08367/) (2022)
- [Nuances in Margin Conditions Determine Gains in Active Learning](https://mlsanity.com/paper/2110.08418/) (2021)
- [Active learning from positive and unlabeled examples](https://mlsanity.com/paper/2602.02081/) (2026)

## Abstract (arXiv)

We present the first adaptive strategy for active learning in the setting of classification with smooth decision boundary. The problem of adaptivity (to unknown distributional parameters) has remained opened since the seminal work of Castro and Nowak (2007), which first established (active learning) rates for this setting. While some recent advances on this problem establish adaptive rates in the case of univariate data, adaptivity in the more practical setting of multivariate data has so far remained elusive. Combining insights from various recent works, we show that, for the multivariate case, a careful reduction to univariate-adaptive strategies yield near-optimal rates without prior knowledge of distributional parameters.