# Near-Polynomially Competitive Active Logistic Regression

arXiv: https://arxiv.org/abs/2503.05981 · HTML: https://mlsanity.com/paper/2503.05981/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 38 references that are in the map.
- First posted on arXiv 7 Mar 2025.

## Builds on (most cited first, 13 of 13)

- [Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Suffices](https://mlsanity.com/paper/1903.08568/) (2019)
- [On Coresets for Logistic Regression](https://mlsanity.com/paper/1805.08571/) (2018)
- [Learning Graphical Models Using Multiplicative Weights](https://mlsanity.com/paper/1706.06274/) (2017)
- [A Benchmark and Comparison of Active Learning for Logistic Regression](https://mlsanity.com/paper/1611.08618/) (2016)
- [Active Regression via Linear-Sample Sparsification](https://mlsanity.com/paper/1711.10051/) (2017)
- [Coresets for Classification -- Simplified and Strengthened](https://mlsanity.com/paper/2106.04254/) (2021)
- [Improved Algorithms for Agnostic Pool-based Active Classification](https://mlsanity.com/paper/2105.06499/) (2021)
- [On the sample complexity of parameter estimation in logistic regression with normal design](https://mlsanity.com/paper/2307.04191/) (2023)
- [Active Learning for Single Neuron Models with Lipschitz Non-Linearities](https://mlsanity.com/paper/2210.13601/) (2022)
- [Agnostic Active Learning of Single Index Models with Linear Sample Complexity](https://mlsanity.com/paper/2405.09312/) (2024)
- [Active Regression by Stratification](https://mlsanity.com/paper/1410.5920/) (2014)
- [A Competitive Algorithm for Agnostic Active Learning](https://mlsanity.com/paper/2310.18786/) (2023)
- [A Provably Accurate Randomized Sampling Algorithm for Logistic Regression](https://mlsanity.com/paper/2402.16326/) (2024)

## Abstract (arXiv)

We address the problem of active logistic regression in the realizable setting. It is well known that active learning can require exponentially fewer label queries compared to passive learning, in some cases using log frac1eps rather than poly(1/eps) labels to get error eps larger than the optimum. We present the first algorithm that is polynomially competitive with the optimal algorithm on every input instance, up to factors polylogarithmic in the error and domain size. In particular, if any algorithm achieves label complexity polylogarithmic in eps, so does ours. Our algorithm is based on efficient sampling and can be extended to learn more general class of functions. We further support our theoretical results with experiments demonstrating performance gains for logistic regression compared to existing active learning algorithms.