# Active Learning for Cost-Sensitive Classification

arXiv: https://arxiv.org/abs/1703.01014 · HTML: https://mlsanity.com/paper/1703.01014/

## Key facts

- Cited by 41 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Mar 2017.

## Built on by (most cited first, 30 of 41)

- [On Statistical Bias In Active Learning: How and When To Fix It](https://mlsanity.com/paper/2101.11665/) (2021)
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- [Sample Efficient Learning of Predictors that Complement Humans](https://mlsanity.com/paper/2207.09584/) (2022)
- [Making Decisions under Outcome Performativity](https://mlsanity.com/paper/2210.01745/) (2022)
- [Efficient Active Learning with Abstention](https://mlsanity.com/paper/2204.00043/) (2022)
- [Oracle-Efficient Online Learning for Beyond Worst-Case Adversaries](https://mlsanity.com/paper/2202.08549/) (2022)
- [Streaming Active Learning with Deep Neural Networks](https://mlsanity.com/paper/2303.02535/) (2023)
- [Improved Algorithms for Efficient Active Learning Halfspaces with Massart and Tsybakov noise](https://mlsanity.com/paper/2102.05312/) (2021)
- [A Survey on Cost Types, Interaction Schemes, and Annotator Performance Models in Selection Algorithms for Active Learning in Classification](https://mlsanity.com/paper/2109.11301/) (2021)
- [Instance-optimal PAC Algorithms for Contextual Bandits](https://mlsanity.com/paper/2207.02357/) (2022)
- [Adapting to Continuous Covariate Shift via Online Density Ratio Estimation](https://mlsanity.com/paper/2302.02552/) (2023)
- [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)
- [Bayesian Active Learning by Disagreements: A Geometric Perspective](https://mlsanity.com/paper/2105.02543/) (2021)
- [Going Beyond Linear RL: Sample Efficient Neural Function Approximation](https://mlsanity.com/paper/2107.06466/) (2021)
- [Pessimistic Nonlinear Least-Squares Value Iteration for Offline Reinforcement Learning](https://mlsanity.com/paper/2310.01380/) (2023)
- [Promises and Pitfalls of Threshold-based Auto-labeling](https://mlsanity.com/paper/2211.12620/) (2022)
- [Test-Time Matching: Unlocking Compositional Reasoning in Multimodal Models](https://mlsanity.com/paper/2510.07632/) (2025)
- [Towards Costless Model Selection in Contextual Bandits: A Bias-Variance Perspective](https://mlsanity.com/paper/2106.06483/) (2021)
- [Active Testing of Large Language Models via Approximate Neyman Allocation](https://mlsanity.com/paper/2605.10075/) (2026)
- [Horizon-Free and Instance-Dependent Regret Bounds for Reinforcement Learning with General Function Approximation](https://mlsanity.com/paper/2312.04464/) (2023)
- [Mitigating Covariate Shift in Misspecified Regression with Applications to Reinforcement Learning](https://mlsanity.com/paper/2401.12216/) (2024)
- [Revisiting Active Learning under (Human) Label Variation](https://mlsanity.com/paper/2507.02593/) (2025)
- [Corruption Robust Active Learning](https://mlsanity.com/paper/2106.11220/) (2021)
- [Robust Offline Policy Learning with Observational Data from Multiple Sources](https://mlsanity.com/paper/2410.08537/) (2024)
- [Enhancing Cost Efficiency in Active Learning with Candidate Set Query](https://mlsanity.com/paper/2502.06209/) (2025)
- [Towards Multimodal Active Learning: Efficient Learning with Limited Paired Data](https://mlsanity.com/paper/2510.03247/) (2025)
- [Efficient and Reliable Probabilistic Interactive Learning with Structured Outputs](https://mlsanity.com/paper/2202.08566/) (2022)
- [Pixel is All You Need: Adversarial Trajectory-Ensemble Active Learning for Salient Object Detection](https://mlsanity.com/paper/2212.06493/) (2022)

## Abstract (arXiv)

We design an active learning algorithm for cost-sensitive multiclass classification: problems where different errors have different costs. Our algorithm, COAL, makes predictions by regressing to each label's cost and predicting the smallest. On a new example, it uses a set of regressors that perform well on past data to estimate possible costs for each label. It queries only the labels that could be the best, ignoring the sure losers. We prove COAL can be efficiently implemented for any regression family that admits squared loss optimization; it also enjoys strong guarantees with respect to predictive performance and labeling effort. We empirically compare COAL to passive learning and several active learning baselines, showing significant improvements in labeling effort and test cost on real-world datasets.