Active learning for regression reduces labeling costs by selecting the most informative samples. Improved Greedy Sampling is a prominent method that balances feature-space diversity and output-space uncertainty using a static, multiplicative rule. We propose Weighted improved Greedy Sampling (WiGS), which replaces this framework with a dynamic, additive criterion. We formulate weight selection as a reinforcement learning problem, enabling an agent to adapt the exploration-investigation balance throughout learning. Experiments on 18 benchmark datasets and a synthetic environment show WiGS outperforms iGS and other baseline methods in both accuracy and labeling efficiency, particularly in domains with irregular data density where the baseline's multiplicative rule ignores high-error samples in dense regions.
Figures & tables
Method
Weight wx(t)
Dynamic
Adaptive
Random Sampling
NA
×
×
GSx
1
×
×
GSy
0
×
×
iGS
NA
×
×
WiGS - Static Weight (investigation focus)
<0.5
×
×
WiGS - Static Weight (exploration focus)
>0.5
×
×
Table 1: Summary of baseline and proposed methods. wx(t) denotes the weight assigned to the feature-space distance at iteration t in Equation 5 . We distinguish between Dynamic strategies (time-varying based on a fixed schedule) and Adaptive strategies (state-dependent based on learned feedback from the data).
Figure 1: Visualization of the synthetic dataset ( N=1000 ). The high-noise region (trap) at x≈0.85 coincides with high data density.
Figure 2: Performance difference relative to iGS (red line). Values below zero indicate superior performance. The adaptive WiGS-SAC agent and exploration-focused static variants (bottom cluster) consistently outperform the baseline, reducing absolute error by up to 0.05.
Figure 3: Global Performance Heatmap. Values represent the ratio of the Area Under the RMSE Curve (AUC) for each method relative to the iGS baseline. Blue cells ( <1.0 ) indicate superior performance (lower cumulative error), while red cells ( >1.0 ) indicate inferior performance. Notably, the WiGS methods (bottom rows) demonstrate consistent robustness across diverse domains.
Figure 4: Relative Label Efficiency ( Nrel ) aggregated across 20 datasets. The distribution represents the labeling budget required to achieve 70% (blue) and 80% (green) of the total possible performance gain. Values to the left ( <1.0 ) indicate superior efficiency. The adaptive WiGS agents (SAC, MAB) not only require fewer labels to reach these milestones than the iGS baseline, but also exhibit narrower variance, highlighting their robust generalization across different datasets.
Appendix figures & tables21 assets
Supplementary material from the paper’s appendix.
Appendix
Parameter
Value
Optimizer
Adam
Learning Rate ( αlr )
3⋅10−4
Discount Factor ( γ )
0.99
Replay Buffer Size ( B )
10,000
Batch Size
64
Soft Update Rate ( τ )
0.005
Appendix
Table 2: Hyperparameters for the WiGS-SAC agent.
Figure 5: Visualization of the synthetic datasets. Shows N=1000 sample data points (dots) and the true underlying function f(x) (solid line). Shaded regions indicate areas of high noise that overlap with dense data regions from the GMM, creating strategic conflicts between exploration and investigation.
Figure 6: Spatial visualization of the learned weighting policy. Each point represents a selected sample, colored by the average weight wx assigned to it by the WiGS-SAC agent. Red indicates high exploration focus; Blue indicates high investigation focus. The agent learns to decouple the strategy, applying exploration to complex oscillations (vertices) and investigation to linear regions.
Figure 7: Average weight trend for WiGS-SAC on the Two-Regime and Three-Regime dataset. The solid line shows the mean weight across 100 seeds, while the shaded region represents ±1 standard deviation. The persistent high variance demonstrates that the agent remains reactive throughout the learning process, rather than converging to a static heuristic.
Table 3: Statistical significance of performance differences on synthetic datasets. Tables display p-values from pairwise Wilcoxon Signed-Rank Tests comparing Full-Pool RMSE traces across 100 independent trials. A p-value <0.05 indicates a statistically significant difference in performance distributions.
no.
Dataset
Source
Size
Features
1
AutoMPG
UCI ML Repository
392
8
2
Beer
Kaggle
365
5
3
Body Fat
Kaggle
252
13
4
Burbidge - Correct
Burbidge et al. [2007]
1000
1
5
Burbidge - Misspecified
Burbidge et al. [2007]
1000
1
6
Burbidge - Low Noise
Burbidge et al. [2007]
1000
1
Appendix
Table 4: Benchmark datasets used in the experiments.
Figure 8: Full-pool RMSE trace plots for benchmark datasets (Part 1 of 2).
Figure 9: Full-pool RMSE trace plots for benchmark datasets (Part 2 of 2).
Baselines
Advanced Baselines
WiGS (Static/Decay)
WiGS (Adaptive)
Dataset
Rand.
GSx
GSy
iGS
QBC
Uncert.
EMCM
EGAL
0.25
0.75
Lin.
Exp.
MAB(2)
SAC
Beer
11.1
11.5
11.8
12.1
17.1
11.3
10.9
11.9
12.5
12.5
12.4
12.2
12.0
225.0
Bodyfat
6.8
7.0
7.2
7.3
10.4
6.9
6.9
7.1
7.3
7.3
7.3
7.3
7.2
205.8
Burb. Correct
25.9
27.9
28.9
31.7
39.7
27.0
26.4
37.2
36.6
36.6
36.7
36.7
36.5
234.6
Burb. Low Noise
25.3
27.1
28.1
31.3
39.0
26.2
25.3
34.2
36.2
36.4
36.4
36.3
35.7
448.5
Burb. Misspecified
25.0
26.8
27.7
30.9
39.1
26.2
25.5
34.1
35.8
35.9
35.9
35.7
35.4
461.2
Appendix
Table 5: Median runtime (seconds) across simulation seeds. ‘Uncert.’ denotes Uncertainty Sampling.
Figure 10: Random Forest Results (Heatmap): Values represent the ratio of the Area Under the RMSE Curve (AUC) relative to the iGS baseline using a Random Forest Regressor. Blue cells ( <1.0 ) indicate superior performance.
Figure 11: Random Forest Results (Efficiency): Relative Label Efficiency ( Nrel ) aggregated across 20 datasets.
Figure 12: Full-pool Random Forest RMSE trace plots for benchmark datasets (Part 1 of 2).
Figure 13: Full-pool Random Forest RMSE trace plots for benchmark datasets (Part 2 of 2).
Figure 14: Full-pool Correlation Coefficients trace plots for benchmark datasets (Part 1 of 2).
Figure 15: Full-pool Correlation Coefficients trace plots for benchmark datasets (Part 2 of 2).
Figure 16: Variance of the full-pool RMSE trace plots for benchmark datasets (Part 1 of 2).
Figure 17: Variance of the full-pool RMSE trace plots for benchmark datasets (Part 2 of 2).
Figure 18: Robust Relative AUC values comparing active learning strategies under robust feature scaling. The results parallel those observed under standard normalization, indicating the method’s robustness to preprocessing techniques.
Figure 19: Relative Label Efficiency ( Nrel ) aggregated across 20 datasets with a robust normalization. Again, the results are similar to those under standard normalization
Figure 20: Full-pool RMSE trace plots for benchmark datasets with robust normalization (Part 1 of 2).
Figure 21: Full-pool RMSE trace plots for benchmark datasets with robust normalization (Part 2 of 2).
Pool-based sequential active learning for regression (ALR) optimally selects a small number of samples sequentially from a large pool of unlabeled samples to label, so that a more accurate regression model can be constructed under a given labeling budget. Representativeness and diversity, which involve computing the distances among different samples, are important considerations in ALR. However, previous ALR approaches do not incorporate the importance of different features in inter-sample distance computation, resulting in inaccurate distances and hence sub-optimal sample selection. This paper proposes four feature weighted single-task ALR approaches and three feature weighted multi-task ALR approaches, where the ridge regression coefficients trained from a small amount of previously labeled samples are used to weight the corresponding features in inter-sample distance computation. Extensive experiments showed that this intuitive and easy-to-implement enhancement almost always improves the performance of five existing ALR approaches, in both single-task and multi-task regression problems. The feature weighting strategy may also be easily extended to stream-based ALR, and classification algorithms.
Dongrui Wu
Ministry of Education Key Laboratory of Image Processing and Intelligent Control, and Hubei Key Laboratory of Brain-inspired Intelligent Systems, School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan, 430074 China.
Over the past couple of decades, many active learning acquisition functions have been proposed, leaving practitioners with an unclear choice of which to use. Bayesian active learning offers principled objectives with explainable intuition, including Expected Error Reduction (EER), Expected Predictive Information Gain (EPIG), and Bayesian Active Learning by Disagreements (BALD). A key challenge of such methods is the difficulty of extending to the batch setting, leading to either computational challenges (BatchBALD) or dramatic performance drops (top-B selection). In this work, we extend active learning's Bayesian Decision Theory framework to derive Partial Batch Label Sampling (ParBaLS) for the EPIG algorithm. We show experimentally that ParBaLS EPIG gives superior performance for a variety of datasets with different budgets using Bayesian logistic regression on embeddings from large pre-trained models. Our code is available at https://github.com/ADDAPT-ML/ParBaLS.
Kangping Hu, Stephen Mussmann
Department of Computer Science, Georgia Institute of Technology, Atlanta, GA 30332
Active Learning (AL) is commonly used in applications where labeling data is expensive or time-consuming. In practice, however, labels are often noisy due to varying labeler expertise and annotation uncertainty, especially for complex or ambiguous samples. Learning from such imperfectly labeled data can degrade classifier performance. We propose an AL framework that explicitly accounts for label noise by optimally assigning labelers and selecting samples to minimize labeling error. Our approach, called OLAS (Optimal Labeler Assignment and Sampling), uses a noise model that depends on both labeler accuracy and model uncertainty to guide these decisions. We develop two tractable optimization formulations: one for assigning samples to labelers to minimize worst-case noise, and another for selecting samples while controlling overall label noise. Theoretical results provide closed-form solutions under mild conditions. Empirical evaluations on benchmark datasets and a real-world warranty claim classification problem show that OLAS achieves the highest or near-highest classification accuracy among existing AL strategies across most settings, using only a single label per sample.
Pouya Ahadi, Blair Winograd, Camille Zaug +3
School of Industrial and Systems Engineering Georgia Institute of Technology Atlanta, GA 30332, USA · Ford Motor Company