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A Lagrangian Duality Approach to Active Learning

arXiv 2202.04108 ↗First posted 8 Feb 2022cs.LG math.OCcited by 24

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Abstract (arXiv)

We consider the pool-based active learning problem, where only a subset of the training data is labeled, and the goal is to query a batch of unlabeled samples to be labeled so as to maximally improve model performance. We formulate the problem using constrained learning, where a set of constraints bounds the performance of the model on labeled samples. Considering a primal-dual approach, we optimize the primal variables, corresponding to the model parameters, as well as the dual variables, corresponding to the constraints. As each dual variable indicates how significantly the perturbation of the respective constraint affects the optimal value of the objective function, we use it as a proxy of the informativeness of the corresponding training sample. Our approach, which we refer to as Active Learning via Lagrangian dualitY, or ALLY, leverages this fact to select a diverse set of unlabeled samples with the highest estimated dual variables as our query set. We demonstrate the benefits of our approach in a variety of classification and regression tasks and discuss its limitations depending on the capacity of the model used and the degree of redundancy in the dataset. We also examine the impact of the distribution shift induced by active sampling and show that ALLY can be used in a generative mode to create novel, maximally-informative samples.

Key facts. Cited by 24 papers in the map (data through 7 Oct 2026). Builds on 41 of its 86 references that are in the map. First posted on arXiv 8 Feb 2022.

Builds on

41 of 86 references.

References · 41

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  1. 2017A Closer Look at Memorization in Deep Networkscited by 936
  2. 2017Deep Bayesian Active Learning with Image Datacited by 812
  3. 2018An Empirical Study of Example Forgetting during Deep Neural Network Learningcited by 669
  4. 2019Deep Batch Active Learning by Diverse, Uncertain Gradient Lower Boundscited by 602
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  6. 2018Not All Samples Are Created Equal: Deep Learning with Importance Samplingcited by 323
  7. 2019Variational Adversarial Active Learningcited by 284
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 3; 2023: 8; 2024: 7; 2025: 5; 2026: 1.

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  1. 2024A Survey on Deep Active Learning: Recent Advances and New Frontierscited by 53
  2. 2023Algorithm Selection for Deep Active Learning with Imbalanced Datasetscited by 18
  3. 2022Automatic Data Augmentation via Invariance-Constrained Learningcited by 17
  4. 2023Resilient Constrained Learningcited by 15
  5. 2024On PI Controllers for Updating Lagrange Multipliers in Constrained Optimizationcited by 12
  6. 2025Cooper: A Library for Constrained Optimization in Deep Learningcited by 10
  7. 2024Near-Optimal Solutions of Constrained Learning Problemscited by 9
  8. 2023Improved Algorithm for Deep Active Learning under Imbalance via Optimal Separationcited by 8
  9. 2023Balancing Act: Constraining Disparate Impact in Sparse Modelscited by 7
  10. 2024Querying Easily Flip-flopped Samples for Deep Active Learningcited by 7
  11. 2024Out-of-Distribution Learning with Human Feedbackcited by 6
  12. 2024Deep Active Learning in the Open Worldcited by 5
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  4. 2025Position: Adopt Constraints Over Fixed Penalties in Deep Learningcited by 4
  5. 2023How To Overcome Confirmation Bias in Semi-Supervised Image Classification By Active Learningcited by 2
  6. 2025Constrained Sliced Wasserstein Embeddingcited by 2
  7. 2025Dual Optimistic Ascent (PI Control) is the Augmented Lagrangian Method in Disguisecited by 1
  8. 2025AL-CoLe: Augmented Lagrangian for Constrained Learningcited by 1
  9. 2022A State-Augmented Approach for Learning Optimal Resource Management Decisions in Wireless Networkscited by 0
  10. 2023Omega: Optimistic EMA Gradientscited by 0
  11. 2023Optimal and Efficient Binary Questioning for Human-in-the-Loop Annotationcited by 0
  12. 2026Active Learning with Foundation Model Priors: Efficient Learning under Class Imbalancecited by 0