# Primal Dual Continual Learning: Balancing Stability and Plasticity through Adaptive Memory Allocation

arXiv: https://arxiv.org/abs/2310.00154 · HTML: https://mlsanity.com/paper/2310.00154/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 66 references that are in the map.
- First posted on arXiv 29 Sep 2023.

## Builds on (most cited first, 30 of 41)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [iCaRL: Incremental Classifier and Representation Learning](https://mlsanity.com/paper/1611.07725/) (2016)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [Experience Replay for Continual Learning](https://mlsanity.com/paper/1811.11682/) (2018)
- [Efficient Lifelong Learning with A-GEM](https://mlsanity.com/paper/1812.00420/) (2018)
- [Dark Experience for General Continual Learning: a Strong, Simple Baseline](https://mlsanity.com/paper/2004.07211/) (2020)
- [PackNet: Adding Multiple Tasks to a Single Network by Iterative Pruning](https://mlsanity.com/paper/1711.05769/) (2017)
- [Speech Commands: A Dataset for Limited-Vocabulary Speech Recognition](https://mlsanity.com/paper/1804.03209/) (2018)
- [Deep Reinforcement Learning for Autonomous Driving: A Survey](https://mlsanity.com/paper/2002.00444/) (2020)
- [MedMNIST v2 -- A large-scale lightweight benchmark for 2D and 3D biomedical image classification](https://mlsanity.com/paper/2110.14795/) (2021)
- [An Empirical Study of Example Forgetting during Deep Neural Network Learning](https://mlsanity.com/paper/1812.05159/) (2018)
- [Deep Batch Active Learning by Diverse, Uncertain Gradient Lower Bounds](https://mlsanity.com/paper/1906.03671/) (2019)
- [Class-incremental learning: survey and performance evaluation on image classification](https://mlsanity.com/paper/2010.15277/) (2020)
- [Not All Samples Are Created Equal: Deep Learning with Importance Sampling](https://mlsanity.com/paper/1803.00942/) (2018)
- [On the Optimization of Deep Networks: Implicit Acceleration by Overparameterization](https://mlsanity.com/paper/1802.06509/) (2018)
- [Loss landscapes and optimization in over-parameterized non-linear systems and neural networks](https://mlsanity.com/paper/2003.00307/) (2020)
- [Class-Incremental Learning: A Survey](https://mlsanity.com/paper/2302.03648/) (2023)
- [Coresets via Bilevel Optimization for Continual Learning and Streaming](https://mlsanity.com/paper/2006.03875/) (2020)
- [A Universal Law of Robustness via Isoperimetry](https://mlsanity.com/paper/2105.12806/) (2021)
- [Training Networks in Null Space of Feature Covariance for Continual Learning](https://mlsanity.com/paper/2103.07113/) (2021)
- [Active Learning on a Budget: Opposite Strategies Suit High and Low Budgets](https://mlsanity.com/paper/2202.02794/) (2022)
- [Class-Incremental Continual Learning into the eXtended DER-verse](https://mlsanity.com/paper/2201.00766/) (2022)
- [On Statistical Bias In Active Learning: How and When To Fix It](https://mlsanity.com/paper/2101.11665/) (2021)
- [Mind Your Outliers! Investigating the Negative Impact of Outliers on Active Learning for Visual Question Answering](https://mlsanity.com/paper/2107.02331/) (2021)
- [Memory Efficient Continual Learning with Transformers](https://mlsanity.com/paper/2203.04640/) (2022)
- [Constrained Learning with Non-Convex Losses](https://mlsanity.com/paper/2103.05134/) (2021)
- [Information-theoretic Online Memory Selection for Continual Learning](https://mlsanity.com/paper/2204.04763/) (2022)

## Built on by (most cited first, 4 of 4)

- [Constrained Entropic Unlearning: A Primal-Dual Framework for Large Language Models](https://mlsanity.com/paper/2506.05314/) (2025)
- [LoRanPAC: Low-rank Random Features and Pre-trained Models for Bridging Theory and Practice in Continual Learning](https://mlsanity.com/paper/2410.00645/) (2024)
- [Constrained Sliced Wasserstein Embedding](https://mlsanity.com/paper/2506.02203/) (2025)
- [Recovery Guarantees for Continual Learning of Dependent Tasks: Memory, Data-Dependent Regularization, and Data-Dependent Weights](https://mlsanity.com/paper/2604.17578/) (2026)

## Abstract (arXiv)

Continual learning is inherently a constrained learning problem. The goal is to learn a predictor under a no-forgetting requirement. Although several prior studies formulate it as such, they do not solve the constrained problem explicitly. In this work, we show that it is both possible and beneficial to undertake the constrained optimization problem directly. To do this, we leverage recent results in constrained learning through Lagrangian duality. We focus on memory-based methods, where a small subset of samples from previous tasks can be stored in a replay buffer. In this setting, we analyze two versions of the continual learning problem: a coarse approach with constraints at the task level and a fine approach with constraints at the sample level. We show that dual variables indicate the sensitivity of the optimal value of the continual learning problem with respect to constraint perturbations. We then leverage this result to partition the buffer in the coarse approach, allocating more resources to harder tasks, and to populate the buffer in the fine approach, including only impactful samples. We derive a deviation bound on dual variables as sensitivity indicators, and empirically corroborate this result in diverse continual learning benchmarks. We also discuss the limitations of these methods with respect to the amount of memory available and the expressiveness of the parametrization.