# Federated Continual Learning as a Distributed Drift-Plus-Penalty Control Problem

arXiv: https://arxiv.org/abs/2608.21539 · HTML: https://mlsanity.com/paper/2608.21539/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 36 of its 51 references that are in the map.
- First posted on arXiv 21 Aug 2026.

## Builds on (most cited first, 30 of 36)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (2016)
- [Federated Learning: Challenges, Methods, and Future Directions](https://mlsanity.com/paper/1908.07873/) (2019)
- [Experience Replay for Continual Learning](https://mlsanity.com/paper/1811.11682/) (2018)
- [Dark Experience for General Continual Learning: a Strong, Simple Baseline](https://mlsanity.com/paper/2004.07211/) (2020)
- [Learning to Learn without Forgetting by Maximizing Transfer and Minimizing Interference](https://mlsanity.com/paper/1810.11910/) (2018)
- [A Survey on Federated Learning Systems: Vision, Hype and Reality for Data Privacy and Protection](https://mlsanity.com/paper/1907.09693/) (2019)
- [FedProto: Federated Prototype Learning across Heterogeneous Clients](https://mlsanity.com/paper/2105.00243/) (2021)
- [Gradient Projection Memory for Continual Learning](https://mlsanity.com/paper/2103.09762/) (2021)
- [No Fear of Heterogeneity: Classifier Calibration for Federated Learning with Non-IID Data](https://mlsanity.com/paper/2106.05001/) (2021)
- [Federated Continual Learning with Weighted Inter-client Transfer](https://mlsanity.com/paper/2003.03196/) (2020)
- [Federated Class-Incremental Learning](https://mlsanity.com/paper/2203.11473/) (2022)
- [TARGET: Federated Class-Continual Learning via Exemplar-Free Distillation](https://mlsanity.com/paper/2303.06937/) (2023)
- [Better Generative Replay for Continual Federated Learning](https://mlsanity.com/paper/2302.13001/) (2023)
- [Optimal Algorithms for Online Convex Optimization with Adversarial Constraints](https://mlsanity.com/paper/2310.18955/) (2023)
- [Asynchronous Federated Continual Learning](https://mlsanity.com/paper/2304.03626/) (2023)
- [FedET: A Communication-Efficient Federated Class-Incremental Learning Framework Based on Enhanced Transformer](https://mlsanity.com/paper/2306.15347/) (2023)
- [Diffusion-Driven Data Replay: A Novel Approach to Combat Forgetting in Federated Class Continual Learning](https://mlsanity.com/paper/2409.01128/) (2024)
- [Closed-form merging of parameter-efficient modules for Federated Continual Learning](https://mlsanity.com/paper/2410.17961/) (2024)
- [Federated Orthogonal Training: Mitigating Global Catastrophic Forgetting in Continual Federated Learning](https://mlsanity.com/paper/2309.01289/) (2023)
- [Personalized Federated Domain-Incremental Learning based on Adaptive Knowledge Matching](https://mlsanity.com/paper/2407.05005/) (2024)
- [A Unified and General Framework for Continual Learning](https://mlsanity.com/paper/2403.13249/) (2024)
- [CBA: Improving Online Continual Learning via Continual Bias Adaptor](https://mlsanity.com/paper/2308.06925/) (2023)
- [FedSOL: Stabilized Orthogonal Learning with Proximal Restrictions in Federated Learning](https://mlsanity.com/paper/2308.12532/) (2023)
- [Federated Learning with Flexible Control](https://mlsanity.com/paper/2212.08496/) (2022)
- [Accurate Forgetting for Heterogeneous Federated Continual Learning](https://mlsanity.com/paper/2502.14205/) (2025)
- [Projection-free Algorithms for Online Convex Optimization with Adversarial Constraints](https://mlsanity.com/paper/2501.16919/) (2025)

## Abstract (arXiv)

Federated Continual Learning (FCL) is fundamental to real-world distributed learning systems, requiring models to adapt to sequential, non-IID data across clients while mitigating catastrophic forgetting and client drift. Existing approaches formulate continual learning (CL) as a sequence of per-task optimization problems, applied locally at each client and coupled through aggregation, using heuristic mechanisms such as replay, regularization, or projection-based constraints. However, forgetting in FCL is inherently a long-term, distributed phenomenon, arising from the interaction of temporal task evolution and cross-client heterogeneity, which is not explicitly regulated. In this work, we cast FCL as a stochastic control problem and propose Federated Queue-regulated Continual Learning (FedQCL), a framework based on Lyapunov drift-plus-penalty (DPP) optimization. FedQCL introduces virtual queues to track the accumulation of forgetting across tasks and clients, enabling explicit control of the stability-plasticity trade-off. By optimizing a DPP objective, the method jointly improves current-task performance while the queue-based formulation provides an interpretable and tunable mechanism to balance adaptation and retention through a single parameter, without requiring gradient projection or additional communication overhead. Empirical evaluations on standard benchmarks, including Split-CIFAR-10, Split-CIFAR-100, and Split-TinyImageNet, demonstrate that FedQCL outperforms state-of-the-art baselines with respect to accuracy while significantly reducing forgetting under heterogeneous data distributions.