# Server-Proximal Aggregation for Federated Domain-Incremental Learning under Partial Participation: Task-Uniform Convergence and Backward Transfer

arXiv: https://arxiv.org/abs/2601.22274 · HTML: https://mlsanity.com/paper/2601.22274/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 42 of its 54 references that are in the map.
- First posted on arXiv 29 Jan 2026.

## Builds on (most cited first, 30 of 42)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
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- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (2016)
- [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)
- [Continual Lifelong Learning with Neural Networks: A Review](https://mlsanity.com/paper/1802.07569/) (2018)
- [On the Convergence of FedAvg on Non-IID Data](https://mlsanity.com/paper/1907.02189/) (2019)
- [Memory Aware Synapses: Learning what (not) to forget](https://mlsanity.com/paper/1711.09601/) (2017)
- [Adaptive Federated Optimization](https://mlsanity.com/paper/2003.00295/) (2020)
- [Deeper, Broader and Artier Domain Generalization](https://mlsanity.com/paper/1710.03077/) (2017)
- [A Comprehensive Survey of Continual Learning: Theory, Method and Application](https://mlsanity.com/paper/2302.00487/) (2023)
- [Large Scale Incremental Learning](https://mlsanity.com/paper/1905.13260/) (2019)
- [Local SGD Converges Fast and Communicates Little](https://mlsanity.com/paper/1805.09767/) (2018)
- [Learning to Learn without Forgetting by Maximizing Transfer and Minimizing Interference](https://mlsanity.com/paper/1810.11910/) (2018)
- [Progress & Compress: A scalable framework for continual learning](https://mlsanity.com/paper/1805.06370/) (2018)
- [Learn to Grow: A Continual Structure Learning Framework for Overcoming Catastrophic Forgetting](https://mlsanity.com/paper/1904.00310/) (2019)
- [Achieving Linear Speedup with Partial Worker Participation in Non-IID Federated Learning](https://mlsanity.com/paper/2101.11203/) (2021)
- [Meta-Learning Representations for Continual Learning](https://mlsanity.com/paper/1905.12588/) (2019)
- [Federated Continual Learning with Weighted Inter-client Transfer](https://mlsanity.com/paper/2003.03196/) (2020)
- [A Proximal Stochastic Gradient Method with Progressive Variance Reduction](https://mlsanity.com/paper/1403.4699/) (2014)
- [TARGET: Federated Class-Continual Learning via Exemplar-Free Distillation](https://mlsanity.com/paper/2303.06937/) (2023)
- [Beyond Not-Forgetting: Continual Learning with Backward Knowledge Transfer](https://mlsanity.com/paper/2211.00789/) (2022)
- [Better Generative Replay for Continual Federated Learning](https://mlsanity.com/paper/2302.13001/) (2023)
- [A distillation-based approach integrating continual learning and federated learning for pervasive services](https://mlsanity.com/paper/2109.04197/) (2021)
- [A Data-Free Approach to Mitigate Catastrophic Forgetting in Federated Class Incremental Learning for Vision Tasks](https://mlsanity.com/paper/2311.07784/) (2023)
- [A Unified Approach to Domain Incremental Learning with Memory: Theory and Algorithm](https://mlsanity.com/paper/2310.12244/) (2023)
- [Towards Efficient Replay in Federated Incremental Learning](https://mlsanity.com/paper/2403.05890/) (2024)
- [Elastic Weight Consolidation (EWC): Nuts and Bolts](https://mlsanity.com/paper/2105.04093/) (2021)

## Abstract (arXiv)

Real-world federated systems seldom operate on static data: input distributions drift while privacy rules forbid raw-data sharing. We study this setting as Federated Domain-Incremental Learning (FDIL), where (i) clients are heterogeneous, (ii) tasks arrive sequentially with shifting domains, yet (iii) the label space remains fixed. Two theoretical pillars remain missing for FDIL under realistic deployment: a guarantee of backward knowledge transfer (BKT) and a convergence rate that holds across the sequence of all tasks with partial participation. We introduce SPECIAL (Server-Proximal Efficient Continual Aggregation for Learning), a simple, memory-free FDIL algorithm that adds a single server-side ``anchor'' to vanilla FedAvg: in each round, the server nudges the uniformly sampled participated clients update toward the previous global model with a lightweight proximal term. This anchor curbs cumulative drift without replay buffers, synthetic data, or task-specific heads, keeping communication and model size unchanged. Our theory shows that SPECIAL (i) preserves earlier tasks: a BKT bound caps any increase in prior-task loss by a drift-controlled term that shrinks with more rounds, local epochs, and participating clients; and (ii) learns efficiently across all tasks: the first communication-efficient non-convex convergence rate for FDIL with partial participation, O((E/NT)^(1/2)), with E local epochs, T communication rounds, and N participated clients per round, matching single-task FedAvg while explicitly separating optimization variance from inter-task drift. Experimental results further demonstrate the effectiveness of SPECIAL.