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

Nazreen Shah; Naveen Kumar Reddy Somireddy; Zubair Shaban; Ranjitha Prasad; B. N. Bharath

cs.LGAug 21, 2026

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

Authors: Nazreen Shah, Naveen Kumar Reddy Somireddy, Zubair Shaban, Ranjitha Prasad, B. N. Bharath

Organizations: IIIT Delhi India · IIT Dharwad India

Abstract

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.

Figures & tables

Method	Split-CIFAR-10		Split-CIFAR-100		Split-TinyImageNet
Method	Acc (%) $\uparrow$	Forget $\downarrow$	Acc (%) $\uparrow$	Forget $\downarrow$	Acc (%) $\uparrow$	Forget $\downarrow$
FedAvg (2017)	70.21 $\pm$ 0.75	0.12 $\pm$ 0.006	29.10 $\pm$ 0.29	0.12 $\pm$ 0.001	10.09 $\pm$ 0.36	0.20 $\pm$ 0.002
FedProto (2022)	73.03 $\pm$ 0.01	0.23 $\pm$ 0.018	35.07 $\pm$ 0.01	0.27 $\pm$ 0.009	19.14 $\pm$ 0.01	0.31 $\pm$ 0.01
EWC-FL (2017)	73.51 $\pm$ 0.01	0.23 $\pm$ 0.01	37.54 $\pm$ 0.01	0.24 $\pm$ 0.03	21.43 $\pm$ 0.01	0.29 $\pm$ 0.003
LwF-FL (2017)	73.42 $\pm$ 0.01	0.23 $\pm$ 0.008	36.76 $\pm$ 0.01	0.31 $\pm$ 0.01	19.38 $\pm$ 0.01	0.38 $\pm$ 0.01
ER-FL (2019)	73.37 $\pm$ 0.02	0.23 $\pm$ 0.01	37.74 $\pm$ 0.01	0.24 $\pm$ 0.007	20.99 $\pm$ 0.01	0.23 $\pm$ 0.01

Table 1: Task Incremental Learning Results (Mean

\pm

Std over 3 seeds) under non-IID data distribution with Dirichlet parameter

\alpha=10.0

, 5 clients, and a total memory buffer size of 500 samples per client.

Panel of Figure 1 — Figure 1: Left two: Comparison against baselines on Split-CIFAR-100. Right two: Plasticity-stability Pareto on Split-CIFAR-100 and Split-TinyImageNet. Each point represents the final average accuracy vs. average forgetting of a method.

Panel of Figure 2 — Figure 2: Ablation on Split-CIFAR-100. Left: Effect of data heterogeneity ( $\alpha$ ), where accuracy (left) and forgetting (right) are shown for $\alpha\in\{0.001,\,10,\,10^{5}\}$ . Right: Effect of memory buffer size ( $M$ ), where accuracy (left) and forgetting (right) are reported for $M\in\{200,\,500,\,1000\}$ exemplars per client.

Panel of Figure 3 — Figure 3: Hyperparameter analysis of FedQCL . Left: Effect of $V$ on Split-CIFAR-100 and Split-TinyImageNet (accuracy and forgetting vs. $V$ ). Right: Effect of $\delta$ shown via plasticity–stability Pareto trade-off on Split-CIFAR-10 and Split-CIFAR-100.

Figure 4: Virtual queue matrix $Q^{(j)}[i]$ under varying penalty weight $V$ on Split-CIFAR-100. Cell $(i,j)$ represents the queue value for past task $j$ accumulated during training on task $i$ , averaged across clients.

\displaystyle\mathbf{w}_{i}^{(t,c,r+1)}

\displaystyle=\mathbf{w}_{i}^{(t,c,r)}-\eta_{t}\Bigg(V\nabla\Phi_{i}(\mathbf{w}_{i}^{(t,c,r)};\mathcal{B}_{i}^{(t,c,r)})+\sum_{k=1}^{t-1}Q^{(k)}_{i}[t-1]\nabla\hat{\Phi}^{(k)}_{i}(\mathbf{w}_{i}^{(t,c,r)})\Bigg).

Algorithm 1 Federated Queue regulated Continual Learning ( FedQCL )

Method	Client Storage	Client Computation	Communication (per round)	Extra Cost at Task Boundary
FedQCL (Ours)	$\mathcal{O}(M+K+d)$ per client	$\mathcal{O}((B+K\cdot B_{m})\cdot d)$ per round	$\mathcal{O}(d)$	$\mathcal{O}(C)$ queue updates per task
	(buffer $+$ prev. task model $+$ $K$ scalar queues)	(current-task grad $+$ $K$ replay grads)	(same as FedAvg)	queues updated in-place)
FOT	$\mathcal{O}(0)$ client-side	$\mathcal{O}(B\cdot d)$	$\mathcal{O}(d)$ per round	$\mathcal{O}(d\cdot s_{\max})$ upload $+$ SVD $\mathcal{O}(d\cdot s_{\max}^{2})$ at server
	(server stores orthogonal subspace $\mathcal{O}(\sum_{\ell}d^{\ell}\cdot r^{\ell})$ )	(standard SGD; projection is server-side)	(FedAvg; $+\,\mathcal{O}(d\cdot s_{\max})$ at task boundary)	(one extra round per task; SVD cost at server.)
BI	$\mathcal{O}(M)$ per client	$\mathcal{O}(P\cdot B\cdot d)$ per round	$\mathcal{O}(d)$	$\mathcal{O}(0)$
	(class-balanced buffer)	( $P$ forward passes per round $+$ replay grad)	(same as FedAvg)	(no extra round at task boundary)

Table 2: Complexity comparison per communication round per client.

N

: total clients;

C

: communication rounds per task;

T

: tasks;

M

: replay buffer size;

d

: model parameter dimension;

B

: mini-batch size;

B_{m}

: memory replay batch size;

K

: number of past tasks (grows with

T

);

P

: number of augmentation passes.

Hyperparameter	Split-CIFAR10	Split-CIFAR100	Split-TinyImageNet
Learning rate	0.005	0.005	0.005
Optimizer	SGD	SGD	SGD
Local epochs	5	5	5
# Clients	5	5	5
Communication rounds per task	10	10	10
# Tasks	5	5	10

Table 3: Hyperparameters used in FedQCL experiments.

Figure 5: Left two: Comparison against baselines on Split-CIFAR-10. Right two: Comparison against baselines on Split-TinyImageNet.

Method	$\alpha=10^{5}$		$\alpha=0.1$
Method	Acc (%) $\uparrow$	Forget $\downarrow$	Acc (%) $\uparrow$	Forget $\downarrow$
FedAvg	12.99	0.39	8.60	0.24
EWC	16.79	0.35	9.53	0.25
LwF	15.75	0.49	6.48	0.26
ER	13.93	0.37	11.69	0.26
DER	16.20	0.43	7.60	0.03

Table 4: Class-incremental learning results on Split-CIFAR-100 under near-IID (

\alpha=10^{5}

) and non-IID (

\alpha=0.1

) client distributions.

Panel of Figure 6 — Figure 6: System-level sensitivity on Split-CIFAR-100. Left: Effect of the number of clients ( $N$ ). Right: Effect of local training epochs.

Panel of Figure 7 — Figure 7: Scalability and training paradigm analysis on Split-CIFAR-100. Left: Effect of increasing the number of tasks ( $T\in\{5,\,10,\,20\}$ ). Right: Comparison between online and offline training settings.

Panel of Figure 8 — Figure 8: Additional hyperparameter analysis. Left: Effect of $\delta$ . Right: Effect of $V$ shown through plasticity–stability Pareto trade-offs.

Figure 9: Virtual queue dynamics under varying $\delta$ . Each cell $(i,j)$ represents the queue value $Q^{(j)}[i]$ for past task $j$ accumulated during training on task $i$ , averaged across clients. Smaller $\delta$ leads to larger queue values, indicating stronger penalization of forgetting.

Figure 10: Virtual queue dynamics under varying data heterogeneity $\alpha$ . Each cell $(i,j)$ represents the queue value $Q^{(j)}[i]$ for past task $j$ accumulated during training on task $i$ , averaged across clients.

Federated Continual Learning

Federated continual learning enables distributed clients to adapt models to changing data while retaining past knowledge and keeping raw data local.

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Federated continual learning: A comprehensive survey on lifelong and privacy-preserving learning over distributed and non-stationary data

Masoume Gholizade, Fabrizio Ruffini, Pietro Ducange, Francesco Marcelloni

Department of Information Engineering, University of Pisa, Largo Lucio Lazzarino 1, Pisa, 56122, Italy

Continual Learning Federated Continual Learning Privacy-Preserving ML Federated Learning

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Federated Learning (FL) enables collaborative and privacy-preserving model training across distributed clients, but most existing FL systems implicitly assume data stationarity. In real-world settings-such as healthcare, industrial IoT (IIOT), cybersecurity, and smart cities-data streams are inherently non-stationary, leading classical FL methods to suffer from performance degradation, instability, and catastrophic forgetting. Continual Learning (CL) addresses learning under evolving data distributions but has been largely studied in centralized settings, overlooking key constraints of federated systems, including privacy, limited communication, and client heterogeneity. Federated Continual Learning (FCL) emerges at the intersection of FL and CL, aiming to support lifelong, adaptive, and privacy-aware learning over distributed and non-stationary data. This survey provides a comprehensive and systematic overview of FCL. We first present a formal definition of the FCL problem and clarify its distinctive characteristics. We then analyze the limitations of classical FL under non-stationary conditions, highlighting how CL principles support long-term adaptation. To organize the rapidly growing literature, we propose a multi-dimensional taxonomy of FCL approaches. Furthermore, we review representative application domains and data modalities, summarize commonly used evaluation metrics, and discuss experimental perspectives for assessing long-term performance and forgetting. Finally, we highlight key open challenges, including handling extreme heterogeneity under temporal drift, designing scalable and privacy-preserving memory mechanisms, and establishing standardized benchmarks. This survey aims to serve as a reference and a roadmap for advancing FCL toward robust and deployable real-world systems.

Abstract

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