Resilience Beyond Stationary Client Unavailability: Unlocking Efficient and Unbiased Federated Learning

Ming Xiang; Stratis Ioannidis; Edmund Yeh; Carlee Joe-Wong; Lili Su

cs.LGSep 4, 2026

Resilience Beyond Stationary Client Unavailability: Unlocking Efficient and Unbiased Federated Learning

Authors: Ming Xiang, Stratis Ioannidis, Edmund Yeh, Carlee Joe-Wong, Lili Su

Organizations: Northeastern University, Boston, MA USA · Carnegie Mellon University, Pittsburgh, PA USA

Abstract

Due to resource constraints or external and internal uncertainties, clients in real-world federated learning systems are often intermittently available edge devices. In highly dynamic environments, the parameter server lacks prior real-time knowledge of clients' availability, making it challenging to adapt traditional federated learning algorithms to be resilient to uncertainties in client availability. If not carefully addressed, complex client availability can introduce significant bias, potentially harming the performance of the trained model. Most prior work either fails to account for non-stationary client availability dynamics or demands significant memory and computational overhead. This paper aims to develop efficient federated learning algorithms that are provably resilient to heterogeneous and non-stationary stochastic client availability. We propose FedSWE, which admits novel algorithmic structures to (i) compensate for missed computations, (ii) stabilize and diffuse the global updates over rounds, and (iii) evenly mix the local updates through implicit gossiping, despite being agnostic to non-stationary dynamics. Compared with the standard FedAvg, FedSWE introduces light additional memory and computation overhead. We show that FedSWE converges to a stationary point of non-convex objectives while achieving the desired linear speedup property in certain special cases. We corroborate our analysis with numerical experiments over diversified client unavailability dynamics on real-world data sets.

Figures & tables

Figure 1: An illustration of heterogeneous and non-stationary availability.

Figure 2: Let $x_{\text{output}}\triangleq\lim_{t\to\infty}\mathbb{E}\left[x^{t}\right]$ . Under most of the choices of $p_{1},p_{2}$ , $x_{\text{output}}$ is far from $x^{*}$ .

Panel of Figure 3 — Figure 3: Train and test accuracy results in percentage (%). In particular, the parameter $\gamma$ signifies the degree of non-stationary. Notice that, as the client availability becomes more non-stationary (a larger $\gamma$ ), FedAvg experiences a significant drop in accuracy. For example, both the train and test accuracies drop by over $10\%$ when $p=0.1$ , and $\gamma$ increases from $0.1$ to $0.5$ .

Figure 4

Bounded Gradient Dissimilarity	References
$\max_{{\bm{x}}}\left\\|{\nabla F_{i}({\bm{x}})}\right\\|_{2}^{2}\leq\zeta^{2},\penalty\ \forall\penalty\ i\in[m]$	( Li et al., 2020b ; Yu et al., 2019b ; Cho et al., 2022 ; Cho et al., 2023b ; Yan et al., 2023 ) .
$\frac{1}{m}\sum_{i=1}^{m}\left\\|{\nabla F_{i}({\bm{x}})}\right\\|_{2}^{2}\leq\beta^{2}\left\\|{\nabla F({\bm{x}})}\right\\|_{2}^{2}$	( Li et al., 2019 ; Li et al., 2020a )
$\frac{1}{m}\sum_{i=1}^{m}\left\\|{\nabla F_{i}({\bm{x}})-\nabla F({\bm{x}})}\right\\|_{2}^{2}\leq\zeta^{2}$	( Yu et al., 2019a ; Wang et al., 2019 ; Huang et al., 2022 ; Karimireddy et al., 2022 ; Wang and Ji, 2022 ; Wang and Ji, 2024 ; Yang et al., 2022 ; Wang et al., 2022 ; Allouah et al., 2023 ) .
$\frac{1}{m}\sum_{i=1}^{m}\left\\|{\nabla F_{i}({\bm{x}})}\right\\|_{2}^{2}\leq\beta^{2}\left\\|{\nabla F({\bm{x}})}\right\\|_{2}^{2}+\zeta^{2}$	( Karimireddy et al., 2020 ; Wang et al., 2020 ; Wang and Joshi, 2021 ; Gu et al., 2021 ; Yuan and Li, 2022 ) .

Table 1: Popular variant assumptions on gradient dissimilarity.

Panel of Figure 4 — Figure 4: Calculated spectral norm results with varying numbers of $k$ . We consider $m=10$ clients with availability dynamics described in the plots. Note that the $y$ -axis of each subplot is of a different range.

Panel of Figure 5 — Figure 5: Visualizations of Algorithm 1 with two clients and a global objective ( 29 ), whose $u_{1}=100$ , $u_{2}=-100$ . The first client is available exclusively in even rounds, while the second client is available in odd rounds only. $x$ -axis is the global round index, the details of $y$ -axis can be found in the subplots. Figs. 5(a) and 5(c) plot the results of Algorithm 1 without interpolation. It can be seen that the outputs alternate between two clients’ local optimums and can deviate far away from the true global minimizer $u_{1}+u_{2}=0$ . Moreover, the clients fail to reach a consensus. In sharp contrast, Figs. 5(b) and 5(d) indicate that Algorithm 1 recovers the global minimizer with interpolation ( $k=1$ ) and allows clients to reach a consensus.

Panel of Figure 6 — Figure 6: Plots of the consensus errors on a logarithmic scale with $m=100$ clients. The 100 clients are evenly divided into two non-overlapping groups ${\mathcal{M}}_{1}$ and ${\mathcal{M}}_{2}$ . The global rounds can be partitioned into periods, each with length $50$ rounds. In all odd periods, the available probability $p^{t}_{i}>0$ if $i\in{\mathcal{M}}_{1}$ while $p^{t}_{i}=0$ otherwise. In all even periods, the available probability $p^{t}_{i}>0$ if $i\in{\mathcal{M}}_{2}$ while $p^{t}_{i}=0$ otherwise. We train CNN networks on the SVHN data set and CIFAR-10 data set for $T=10000$ and $T=20000$ rounds, respectively. When a client becomes available, it performs $s=10$ steps of local computation. The results are obtained under 3 random seeds and sampled every $P_{\delta}$ round. The solid curves differ from each other by the values of $k$ , and the shaded areas plot the standard deviation. It can be observed from the plots that clients fail to reach a consensus when $k=0$ .

Panel of Figure 7 — Figure 7: Test accuracy results with $m=100$ clients, who are divided into two non-overlapping but evenly sized groups. We train CNN networks on the SVHN data set for $T=10000$ rounds. When a client becomes available, it performs $s=10$ steps of local computation. The results are obtained under 3 random seeds and sampled every $P_{\delta}$ round. The curves plot the averaged results, while the shaded areas plot the standard deviation.

Panel of Figure 8 — Figure 8: Test accuracy of FedSWE with different $k$ ’s on SVHN data set under different unavailability dynamics. The reported results are averaged over the last 500 rounds. Consistent with Remark 15 , we observe an initial increase in test accuracy, followed by a decline, peaking around $k=m=100$ .

Panel of Figure 9 — Figure 9: The number of rounds needed to achieve 40% test accuracy of FedSWE with various $k$ values on the SVHN data set under different unavailability dynamics. We can observe a similar trend as in Fig. 8 that a slight speedup in the beginning but a significant slowdown after $k=m$ .

Panel of Figure 10 — Figure 10: Test accuracy results with $m=100$ clients, who are divided into two non-overlapping but evenly sized groups. Only a single client group is available in each training round. Inside an available window of $P$ rounds, a client $i$ in each group is available with probability $p_{i}^{t}$ . We train CNN networks on the CIFAR-10 data set for $T=20000$ rounds. When a client becomes available, it performs $s=10$ steps of local computation. The results are obtained under 3 random seeds and sampled every $P$ round. The curves plot the averaged results, while the shaded areas plot the standard deviation.

Panel of Figure 11 — Figure 11: Test accuracy of FedSWE with different $k$ ’s on CIFAR-10 data set under different unavailability dynamics. The reported results are averaged over the last 500 rounds. Consistent with Remark 15 , we observe an initial increase in test accuracy, followed by a decline, peaking around $k=m=100$ .

Panel of Figure 12 — Figure 12: The number of rounds needed to achieve 40% test accuracy of FedSWE with various $k$ values on CIFAR-10 data set under different unavailability dynamics. We can observe a similar trend as in Fig. 11 that a slight speedup in the beginning but a significant slowdown after $k=m$ .

Unavailable Dynamics	Data sets	SVHN		CIFAR-10		CINIC-10
Unavailable Dynamics	Algorithms	Train	Test	Train	Test	Train	Test
Stationary	FedSWE ( ours, $k=0$ )	86.5 $\pm$ 0.7 %	86.1 $\pm$ 0.7 %	68.1 $\pm$ 1.4 %	66.3 $\pm$ 1.1 %	47.9 $\pm$ 2.1 %	47.3 $\pm$ 2.0 %
	FedSWE ( ours, $k=100$ )	86.3 $\pm$ 1.1%	85.4 $\pm$ 1.0%	68.7 $\pm$ 1.0 %	66.9 $\pm$ 0.9 %	48.3 $\pm$ 1.7 %	47.9 $\pm$ 1.6 %
	FedAvg over active	82.6 $\pm$ 1.0 %	82.4 $\pm$ 1.1 %	64.1 $\pm$ 1.9 %	62.9 $\pm$ 1.4 %	43.6 $\pm$ 2.4 %	43.1 $\pm$ 2.4 %
	FedAvg over all	76.1 $\pm$ 2.1 %	76.1 $\pm$ 2.4 %	55.8 $\pm$ 2.1 %	55.4 $\pm$ 1.8 %	38.4 $\pm$ 2.1 %	38.0 $\pm$ 2.1 %
	gFedAvg	83.5 $\pm$ 1.5 %	83.0 $\pm$ 1.2%	64.5 $\pm$ 1.7%	63.8 $\pm$ 1.7%	45.3 $\pm$ 1.4%	44.9 $\pm$ 1.2%

Table 2: Results and comparisons on real-world data sets in the form of mean accuracy

\pm

standard deviation and are obtained over 3 repetitions in different random seeds. Results are averaged over the last

50

rounds. The total number of global rounds is 2000 for SVHN, CIFAR-10 and CINIC-10. Algorithms are categorized into two groups: (1) ones not aided by memory or known statistics; (2) ones assisted by memory. For a fair competition, we boldface the best accuracy in the first group, while the second best is underlined .

Appendix figures & tables11 assets

Supplementary material from the paper’s appendix.

Appendix

Notation(s)	Definition
${\mathcal{A}}^{t}$	The set of active clients in round $t$ .
$W^{t}$	A doubly stochastic matrix to capture the information mixing error. Its definition can be found in ( 9 ).
$p_{i}^{t}$	The probability that a client $i$ becomes available in round $t$ .
$\tau_{i}(t)$	$\tau_{i}(t)\triangleq\sup\{t^{\prime}\mid t^{\prime}<t,i\in{\mathcal{A}}^{t^{\prime}}\}$ defines client $i$ ’s most recent active round. In particular, $\tau_{i}(0)=-1$ for all $i\in[m]$ .
${\bm{x}}_{i}^{t}$	The real model at client $i$ at the beginning of round $t$ in Algorithm 1 .
${\bm{z}}_{i}^{t}$	The auxiliary model at client $i$ at the beginning of round $t$ . Refer to Definition 6 for more details. The sequence is for analysis only and is not computed by any clients.

Appendix

Table 3: Nomenclature table

$\delta$	An absolute constant that is the lower bound on the client unavailability.
$P_{\delta}$ , $P$	The period in Assumption 1 .
$L$	Lipschitz constant in Assumption 2 .
$\sigma^{2}$	The upper bound of the stochastic gradient variance.
$(\beta,\penalty\ \zeta)$	Parameters that capture the averaged gradient dissimilarity between global and local objectives.
$\rho$	The spectral norm of a stochastic matrix in expectation.
$s$	The number of local computation steps.

Appendix

Table 4: Variable table

Panel of Figure 13 — Figure 13: An illustration of a directed path from node $i$ to $j$ through an intermediate virtual node. The dashed arcs are self-loops. The weights next to the dashed arcs and solid lines are the lower bounds of each edge weight, respectively.

Figure 14: An example of data heterogeneity using

\mathsf{Dirichlet}(\alpha=0.1)

distribution with

20

clients.

x

-axis denotes the categories of images, while

y

-axis denotes the client index. The size of a circle refers to the proportion of pictures in a given class. The color of a circle distinguishes images with different categories.

Data sets	SVHN	CIFAR-10	CINIC-10
Neural network	CNN	CNN	CNN
Model architecture ∗	C (3,32) – R – M – C (32,32) – R – M – L (128) – R – L (10)	C (3,32) – R – M – C (32,32) – R – M – L (256) – R – L (64) – R – L (10)	C (3,32) – R – M – C (32,32) – R – M – D – L (512) – R – D – L (256) – R – D – L (10)
Loss function	Cross-entropy loss
Local learning rate $\eta_{l}$ scheduling	$\eta_{l}=\eta_{0}$ in Section 7.1 ; $\eta_{l}=\frac{\eta_{0}}{\sqrt{t/10+1}}$ in Section 7.2 , where $t$ denotes the global round.
Number of local steps $s$	10
Number of global rounds $T$ in Section 7.1	10000	20000	–

Appendix

Table 5: Neural network architecture, loss function, learning rate scheduling, training steps and batch size specifications

Algorithms	FedAvg active		FedAvg known		FedAvg all		FedAU		F3AST		FedSWE		MIFA
SVHN	$\eta_{0}$	$\eta_{g}$	$\eta_{0}$	$\eta_{g}$	$\eta_{0}$	$\eta_{g}$	$\eta_{0}$	$\eta_{g}$	$\eta_{0}$	$\eta_{g}$	$\eta_{0}$	$\eta_{g}$	$\eta_{0}$	$\eta_{g}$
SVHN	0.05	1.0	0.1	1.0	0.05	1.0	0.05	1.0	0.05	1.0	0.1	1.0	0.05	1.0
CIFAR-10	$\eta_{0}$	$\eta_{g}$	$\eta_{0}$	$\eta_{g}$	$\eta_{0}$	$\eta_{g}$	$\eta_{0}$	$\eta_{g}$	$\eta_{0}$	$\eta_{g}$	$\eta_{0}$	$\eta_{g}$	$\eta_{0}$	$\eta_{g}$
CIFAR-10	0.05	1.0	0.1	1.0	0.05	1.0	0.05	1.0	0.05	1.0	0.1	1.0	0.05	1.0
CINIC-10	$\eta_{0}$	$\eta_{g}$	$\eta_{0}$	$\eta_{g}$	$\eta_{0}$	$\eta_{g}$	$\eta_{0}$	$\eta_{g}$	$\eta_{0}$	$\eta_{g}$	$\eta_{0}$	$\eta_{g}$	$\eta_{0}$	$\eta_{g}$
CINIC-10	0.05	1.0	0.1	1.0	0.05	1.0	0.05	1.0	0.05	1.0	0.1	1.0	0.05	1.0

Appendix

Table 6: Initial learning rate

\eta_{0}

and global learning rate

\eta_{g}

Figure 15: A histogram of one generated

p_{i}

’s example with a total of

m=100

clients. It can be seen that the majority of

p_{i}

’s are below

0.5

Panel of Figure 16 — Figure 16: Examples of client unavailability with probabilistic trajectories. The first row in each sub-figure plots the probabilistic trajectory of each dynamics. The second row visualizes the simulated client availability by using a colored box to denote that a client is available in that round. The y-axis is the base probability $p_{i}$ to construct $p_{i}^{t}$ . In other words, more blank space means that a client is more scarcely available. We simulate the cases where $p_{i}\in\left\{0.1,0.5,0.9\right\}$ . The detailed construction of $p_{i}^{t}$ can be found in Appendix H.2

Data sets	SVHN				CIFAR-10				CINIC-10
Quarters	$1/4$	$1/2$	$3/4$	$1$	$1/4$	$1/2$	$3/4$	$1$	$1/4$	$1/2$	$3/4$	$1$
Test accuracy	$20\%$	$40\%$	$60\%$	$80\%$	$15\%$	$30\%$	$45\%$	$60\%$	$10\%$	$20\%$	$30\%$	$40\%$
FedSWE ( ours , $k=0$ )	40	120	200	820	20	60	200	1360	0	20	120	540
FedAvg over active clients	20	80	160	900	10	20	120	1060	0	20	40	800
FedAvg over all clients	100	420	960	—	20	60	520	—	0	20	200	—
FedAU	60	100	160	840	10	20	100	960	0	20	80	460

Appendix

Table 7: The first round to reach a targeted test accuracy under non-stationary of sine trajectory over 3 random seeds. We study the first round to reach

1/4

1/2

3/4

and

1

of the best test accuracy of each data set in Table 2 , which is rounded up to the nearest

10\%

below for ease of presentation. In addition, we sample the mean of test accuracy every 20 global rounds to mitigate noisy progress. Some algorithms may never attain the targeted accuracy due to their inferior performance, where we use “—” as a placeholder.

Unavailable Dynamics	Data sets	$\gamma=0.3$		$\gamma=0.2$		$\gamma=0.1$
Unavailable Dynamics	Algorithms	Train	Test	Train	Test	Train	Test
Non -stationary ( Sine )	FedSWE ( ours , $k=0$ )	85.7 $\pm$ 0.9 %	85.6 $\pm$ 0.9 %	85.7 $\pm$ 0.5 %	85.7 $\pm$ 0.5 %	85.8 $\pm$ 0.6 %	85.7 $\pm$ 0.7 %
	FedAvg over active	82.1 $\pm$ 1.1 %	82.0 $\pm$ 1.3 %	82.0 $\pm$ 1.2 %	81.9 $\pm$ 1.2 %	82.3 $\pm$ 0.9 %	82.2 $\pm$ 1.0 %
	FedAvg over all	71.3 $\pm$ 2.5 %	71.3 $\pm$ 2.8 %	73.2 $\pm$ 2.5 %	73.2 $\pm$ 2.8 %	74.0 $\pm$ 2.1 %	74.9 $\pm$ 2.4 %
	FedAU	82.5 $\pm$ 1.4 %	82.5 $\pm$ 1.3 %	83.5 $\pm$ 0.3 %	83.4 $\pm$ 0.4 %	83.7 $\pm$ 0.3 %	83.6 $\pm$ 0.3 %
	F3AST	82.3 $\pm$ 1.0 %	82.3 $\pm$ 1.0 %	82.3 $\pm$ 0.9 %	82.6 $\pm$ 0.8 %	82.9 $\pm$ 0.7 %	82.9 $\pm$ 0.6 %

Appendix

Table 8: Results after different parameter

\gamma

p_{i}^{t}=p_{i}\cdot(\gamma\sin(2\pi/P\cdot t)+(1-\gamma))

Unavailable Dynamics	Data sets	$\alpha=0.05$		$\alpha=0.1$		$\alpha=1.0$
Unavailable Dynamics	Algorithms	Train	Test	Train	Test	Train	Test
Non -stationary ( Sine )	FedSWE ( ours , $k=0$ )	82.5 $\pm$ 2.1 %	82.5 $\pm$ 2.4 %	85.7 $\pm$ 0.9 %	85.6 $\pm$ 0.9 %	90.6 $\pm$ 0.2 %	89.7 $\pm$ 0.3 %
	FedAvg over active	78.9 $\pm$ 1.6 %	78.5 $\pm$ 1.8 %	82.1 $\pm$ 1.1 %	82.0 $\pm$ 1.3 %	88.3 $\pm$ 0.1 %	87.5 $\pm$ 0.1 %
	FedAvg over all	58.5 $\pm$ 3.0 %	58.5 $\pm$ 3.8 %	71.3 $\pm$ 2.5 %	71.3 $\pm$ 2.8 %	82.0 $\pm$ 0.7 %	81.9 $\pm$ 0.6 %
	FedAU	79.5 $\pm$ 1.6 %	79.5 $\pm$ 1.7 %	82.5 $\pm$ 1.4 %	82.5 $\pm$ 1.3 %	88.4 $\pm$ 0.1 %	87.6 $\pm$ 0.2 %
	F3AST	78.9 $\pm$ 1.3 %	78.9 $\pm$ 1.3 %	82.3 $\pm$ 1.0 %	82.3 $\pm$ 1.0 %	87.6 $\pm$ 0.1 %	87.0 $\pm$ 0.1 %

Appendix

Table 9: Results after different

\mathsf{Dirichlet}

parameter

\alpha

p_{i}^{t}=p_{i}(\gamma\sin(2\pi/P\cdot t)+(1-\gamma))

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