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 xoutput≜limt→∞E[xt] . Under most of the choices of p1,p2 , xoutput is far from x∗ .
Figure 3: Train and test accuracy results in percentage (%). In particular, the parameter γ signifies the degree of non-stationary. Notice that, as the client availability becomes more non-stationary (a larger γ ), FedAvg experiences a significant drop in accuracy. For example, both the train and test accuracies drop by over 10% when p=0.1 , and γ increases from 0.1 to 0.5 .
Figure 4
Bounded Gradient Dissimilarity
References
maxx∥∇Fi(x)∥22≤ζ2,\penalty∀\penaltyi∈[m]
( Li et al., 2020b ; Yu et al., 2019b ; Cho et al., 2022 ; Cho et al., 2023b ; Yan et al., 2023 ) .
m1∑i=1m∥∇Fi(x)∥22≤β2∥∇F(x)∥22
( Li et al., 2019 ; Li et al., 2020a )
m1∑i=1m∥∇Fi(x)−∇F(x)∥22≤ζ2
( 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 ) .
m1∑i=1m∥∇Fi(x)∥22≤β2∥∇F(x)∥22+ζ2
( 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.
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.
Figure 5: Visualizations of Algorithm 1 with two clients and a global objective ( 29 ), whose u1=100 , u2=−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 u1+u2=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.
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 M1 and M2 . The global rounds can be partitioned into periods, each with length 50 rounds. In all odd periods, the available probability pit>0 if i∈M1 while pit=0 otherwise. In all even periods, the available probability pit>0 if i∈M2 while pit=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 Pδ 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 .
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 Pδ round. The curves plot the averaged results, while the shaded areas plot the standard deviation.
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 .
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 .
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 pit . 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.
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 .
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
Algorithms
Train
Test
Train
Test
Train
Test
Stationary
FedSWE ( ours, k=0 )
86.5 ± 0.7 %
86.1 ± 0.7 %
68.1 ± 1.4 %
66.3 ± 1.1 %
47.9 ± 2.1 %
47.3 ± 2.0 %
FedSWE ( ours, k=100 )
86.3 ± 1.1%
85.4 ± 1.0%
68.7 ± 1.0 %
66.9 ± 0.9 %
48.3 ± 1.7 %
47.9 ± 1.6 %
FedAvg over active
82.6 ± 1.0 %
82.4 ± 1.1 %
64.1 ± 1.9 %
62.9 ± 1.4 %
43.6 ± 2.4 %
43.1 ± 2.4 %
FedAvg over all
76.1 ± 2.1 %
76.1 ± 2.4 %
55.8 ± 2.1 %
55.4 ± 1.8 %
38.4 ± 2.1 %
38.0 ± 2.1 %
gFedAvg
83.5 ± 1.5 %
83.0 ± 1.2%
64.5 ± 1.7%
63.8 ± 1.7%
45.3 ± 1.4%
44.9 ± 1.2%
Table 2: Results and comparisons on real-world data sets in the form of mean accuracy ± 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
At
The set of active clients in round t .
Wt
A doubly stochastic matrix to capture the information mixing error. Its definition can be found in ( 9 ).
pit
The probability that a client i becomes available in round t .
τi(t)
τi(t)≜sup{t′∣t′<t,i∈At′} defines client i ’s most recent active round. In particular, τi(0)=−1 for all i∈[m] .
xit
The real model at client i at the beginning of round t in Algorithm 1 .
zit
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
δ
An absolute constant that is the lower bound on the client unavailability.
Pδ , P
The period in Assumption 1 .
L
Lipschitz constant in Assumption 2 .
σ2
The upper bound of the stochastic gradient variance.
(β,\penaltyζ)
Parameters that capture the averaged gradient dissimilarity between global and local objectives.
ρ
The spectral norm of a stochastic matrix in expectation.
s
The number of local computation steps.
Appendix
Table 4: Variable table
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 Dirichlet(α=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 ηl scheduling
ηl=η0 in Section 7.1 ; ηl=t/10+1η0 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
η0
ηg
η0
ηg
η0
ηg
η0
ηg
η0
ηg
η0
ηg
η0
ηg
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
η0
ηg
η0
ηg
η0
ηg
η0
ηg
η0
ηg
η0
ηg
η0
ηg
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
η0
ηg
η0
ηg
η0
ηg
η0
ηg
η0
ηg
η0
ηg
η0
ηg
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 η0 and global learning rate ηg
Figure 15: A histogram of one generated pi ’s example with a total of m=100 clients. It can be seen that the majority of pi ’s are below 0.5 .
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 pi to construct pit . In other words, more blank space means that a client is more scarcely available. We simulate the cases where pi∈{0.1,0.5,0.9} . The detailed construction of pit 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
γ=0.3
γ=0.2
γ=0.1
Algorithms
Train
Test
Train
Test
Train
Test
Non -stationary ( Sine )
FedSWE ( ours , k=0 )
85.7 ± 0.9 %
85.6 ± 0.9 %
85.7 ± 0.5 %
85.7 ± 0.5 %
85.8 ± 0.6 %
85.7 ± 0.7 %
FedAvg over active
82.1 ± 1.1 %
82.0 ± 1.3 %
82.0 ± 1.2 %
81.9 ± 1.2 %
82.3 ± 0.9 %
82.2 ± 1.0 %
FedAvg over all
71.3 ± 2.5 %
71.3 ± 2.8 %
73.2 ± 2.5 %
73.2 ± 2.8 %
74.0 ± 2.1 %
74.9 ± 2.4 %
FedAU
82.5 ± 1.4 %
82.5 ± 1.3 %
83.5 ± 0.3 %
83.4 ± 0.4 %
83.7 ± 0.3 %
83.6 ± 0.3 %
F3AST
82.3 ± 1.0 %
82.3 ± 1.0 %
82.3 ± 0.9 %
82.6 ± 0.8 %
82.9 ± 0.7 %
82.9 ± 0.6 %
Appendix
Table 8: Results after different parameter γ . pit=pi⋅(γsin(2π/P⋅t)+(1−γ)) .
Unavailable Dynamics
Data sets
α=0.05
α=0.1
α=1.0
Algorithms
Train
Test
Train
Test
Train
Test
Non -stationary ( Sine )
FedSWE ( ours , k=0 )
82.5 ± 2.1 %
82.5 ± 2.4 %
85.7 ± 0.9 %
85.6 ± 0.9 %
90.6 ± 0.2 %
89.7 ± 0.3 %
FedAvg over active
78.9 ± 1.6 %
78.5 ± 1.8 %
82.1 ± 1.1 %
82.0 ± 1.3 %
88.3 ± 0.1 %
87.5 ± 0.1 %
FedAvg over all
58.5 ± 3.0 %
58.5 ± 3.8 %
71.3 ± 2.5 %
71.3 ± 2.8 %
82.0 ± 0.7 %
81.9 ± 0.6 %
FedAU
79.5 ± 1.6 %
79.5 ± 1.7 %
82.5 ± 1.4 %
82.5 ± 1.3 %
88.4 ± 0.1 %
87.6 ± 0.2 %
F3AST
78.9 ± 1.3 %
78.9 ± 1.3 %
82.3 ± 1.0 %
82.3 ± 1.0 %
87.6 ± 0.1 %
87.0 ± 0.1 %
Appendix
Table 9: Results after different Dirichlet parameter α . pit=pi(γsin(2π/P⋅t)+(1−γ)) .
Federated Learning (FL) enables training shared models on private, on-device data, but production deployments remain constrained to slow, multi-day refresh cycles due to the complexity of coordinating massive client populations. For applications such as feed ranking, ad targeting, and personalized recommendation, model freshness: the ability to rapidly adapt to new user-local data is critical for maximizing objectives like click-through rate. This lag leaves models stale and unresponsive to volatile data distributions driven by viral trends and shifting user intent. Bridging this gap requires addressing three challenges overlooked by existing FL systems: transient client availability, dynamic data heterogeneity, and delays between model predictions and observable outcomes. We present FeLiX, an FL orchestration framework that minimizes wall-clock time-to-target accuracy on live interaction streams. FeLiX introduces three primitives: (i) streaming-aware availability tiers that leverage lightweight telemetry to identify ready clients at scale; (ii) fresh-utility selection, a dual-tier mechanism that prioritizes statistically valuable updates from devices able to meet tight refresh deadlines; and (iii) informativeness-aware, delay-robust aggregation that incorporates late, high-value updates containing ground-truth outcomes without biasing the global model toward stale distributions. Unlike prior systems that rely on unrealistic oracular knowledge of client availability, FeLiX achieves near-oracular performance in real-world settings. Across CIFAR-10, Google Speech, and realistic low-availability traces, FeLiX reduces wall-clock time-to-target accuracy by up to 2.37X while reducing communication bandwidth by 1.30X compared to state-of-the-art synchronous and asynchronous FL baselines.
Federated learning (FL) enables collaborative model training without sharing raw data, but its performance degrades under non-IID data and stochastic client participation. Remedies built on classical Federated Averaging (FedAvg) typically presuppose that client participation probabilities are known to the server, which is rarely the case in deployed systems. We first discuss and then characterize the optimization problem that \emph{distributionally agnostic} FedAvg actually solves when participation is entirely unknown, possibly highly skewed, and of variable size across rounds: uniform aggregation is shown to minimize a well-defined stochastic objective, weighted by the participation-induced marginal, at a standard O(1/T) rate for convex and possibly nonsmooth losses. Building on this characterization, we propose \emph{Federated Risk-Averse Averaging} (\textsc{FedeRage}), a risk-averse extension of FedAvg that embeds the \emph{Conditional Value-at-Risk} (CVaR) into the local objective within a natural distributionally robust optimization (DRO) framework. \textsc{FedeRage} implicitly upweights high-loss and infrequently participating clients while adding only a \emph{single scalar per-client}, and admits an O(κ/T) rate in which the factor κ is the upper bound on the ``price" of risk aversion. In contrast with aggregation-alignment schemes based on optimal transport, which require the availability distribution as an input, \textsc{FedeRage} remains agnostic to it. Several experiments on three heterogeneous benchmarks indicate consistent improvements over state-of-the-art methods in accuracy, fairness, and convergence speed.
Probabilistic Synchronous Parallel (PSP) is a technique in distributed learning systems to reduce synchronization bottlenecks by sampling a subset of participating nodes per round. In Federated Learning (FL), where edge devices are often unreliable due to factors including mobility, power constraints, and user activity, PSP helps improve system throughput. However, PSP has a key limitation: it assumes device behavior is static and different devices are independent. This can lead to unfair distributed synchronization, due to highly available nodes dominating training while those that are often unavailable rarely participate and so their data may be missed. If both data distribution and node availability are simultaneously correlated with the device, then both PSP and standard FL algorithms will suffer from persistent under-representation of certain classes or groups resulting in inefficient or ineffective learning of certain features. We introduce Availability-Weighted PSP (AW-PSP), an extension to PSP that addresses the issue of co-correlation of unfair sampling and data availability by dynamically adjusting node sampling probabilities using real-time availability predictions, historical behavior, and failure correlation metrics. A Markov-based availability predictor distinguishes transient \emph{vs} chronic failures, while a Distributed Hash Table (DHT) layer decentralizes metadata, including latency, freshness, and utility scores. We implement AW-PSP and trace-driven evaluation shows that it improves robustness to both independent and correlated failures, increases label coverage, and reduces fairness variance compared to standard PSP. AW-PSP thus provides an availability-aware, and fairness-conscious node sampling protocol for FL deployments that will scale to large numbers of nodes even in heterogeneous and failure-prone environments.
Stefan Behfar, Richard Mortier
Computer Lab, University of Cambridge, Cambridge, United Kingdom