Participation in federated learning (FL) comes at a cost. Clients trade off privacy, communication, and compute costs for potentially greater gains in model efficacy. This paper explores this tradeoff under the aegis of individual rationality (IR) versus autarky, the basic game-theoretic requirement that the federation provide utility no worse than local training. Using the above as the design target, we examine pathwise performance of FL, as a per-round bound on cumulative surplus rather than only an asymptotic equilibrium guarantee under different degrees of client data heterogeneity. Along the learning path, clients can remain below their local-training baseline for hundreds of rounds. The natural remedy is to cap each client's per-round contribution so that this shortfall stays bounded. We prove that such a cap drives all contributions to zero, with high probability, when its tolerance is small relative to the warm-up deficit, and we observe learning collapse under it even at low heterogeneity. We then propose a design that combines a short-term participation guarantee, enforced after an announced grace window, with personalized model evaluation, while preserving the incentive properties of the underlying mechanism. We provide a theoretical basis for this approach and empirically demonstrate that, after the grace window, clients meet IR on nearly all rounds without harming overall performance under low to moderate heterogeneity; under severe heterogeneity, the design shows promising outcomes for clients compared to their local baseline at some cost in accuracy.
Figures & tables
Figure 1: CIFAR-10, α=0.1 , size-weighted, Tg=100 (dotted line), Δi=1 , seed 123; the other five seeds are in Appendix C.2 . (a) Per-round IR, 20-round rolling mean: mechanism IR for FedBR-BG and the grace contract, participation IR for the co-design, scored on different ledgers. (b) Total contribution ∑isit : the grace contract collapses ten rounds after Tg and stops training; the co-design keeps contributing. (c) Mean post-grace ledgers across clients, symmetric-log axis: the participation ledger Ψi,persTg , which the clip enforces, and the mechanism ledger Ψi,MTg of the same run, which nothing enforces. The shaded gap is ∑τ=Tgtδi(sτ) ; the dashed line marks −Δi=−1 .
Method
α=10
α=1
α=0.1
CIFAR-10
Pathwise IR not enforced
FedAvg
85.1±0.3 ( 91.4±0.3 )
83.9±0.5 ( 82.2±2.0 )
67.3±4.8 ( 8.2±4.8 )
FedBR-BG
84.4±0.1 ( 83.5±0.2 )
86.6±0.4 ( 83.3±0.9 )
64.9±4.8 ( 11.6±3.5 )
Pathwise IR enforced, all on FedBR-BG
+ bare clipping, Δ=1
17.4±1.9 ( 0.0±0.0 )
16.2±3.1 ( 0.0±0.0 )
12.3±2.8 ( 2.1±2.7 )
+ grace contract, Δ=0.005
82.9±0.2 ( 98.6±0.2 )
84.9±0.2 ( 95.5±1.2 )
22.4±6.7 ( 3.7±2.3 )
Table 1: Accuracy and per-round IR (in parentheses), in percent; mean ± standard deviation over seeds {123,456,789} , plus {2024,2025,2026} at CIFAR-10 α=0.1 . Size-weighted aggregation, Tg=100 , costs Uniform[4,5]×10−4 . Accuracy is the final-50-round mean. IR is the share of agent-rounds with non-negative surplus over each row’s contract period: the full run for FedAvg, FedBR-BG and bare clipping, which have no grace period; rounds after Tg for the grace contract and the co-design. In FedAvg, each agent contributes its full training set and there is no payment term; co-design rows report participation IR (Section 6 ). The IR fractions here count rounds with ψi(t)≥0 , a stronger condition than the contract’s ΨiTg(t)≥−Δi . The last row of each block is the mean personalization gain δi over the final 50 rounds, in points.
Appendix figures & tables15 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 2: Total contribution ∑isit under bare clipping at Δi∈{1,5,20} (reds; solid, dashed, dotted) against the unconstrained dynamics ( Δi=∞ , black), size-weighted aggregation, 30 agents, on CIFAR-10 and MNIST (rows) at α∈{10,1.0,0.1} (columns), symmetric-log axis. Each line is one seed (three per tolerance; six at CIFAR-10 α=0.1 for Δi∈{∞,1} ); seeds are not averaged because at large Δi some collapse and some do not, so a mean would not describe any individual run. All panels use a 150-round window. The shaded band is ∑isi<1 , below one batch across the whole federation; a curve that plateaus inside it has functionally collapsed even where tcoll , defined by ∑isi=0 , records no collapse. The dash-dot line is the sampler’s expected cover time ( ≈10.5 rounds), a timescale marker rather than a fit or a prediction of tcoll .
Figure 3: Collapse round tcoll under bare clipping against the number of agents sampled per round, m , with n=30 , α=0.1 , Δi=1 , three seeds per dataset. Markers are individual runs (CIFAR-10 circles, MNIST squares, offset horizontally for legibility); black diamonds are the mean ± standard deviation over the runs that collapse. One of the six runs at m=20 (CIFAR-10, seed 456) does not collapse within its 150 rounds and holds ∑isi at 8.9. The dash-dot curve is the sampler’s exact expected cover time, the number of rounds until every agent has been sampled at least once when m distinct agents are drawn per round. It is a timescale marker: tcoll cannot fall below a run’s realized cover time, and at small m the cover time itself varies widely between draws. Runs at m=10 are from the main sweep; the others ran for 150 rounds.
Figure 4: Headline CIFAR-10 α=0.1 trajectories for seed 456 , size-weighted, Tg=100 , Δi=1 ; panels as in Figure 1 .
Figure 5: Headline CIFAR-10 α=0.1 trajectories for seed 789 , size-weighted, Tg=100 , Δi=1 ; panels as in Figure 1 .
Figure 6: Headline CIFAR-10 α=0.1 trajectories for seed 2024 , size-weighted, Tg=100 , Δi=1 ; panels as in Figure 1 .
Figure 7: Headline CIFAR-10 α=0.1 trajectories for seed 2025 , size-weighted, Tg=100 , Δi=1 ; panels as in Figure 1 .
Figure 8: Headline CIFAR-10 α=0.1 trajectories for seed 2026 , size-weighted, Tg=100 , Δi=1 ; panels as in Figure 1 .
Figure 9: Post-grace cumulative surplus on the mechanism ledger Ψi,MTg(t) (dark gray) and the participation ledger Ψi,persTg(t) (blue), mean across clients, for the co-design at Tg=100 , Δi=1 , size-weighted aggregation, seed 123. The shaded region between the two equals ∑τ=Tgtδi(sτ) (Corollary 2), blue where the participation ledger is above; a negative cumulative gain would be shaded orange but is too small to see in any panel. The dashed line marks −Δi=−1 . At α=10 the two ledgers coincide to within the line width (the mean δi in Table 1 is −0.12 points on CIFAR-10 and −0.04 on MNIST, the optimization and finite-sample slack of Lemma 3’s remark); at α=1 a small positive gain appears on CIFAR-10; at α=0.1 the gap is large on CIFAR-10, where the global head is compromised, and positive but small on MNIST, where autarky saturation limits it.
Method
α=10
α=1
α=0.1
CIFAR-10
unconstrained
82.5±0.4 ( 86.6±0.4 )
83.7±0.2 ( 84.6±2.2 )
65.6±4.2 ( 12.8±6.2 )
+ bare clipping
18.2±5.8 ( 0.0±0.0 )
18.8±4.2 ( 0.0±0.0 )
12.5±2.2 ( 4.4±1.9 )
+ grace contract
83.0±0.7 ( 99.8±0.1 )
84.3±0.6 ( 97.2±1.5 )
19.3±1.9 ( 2.4±2.1 )
+ co-design
82.4±0.9 ( 99.7±0.4 )
83.9±1.3 ( 99.9±0.1 )
61.3±7.0 ( 87.9±3.9 )
mean δi (pts)
−0.15±0.02
+1.78±0.42
+31.06±9.19
MNIST
unconstrained
99.0±0.1 ( 92.0±0.7 )
98.9±0.1 ( 83.6±2.7 )
98.5±0.2 ( 15.5±5.0 )
Appendix
Table 2: Accuracy and per-round IR fraction under MShap , both in percent (IR in parentheses), mean ± standard deviation over seeds {123,456,789} ; size-weighted aggregation, Δi=1 , Tg=100 , costs Uniform[4,5]×10−4 . Conventions as in Table 1 .
CIFAR-10
MNIST
Arm
α=10
α=1
α=0.1
α=10
α=1
α=0.1
Grace contract
84.5 ( 98.9 )
86.0 ( 97.2 )
23.9 ( 2.8 )
99.0 ( 97.9 )
99.0 ( 94.0 )
96.6 ( 17.9 )
Co-design
84.3 ( 98.7 )
86.6 ( 100.0 )
59.4 ( 87.7 )
99.0 ( 97.5 )
99.0 ( 94.3 )
98.5 ( 42.7 )
Heads only, Δi=∞
84.3 ( 98.8 )
86.6 ( 100.0 )
64.7 ( 91.2 )
99.0 ( 97.5 )
99.0 ( 94.3 )
98.6 ( 42.4 )
Heads, clip from round 1
17.6 ( 0.0 )
22.6 ( 2.0 )
15.6 ( 19.1 )
63.6 ( 0.4 )
79.3 ( 8.7 )
96.9 ( 37.7 )
Appendix
Table 3: Ablations at Δi=1 (where a tolerance applies), size-weighted aggregation, mean over seeds {123,456,789} , and over six seeds at CIFAR-10 α=0.1 in every row but the last, which uses three; per-seed spreads for the grace and co-design rows are in Table 1 . Accuracy and per-round IR fraction in percent (IR in parentheses), conventions as in Table 1 ; IR is the participation ledger for the three head-bearing arms and the mechanism ledger for the grace contract, averaged over the rounds each arm’s contract covers. Accuracy in the last row is frozen-model drift after collapse at α≥1 , where the spread across seeds reaches ±21.7 points.
CIFAR-10
MNIST
Arm
α=10
α=1
α=0.1
α=10
α=1
α=0.1
Grace contract
2
13
179
0
0
69
Co-design
2
0
23
0
0
7
Heads only (no enforcement)
2
0
23
0
0
9
Appendix
Table 4: Agent-seed pairs whose post-grace ledger crosses −Δi at some round, at Δi=1 , size-weighted aggregation; out of 90 (30 agents × 3 seeds), and out of 180 at CIFAR-10 α=0.1 . The grace contract is scored on the mechanism ledger, the co-design and heads-only arms on the participation ledger. Heads-only enforces nothing; it is counted against the same −1 and shown for reference.
Δi
Accuracy
IR
Clip rate
Floored
Below −Δi
Below −1
1
56.8±9.9
86.1
10.2
8
12
12
2
60.0±7.9
88.0
5.6
5
6
11
5
62.2±5.8
89.3
3.8
3
4
11
20
65.8±4.5
91.0
0.0
0
0
11
∞ (heads only)
65.8±4.5
91.0
0.0
0
–
11
Appendix
Table 5: Tolerance sweep for the co-design, CIFAR-10, α=0.1 , Tg=100 , size-weighted aggregation, seeds {123,456,789} throughout, so the Δi=1 row repeats Table 1 ’s co-design cell over these three seeds rather than all six. Accuracy is the final-50-round mean ± standard deviation over seeds; IR is the participation IR over rounds after Tg ; the clip rate is the share of sampled agents clipped per post-grace round. Floored agent-seeds are at zero contribution throughout the final 50 rounds. The last two columns count agent-seeds (of 90) whose post-grace ledger ever falls below −Δi and below −1 .
Aggregation
α
Tg
Entry IR
Post-grace IR
Accuracy
Collapsed seeds
size-weighted
10
100
0.42
98.9
84.5
0
size-weighted
1
100
0.52
97.2
86.0
0
size-weighted
0.1
100
0.02
4.4
27.9
3
uniform
10
100
0.00
0.0
32.7
3
uniform
10
200
0.01
2.1
44.7
2
uniform
10
300
0.23
61.3
60.4
0
Appendix
Table 6: Entry state and outcome of the grace contract, CIFAR-10, Δi=1 , mean over seeds {123,456,789} throughout, including the size-weighted α=0.1 row, which Table 1 reports over six. Entry IR is the share of agent-rounds with non-negative mechanism surplus over the ten rounds ending at Tg , measured on the unconstrained run. Post-grace IR is the mechanism IR over rounds after Tg ; accuracy is the mean over the final 50 rounds; the last column counts seeds whose total contribution reaches zero.
ξi=0
0.001
0.005
0.01
CIFAR-10
α=10
98.7
98.6
98.5
98.2
α=1
100.0
100.0
100.0
99.9
α=0.1
87.7
86.7
84.4
81.8
MNIST
α=10
97.5
96.9
91.7
82.2
α=1
94.3
93.5
83.7
66.2
α=0.1
42.7
35.9
23.2
12.2
Appendix
Table 7: Post-grace participation IR (%) of the co-design at Δi=1 when a per-round head-fitting cost ξi is charged post hoc, holding the logged trajectories fixed. Seeds as in Table 1 : three, and six at CIFAR-10 α=0.1 .
CIFAR-10
MNIST
Federation
Clients n
30
30
Sampled per round m
10
10
Local epochs E
2
2
Dirichlet α
{10,1,0.1}
Aggregation
size-weighted, server step size 1
Appendix
Table 8: Hyperparameters for the main experiments. Values not split by dataset are shared. Contributions follow the best-response update of Appendix B.1 , with ∂ai/∂si estimated by the probe scheme of Appendix B.2 ; the IR ledger is scored on the mechanism utility uiM=ai−cisi+pi , after transfers, and on the participation utility for the co-design.
Federated Learning (FL) algorithms implicitly assume that clients passively comply with server-side orchestration by sharing local model updates upon server request. However, this overlooks an important aspect in real-world cross-silo environments: clients are often rational agents who may prioritize their utilities such as local model performance over that of the global model. In settings with significant statistical heterogeneity, rational clients may opt out of the federation if the perceived benefits of collaboration fail to meet their local utility thresholds. Such attrition degrades the global model performance and can lead to the collapse of the federated training process. In this work, we introduce FedUCA, (Federated Learning by Utility-Constrained Stochastic Aggregation for Improving Rational Participation), a framework that formalizes the server's role as an optimizer seeking to maximize global model performance by sustaining client participation. We substantiate our framework through extensive experiments on standard datasets demonstrating that by prioritizing participation feasibility, FedUCA achieves significantly higher client retention and, consequently, a superior global model performance.
M Yashwanth, Arunabh Singh, Ashok Nayak +2
Indian Institute of Science, Bangalore · Indian Institute of Technology Bombay · IIIT Hyderabad
Federated learning (FL) commonly involves clients with diverse communication and computational capabilities. Such heterogeneity can significantly distort the optimization dynamics and lead to objective inconsistency, where the global model converges to an incorrect stationary point potentially far from the pursued optimum. Despite its critical impact, the joint effect of communication and computation heterogeneity has remained largely unexplored, due to the intrinsic complexity of their interaction. In this paper, we reveal the fundamentally distinct mechanisms through which heterogeneous communication and computation drive inconsistency in FL. To the best of our knowledge, this is the first unified theoretical analysis of general heterogeneous FL, offering a principled understanding of how these two forms of heterogeneity jointly distort the optimization trajectory under arbitrary choices of local solvers. Motivated by these insights, we propose Federated Heterogeneity-Aware Client Sampling, FedACS, a universal method to eliminate all types of objective inconsistency. We theoretically prove that FedACS converges to the correct optimum at a rate of O(1/R), even in dynamic heterogeneous environments. Extensive experiments across multiple datasets show that FedACS outperforms state-of-the-art and category-specific baselines by 4.3%-36%, while reducing communication costs by 22%-89% and computation loads by 14%-105%, respectively.
Shudi Weng, Chao Ren, Ming Xiao +1
Division of Information Science and Engineering, School of Electrical Engineering and Computer Science (EECS), KTH Royal Institute of Technology, 11428 Stockholm, Sweden
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.