FedPCD: Priority-Constrained Federated Aggregation

Yousef Irshaid; Dara Varam; Mohamed I. AlHajri

cs.LGOct 9, 2026

FedPCD: Priority-Constrained Federated Aggregation

Authors: Yousef Irshaid, Dara Varam, Mohamed I. AlHajri

Organizations: Department of Computer Science & Engineering, American University of Sharjah · Senseable City Laboratory, Massachusetts Institute of Technology

Abstract

Federated learning (FL) seeks to optimize a shared global model from decentralized client data. While effective for average performance, this process can produce unfair performance across clients, particularly under statistically heterogeneous data distributions. Existing fairness-aware and multi-objective FL methods address this through client re-weighting, gradient correction, or common-descent formulations, but often change the global optimization direction or treat client objectives symmetrically. We propose FedPCD, a priority-constrained federated optimization framework that separates the global optimization objective from client protection. FedPCD preserves the conventional federated aggregate as the primary objective, while allowing only the minimum correction necessary to meet client performance constraints. Across heterogeneous FL benchmarks, FedPCD consistently outperforms state-of-the-art baselines, achieving the highest global accuracy across all configurations and leading worst-10% client accuracy in nearly all. FedPCD further preserves competitive trade-offs between global accuracy and client performance variability. Beyond this trade-off, FedPCD demonstrates faster empirical convergence, reaching matching or superior performance in substantially fewer communication rounds.

Figures & tables

Panel of Figure 1 — Figure 1: A taxonomy of the fairness-aware federated learning methods discussed in Sec. 2 .

Figure 2: FedPCD system diagram, showing an example with three participating clients at communication round $t$ . Left: Algorithmic steps taken to obtain a final direction in gradient space ( $\tilde{d}^{\star}$ ). Right: Objective space view, showing the resultant $\tilde{d}^{\star}$ . The half-space projection of each gradient is used to find the feasible region, which then allows us to see the minimum distortion required to satisfy all secondary constraints.

Figure 3: Demonstration of history for FedPCD, with $N=30$ clients, $10\%$ participation and $H=10$ . Top: PCD program at 4 selected rounds, marked on the curve. Paler arrows are older cache entries, and red arrows are minority clients that do not satisfy the PCD condition. Bottom: number of secondary constraints per round, which grows from 3 participants as a function of the communication rounds.

CIFAR-10
Method	5% participation									10% participation
	$\alpha=0.01$			$\alpha=0.1$			$\alpha=1$			$\alpha=0.01$			$\alpha=0.1$			$\alpha=1$
	$\bar{a}\!\uparrow$	$\sigma_{c}\!\downarrow$	$\mathrm{W}_{10\%}\!\uparrow$	$\bar{a}\!\uparrow$	$\sigma_{c}\!\downarrow$	$\mathrm{W}_{10\%}\!\uparrow$	$\bar{a}\!\uparrow$	$\sigma_{c}\!\downarrow$	$\mathrm{W}_{10\%}\!\uparrow$	$\bar{a}\!\uparrow$	$\sigma_{c}\!\downarrow$	$\mathrm{W}_{10\%}\!\uparrow$	$\bar{a}\!\uparrow$	$\sigma_{c}\!\downarrow$	$\mathrm{W}_{10\%}\!\uparrow$	$\bar{a}\!\uparrow$	$\sigma_{c}\!\downarrow$	$\mathrm{W}_{10\%}\!\uparrow$
FedAvg	48.09	19.55	18.74	60.96	13.68	37.08	71.93	5.78	61.68	57.47	15.93	29.93	64.43	11.67	43.27	72.94	5.65	63.28
AFL	26.82	18.50	7.19	46.20	10.83	25.93	64.08	5.64	54.42	43.86	11.37	22.16	53.79	8.97	36.99	65.49	5.53	56.18
q-FFL	50.62	17.16	24.00	60.30	13.12	37.95	71.18	5.75	61.03	56.60	15.02	30.21	63.31	11.43	42.77	71.96	5.61	62.04

Table 1: Results on CIFAR-10, CIFAR-100, and Fashion-MNIST.

\bar{a}

: global accuracy;

\sigma_{c}

: within-run std. across client accuracies;

\mathrm{W}_{10\%}

: worst-10% client accuracy. Within each dataset block, bold marks the best overall value in a column and underline marks the best value from the competing method group, such that the strongest FedPCD configuration and strongest baseline are both highlighted.

Figure 4: Global accuracy against client-accuracy spread at

\alpha=0.01

for both participation rates. Higher accuracy and lower

\sigma_{c}

are preferred. Crosses indicate variation across the 5 seeds

Figure 5: Client test-accuracy distributions at $\alpha=0.01$ across datasets and participation rates. Methods are ordered by global accuracy with each violin representing the kernel density of client accuracies pooled over the 5 seeds.

Figure 6: Client test accuracy distributions for FedPCD, FedAvg, and the strongest non-FedPCD baseline at

\alpha=0.01

. The distribution means are shown as dashed lines and their values are reported per panel.

Figure 7: Global accuracy against communication rounds at

\alpha=0.01

. Dots mark when FedPCD reaches FedAvg’s final accuracy, while stars mark when it reaches the strongest baseline’s final accuracy. When the latter is not reached, a hollow ring marks when that baseline reaches FedAvg’s final accuracy.

Appendix figures & tables14 assets

Supplementary material from the paper’s appendix.

Appendix

Method	Parameters
AFL	$\eta_{\lambda}\in\{0.01,\,0.1,\,0.5\}$
q-FFL	$q\in\{0.1,\,1,\,10\}$
Ditto	$\lambda\in\{0.1,\,1,\,2\}$
FedMGDA+	$\epsilon\in\{0.1,\,0.5,\,1\}$
FedFV	$H=10,\quad\alpha\in\{0.1,\,0.3,\,0.5\}$
FedLF	$H=10$

Appendix

Table 2: Hyperparameter search spaces.

Figure 8: Comparison of FedPCD to its closest fair FL neighbors used as baselines in this study.

Figure 9: Client test-accuracy distributions at $\alpha=0.1$ across datasets and participation rates. Methods are ordered by global accuracy with each violin representing the kernel density of client accuracies pooled over the 5 seeds.

Figure 10: Client test-accuracy distributions at $\alpha=1$ across datasets and participation rates. Methods are ordered by global accuracy with each violin representing the kernel density of client accuracies pooled over the 5 seeds.

Figure 11: Client test accuracy distributions for FedPCD, FedAvg, and the strongest non-FedPCD baseline at

\alpha=0.1

. The distribution means are shown as dashed lines and their values are reported per panel.

Figure 12: Client test accuracy distributions for FedPCD, FedAvg, and the strongest non-FedPCD baseline at

\alpha=1

. The distribution means are shown as dashed lines and their values are reported per panel.

Figure 13: Global accuracy against communication rounds at

\alpha=0.1

Figure 14: Global accuracy against communication rounds at

\alpha=1

Figure 15: Global accuracy against client-accuracy spread at

\alpha=0.1

for both participation rates. Higher accuracy and lower

\sigma_{c}

are preferred. Crosses indicate variation across the 5 seeds.

Figure 16: Global accuracy against client-accuracy spread at

\alpha=1

for both participation rates. Higher accuracy and lower

\sigma_{c}

are preferred. Crosses indicate variation across the 5 seeds.

CIFAR-10
Method	5% participation			10% participation
	$\alpha=0.01$	$\alpha=0.1$	$\alpha=1$	$\alpha=0.01$	$\alpha=0.1$	$\alpha=1$
FedAvg	0.8574	0.9516	0.9935	0.9256	0.9674	0.9940
AFL	0.6285	0.9476	0.9923	0.9346	0.9727	0.9929
q-FFL	0.8958	0.9545	0.9935	0.9320	0.9678	0.9940
Ditto	0.8593	0.9514	0.9933	0.9258	0.9676	0.9941

Appendix

Table 3: Jain’s fairness index over the per-client accuracies, under the same settings as Table 1 . Higher is better. Within each dataset block, bold marks the best overall value in a column and underline marks the best value from the competing method group, such that the strongest FedPCD configuration and strongest baseline are both highlighted.

Method	$\alpha=0.01$			$\alpha=0.1$			$\alpha=1$
	$\bar{a}\uparrow$	$\bar{\sigma}_{c}\downarrow$	$W_{10\%}\uparrow$	$\bar{a}\uparrow$	$\bar{\sigma}_{c}\downarrow$	$W_{10\%}\uparrow$	$\bar{a}\uparrow$	$\bar{\sigma}_{c}\downarrow$	$W_{10\%}\uparrow$
FedAvg	57.47	15.93	29.93	64.43	11.67	43.27	72.94	5.65	63.28
FedPCD	74.84	8.89	58.03	75.69	7.45	61.28	77.51	4.68	69.24
FedPCD w/o history	59.26	16.24	29.65	65.50	11.64	44.13	73.00	5.69	63.16
FedPCD τ=0	74.31	9.15	57.55	74.88	7.90	59.91	76.96	5.12	67.85
FedPCD w/o normalization	72.99	9.40	54.44	75.08	7.46	60.85	76.96	4.66	68.81

Appendix

Table 4: Component ablation on CIFAR-10 at 10% participation.

Figure 17: Impact of increasing history window size

H

on the global accuracy, the worst-10% across clients, and the number of active secondary constraints. This is reported across all three datasets, with

\tau=0.02

and

\alpha=0.01

Normalization	$\alpha=0.01$			$\alpha=0.1$			$\alpha=1$
	$\bar{a}\uparrow$	$\bar{\sigma}_{c}\downarrow$	$W_{10\%}\uparrow$	$\bar{a}\uparrow$	$\bar{\sigma}_{c}\downarrow$	$W_{10\%}\uparrow$	$\bar{a}\uparrow$	$\bar{\sigma}_{c}\downarrow$	$W_{10\%}\uparrow$
Instantaneous $\ell_{2}$	74.84	8.89	58.03	75.69	7.45	61.28	77.51	4.68	69.24
Scalar EMA ( $\beta=0.5$ )	74.77	8.98	57.61	75.54	7.66	60.68	77.46	4.83	68.77
Scalar EMA ( $\beta=0.8$ )	74.69	9.17	56.77	75.69	7.44	61.83	77.35	4.82	68.73
Scalar EMA ( $\beta=0.9$ )	74.81	9.07	57.30	75.51	7.68	60.66	77.29	4.78	68.90

Appendix

Table 5: Normalization ablation on CIFAR-10 at 10% participation and round 500. Results are averaged over five seeds with

H=10

. We use

\tau=(0.01,0.02,0.075)

for

\alpha=(0.01,0.1,1)

, respectively.

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Federated Learning Aggregation Algorithmic Fairness Shapley Value Attribution Federated Learning Heterogeneous Federated Learning

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Federated learning is an emerging distributed paradigm that addresses the challenges posed by heterogeneous, privacy-sensitive data. It enables multiple clients to train a model collaboratively by aggregating their local updates at a server. However, conventional aggregation schemes typically use fixed weights that fail to reflect unequal and time-varying client contributions, leading to biased and unstable learning. To improve fairness and stability, we propose the Trajectory Shapley Value (TSV), a contribution metric that evaluates how each client influences the optimization trajectory of the global model using a validation-based, temporally consistent utility. Building on TSV, we design FedTSV, an adaptive aggregation method that converts per-round evaluations into dynamic client weights, allowing the server to respond to heterogeneous and adversarial participation in real time. Experiments on benchmark datasets show that FedTSV accelerates convergence, improves robustness, and yields more equitable contribution assessments, thereby providing a principled foundation for fairness-aware federated optimization.

Abstract

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