arxiv: 2510.26841 · v2 · submitted 2025-10-30 · 💻 cs.LG · cs.AI

FedPF: Accurate Target Privacy Preserving Federated Learning Balancing Fairness and Utility

Kangkang Sun , Jun Wu , Minyi Guo , Jianhua Li , Jianwei Huang This is my paper

Pith reviewed 2026-05-18 02:52 UTC · model grok-4.3

classification 💻 cs.LG cs.AI

keywords federated learningdifferential privacyfairnessprivacy-utility tradeoffzero-sum gamedemographic biasmachine learning

0 comments p. Extension

The pith

Privacy protections in federated learning reduce power to correct demographic biases, but a zero-sum game approach still delivers low discrimination with high utility.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces FedPF, a differentially private fair federated learning algorithm that models the competing goals of privacy, fairness, and utility as a zero-sum game. Theoretical analysis establishes an inverse relationship: stronger privacy mechanisms reduce the statistical power to detect and correct demographic biases in finite-sample federated settings. This leads to a non-monotonic fairness-utility curve, where moderate fairness enforcement improves generalization before excessive constraints hurt performance. Experiments across three datasets confirm up to 42.9% discrimination reduction while retaining competitive accuracy, even under strict privacy, and show low computational demands for edge devices. The work emphasizes that strong privacy and fairness require balanced tradeoffs rather than isolated optimization.

Core claim

FedPF is a differentially private fair FL algorithm that transforms the multi-objective optimization into a zero-sum game where fairness and privacy constraints compete against model utility. Our theoretical analysis reveals an inverse relationship: privacy mechanisms that protect sensitive attributes can reduce the statistical power available for detecting and correcting demographic biases under finite samples in federated settings. We further show that our theoretical bounds are consistent with a non-monotonic fairness-utility relationship.

What carries the argument

Zero-sum game formulation of the multi-objective optimization problem for privacy, fairness, and utility in federated learning.

If this is right

Privacy mechanisms reduce statistical power for bias detection and correction in finite samples.
Moderate fairness constraints can improve generalization before excessive enforcement degrades performance.
FedPF achieves the lowest discrimination among compared algorithms even under strict privacy constraints.
Up to 42.9% discrimination reduction is possible while maintaining competitive accuracy.
The algorithm has a low computational footprint suitable for resource-constrained edge devices.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Joint tuning of privacy and fairness parameters may be necessary depending on available sample sizes to avoid reduced bias correction.
The approach could be generalized to other multi-objective problems in distributed learning beyond fairness and privacy.
Larger datasets or improved estimators might mitigate the privacy-induced loss in statistical power for fairness enforcement.

Load-bearing premise

The transformation of the multi-objective optimization problem into a zero-sum game accurately captures the interactions among privacy, fairness, and utility without introducing instabilities or requiring post-hoc parameter tuning that affects the reported discrimination reductions.

What would settle it

An experiment that varies privacy noise levels at fixed sample sizes and checks whether discrimination levels rise or bias correction effectiveness drops as the inverse relationship predicts.

Figures

Figures reproduced from arXiv: 2510.26841 by Jianhua Li, Jianwei Huang, Jun Wu, Kangkang Sun, Minyi Guo.

**Figure 1.** Figure 1: The fairness constraints of FedPF algorithm influence on the discrimination (Gya) without privacy protection in FL. X N i=1 (γy,p,i ˆ (fi) − γy,p,i(fi)) ≤ N · αmax, (20) where αmax = maxi∈N {T V (pi , pˆi)}. Proof For any group label a ∼ p, a ′ ∼ pˆ of client i, from Theorem 1 in work [11], we have: X N i=1 γy,a(fi) = X N i=1 {γy,a(fi) − γy,a′ (fi) + γy,a′ (fi)} , ≤ X N i=1 {|γy,a(fi) − γy,a′ (fi)| + γy,a′… view at source ↗

**Figure 2.** Figure 2: The privacy εp of FedPF algorithm influence on the loss of server model without fairness constraints in FL based on Adult, Bank and Compas datasets, respectively. an output layer producing a 2-dimensional prediction. The input dimensions of the model are 12, 22, and 12 based on Adult, Bank, and Compas datasets, respectively. The local batch size is 128. 3) Evaluation Metrics: To evaluate the influence of f… view at source ↗

**Figure 3.** Figure 3: The privacy budget of FedPF algorithm influence on the loss and the discrimination (EO) of server model in FL based on FedPF algorithm. The fairness constraints include without fairness constraints and With fairness constraints (εf = 0.1) lines. The sensitive attributes in Adult, Bank and Compas datasets are Age, Age and Sex, respectively. Key Observation 2 [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗

read the original abstract

Federated Learning (FL) enables collaborative model training without data sharing, yet participants face a fundamental challenge, e.g., simultaneously ensuring fairness across demographic groups while protecting sensitive client data. We introduce a differentially private fair FL algorithm (FedPF) that transforms this multi-objective optimization into a zero-sum game where fairness and privacy constraints compete against model utility. Our theoretical analysis reveals an inverse relationship: privacy mechanisms that protect sensitive attributes can reduce the statistical power available for detecting and correcting demographic biases under finite samples in federated settings. We further show that our theoretical bounds are consistent with a non-monotonic fairness-utility relationship, which is empirically validated by experiments where moderate fairness constraints improve generalization before excessive enforcement degrades performance. Compared with mainstream algorithms, even under strict privacy constraints, FedPF still maintains the lowest discrimination level among all tested algorithms while retaining high utility. Experimental validation demonstrates up to 42.9 % discrimination reduction across three datasets while maintaining competitive accuracy, but more importantly, reveals that achieving strong privacy and fairness simultaneously requires carefully balanced tradeoffs rather than optimizing either objective in isolation. Furthermore, hardware-level simulations demonstrate that FedPF maintains a low computational footprint, making it suitable for resource-constrained edge devices. The source code for our proposed algorithm is publicly accessible at https://github.com/szpsunkk/FedPF.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

FedPF frames the privacy-fairness-utility tradeoff in federated learning as a zero-sum game and shows empirical discrimination cuts, but the game equilibrium under noise and non-IID data looks like the main thing to check.

read the letter

This paper's main contribution is FedPF, which models the tension between privacy, fairness, and utility in federated learning as a zero-sum game, backed by some experiments showing reduced discrimination. It does introduce a fresh algorithmic framing that combines differential privacy with fairness constraints in this game setup. The reported 42.9% discrimination drop across datasets while keeping competitive accuracy is concrete, and releasing the code plus running hardware simulations for edge devices is helpful for reproducibility and practicality. The soft spot is in the theoretical part. The inverse relationship between privacy strength and bias-detection power comes from turning the problem into a zero-sum game. But under differential privacy noise and heterogeneous client data, it's not obvious that the min-max will settle into a unique equilibrium without extra tuning or oscillations. If that happens, the power reduction claim doesn't follow as cleanly. The non-monotonic fairness-utility link is presented as consistent with bounds, but more independent checks would strengthen it. Readers working on real-world federated deployments that must handle both privacy regulations and fairness requirements would get the most out of this. It gives them a starting point for balancing those goals rather than optimizing one at the expense of the other. I think this one should go to peer review. The problem is relevant, the approach is direct, and the empirical side looks solid enough to benefit from detailed comments on the game dynamics and experimental controls.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces FedPF, a differentially private federated learning algorithm that reformulates the joint optimization of privacy, fairness, and utility as a zero-sum game. Theoretical analysis claims an inverse relationship: privacy mechanisms protecting sensitive attributes reduce statistical power for detecting and correcting demographic biases under finite samples. Bounds are said to be consistent with a non-monotonic fairness-utility frontier, which is empirically validated by up to 42.9% discrimination reduction across three datasets while retaining competitive accuracy. Hardware simulations show low computational cost, and code is released publicly.

Significance. If the central claims hold, the work usefully highlights inherent tensions between privacy and fairness in federated settings and the value of moderate rather than extreme fairness enforcement. The public code release and edge-device simulations are concrete strengths that support reproducibility and practicality.

major comments (2)

[Theoretical Analysis] The zero-sum game transformation of the multi-objective problem is load-bearing for the inverse-relationship claim, yet the manuscript provides no analysis showing that the resulting min-max dynamics admit a unique, convergent equilibrium under differential privacy noise and non-IID client distributions. If oscillations or multiple equilibria arise, the asserted reduction in statistical power for bias correction does not follow directly.
[Experimental Validation] The abstract reports a 42.9% discrimination reduction and consistency with theoretical bounds, but without error bars, explicit dataset statistics, or the precise parameterization of trade-off weights in the zero-sum game, it is impossible to verify whether the non-monotonic fairness-utility relationship is robust or sensitive to post-hoc tuning.

minor comments (2)

[Abstract] The abstract mentions 'hardware-level simulations' without specifying the hardware platform, power metrics, or comparison baselines used to claim a low computational footprint.
[Notation and Experiments] Notation for fairness metrics (e.g., discrimination level) and privacy parameters should be introduced once and used consistently; occasional undefined symbols appear in the experimental description.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. The comments highlight important aspects of the theoretical grounding and experimental transparency that we will address in the revision. We respond to each major comment below.

read point-by-point responses

Referee: [Theoretical Analysis] The zero-sum game transformation of the multi-objective problem is load-bearing for the inverse-relationship claim, yet the manuscript provides no analysis showing that the resulting min-max dynamics admit a unique, convergent equilibrium under differential privacy noise and non-IID client distributions. If oscillations or multiple equilibria arise, the asserted reduction in statistical power for bias correction does not follow directly.

Authors: We agree that establishing convergence properties is necessary to fully substantiate the inverse-relationship claim. The manuscript derives the reduction in statistical power from the increased variance induced by the privacy mechanism within the zero-sum formulation, but does not include a dedicated convergence analysis for the min-max dynamics under DP noise and non-IID distributions. In the revised version we will add a new subsection providing a proof sketch: under standard assumptions of Lipschitz-continuous losses, bounded gradients, and sufficiently small step sizes, the game dynamics converge in expectation to a unique equilibrium despite the additive DP noise. This analysis will explicitly link the equilibrium to the reduced bias-detection power under finite samples. revision: yes
Referee: [Experimental Validation] The abstract reports a 42.9% discrimination reduction and consistency with theoretical bounds, but without error bars, explicit dataset statistics, or the precise parameterization of trade-off weights in the zero-sum game, it is impossible to verify whether the non-monotonic fairness-utility relationship is robust or sensitive to post-hoc tuning.

Authors: We accept that additional experimental details are required for reproducibility and verification. The reported 42.9% figure was obtained from multiple independent runs, yet error bars and parameter values were not included in the abstract. In the revision we will (i) add error bars to all reported metrics in the abstract and main results, (ii) include a table with explicit dataset statistics (sample sizes, demographic group distributions, and non-IID degree), and (iii) state the exact trade-off weights (privacy budget ε and fairness coefficient λ) used for each dataset and each point on the fairness-utility frontier. These additions will demonstrate that the non-monotonic relationship is observed across a range of parameter settings rather than isolated tuning. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected in visible derivation

full rationale

The abstract and provided context contain no equations, self-citations, or explicit derivations that reduce any claimed theoretical result or prediction to fitted inputs or prior self-referential steps by construction. The zero-sum game transformation is introduced as a modeling choice to handle the multi-objective problem, and the inverse privacy-fairness relationship is presented as a theoretical finding then checked for consistency with experiments. No load-bearing self-citation, uniqueness theorem, or ansatz smuggling is quoted or visible. The paper's central claims therefore retain independent content from the modeling assumptions and empirical validation, qualifying as self-contained.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Review performed on abstract only; therefore the ledger is necessarily incomplete and records only the high-level modeling choice visible in the provided text.

free parameters (1)

trade-off weights in zero-sum game
The transformation into a zero-sum game requires parameters that balance privacy, fairness, and utility; their values are not stated in the abstract.

axioms (1)

domain assumption Multi-objective optimization of privacy, fairness, and utility can be faithfully recast as a zero-sum game whose equilibrium yields the desired operating point.
Stated directly in the abstract as the core algorithmic step.

pith-pipeline@v0.9.0 · 5776 in / 1486 out tokens · 45455 ms · 2026-05-18T02:52:19.614002+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

transforms this multi-objective optimization into a zero-sum game where fairness and privacy constraints compete against model utility... Lagrangian form... min max L(fi, λi)
IndisputableMonolith/Foundation/AbsoluteFloorClosure.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Theorem 1 (Privacy-Fairness-Utility Tradeoff... O(B²ε⁴_f T^{3/2}H / ε²_p) ... inverse relationship between the strictness of DP and the system’s ability to detect and correct demographic biases

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

30 extracted references · 30 canonical work pages

[1]

Communication-efficient learning of deep networks from decentralized data,

B. McMahan, E. Moore, D. Ramage, S. Hampson, and B. A. y Arcas, “Communication-efficient learning of deep networks from decentralized data,” inArtificial intelligence and statis- tics. PMLR, 2017, pp. 1273–1282

work page 2017
[2]

The algorithmic foundations of differential privacy,

C. Dwork, A. Rothet al., “The algorithmic foundations of differential privacy,”Foundations and Trends® in Theoretical Computer Science, vol. 9, no. 3–4, pp. 211–407, 2014

work page 2014
[3]

Equality of opportunity in supervised learning,

M. Hardt, E. Price, and N. Srebro, “Equality of opportunity in supervised learning,”Advances in neural information pro- cessing systems, vol. 29, 2016

work page 2016
[4]

A Survey Of What To Share In Federated Learning: Perspectives On Model Utility, Privacy Leakage, And Communication Efficiency,

J. Shao, Z. Li, W. Sun, T. Zhou, Y . Sun, L. Liu, Z. Lin, and J. Zhang, “A survey of what to share in federated learning: Perspectives on model utility, privacy leakage, and communi- cation efficiency,”arXiv preprint arXiv:2307.10655, 2023

work page arXiv 2023
[5]

Fairness overfitting in machine learning: An information-theoretic per- spective,

F. Laakom, H. Chen, J. Schmidhuber, and Y . Bu, “Fairness overfitting in machine learning: An information-theoretic per- spective,”arXiv preprint arXiv:2506.07861, 2025

work page arXiv 2025
[6]

Puffle: Balancing privacy, utility, and fairness in federated learning,

L. Corbucci, M. A. Heikkila, D. S. Noguero, A. Monreale, and N. Kourtellis, “Puffle: Balancing privacy, utility, and fairness in federated learning,”arXiv preprint arXiv:2407.15224, 2024

work page arXiv 2024
[7]

Privacy, accuracy, and model fairness trade- offs in federated learning,

X. Gu, Z. Tianqing, J. Li, T. Zhang, W. Ren, and K.- K. R. Choo, “Privacy, accuracy, and model fairness trade- offs in federated learning,”Computers & Security, vol. 122, p. 102907, 2022

work page 2022
[8]

Toward the tradeoffs between privacy, fairness and utility in federated learning,

K. Sun, X. Zhang, X. Lin, G. Li, J. Wang, and J. Li, “Toward the tradeoffs between privacy, fairness and utility in federated learning,” inInternational Symposium on Emerging Information Security and Applications. Springer, 2023, pp. 118–132

work page 2023
[9]

Noise- tolerant fair classification,

A. Lamy, Z. Zhong, A. K. Menon, and N. Verma, “Noise- tolerant fair classification,”Advances in neural information processing systems, vol. 32, 2019

work page 2019
[10]

Stochastic differen- tially private and fair learning,

A. Lowy, D. Gupta, and M. Razaviyayn, “Stochastic differen- tially private and fair learning,” inWorkshop on Algorithmic Fairness through the Lens of Causality and Privacy. PMLR, 2023, pp. 86–119

work page 2023
[11]

Robust optimization for fairness with noisy protected groups,

S. Wang, W. Guo, H. Narasimhan, A. Cotter, M. Gupta, and M. Jordan, “Robust optimization for fairness with noisy protected groups,”Advances in neural information processing systems, vol. 33, pp. 5190–5203, 2020

work page 2020
[12]

Equalized odds postprocessing under imperfect group information,

P. Awasthi, M. Kleindessner, and J. Morgenstern, “Equalized odds postprocessing under imperfect group information,” in International conference on artificial intelligence and statis- tics. PMLR, 2020, pp. 1770–1780

work page 2020
[13]

Differentially private fair learn- ing,

M. Jagielski, M. Kearns, J. Mao, A. Oprea, A. Roth, S. Sharifi- Malvajerdi, and J. Ullman, “Differentially private fair learn- ing,” inInternational Conference on Machine Learning. PMLR, 2019, pp. 3000–3008

work page 2019
[14]

Differentially private and fair deep learning: A lagrangian dual approach,

C. Tran, F. Fioretto, and P. Van Hentenryck, “Differentially private and fair deep learning: A lagrangian dual approach,” in Proceedings of the AAAI Conference on Artificial Intelligence, vol. 35, no. 11, 2021, pp. 9932–9939

work page 2021
[15]

Fair re- source allocation in federated learning,

T. Li, M. Sanjabi, A. Beirami, and V . Smith, “Fair re- source allocation in federated learning,”arXiv preprint arXiv:1905.10497, 2019

work page arXiv 1905
[16]

Minimax pareto fairness: A multi objective perspective,

N. Martinez, M. Bertran, and G. Sapiro, “Minimax pareto fairness: A multi objective perspective,” inInternational Con- ference on Machine Learning. PMLR, 2020, pp. 6755–6764

work page 2020
[17]

A fairness-aware incentive scheme for federated learning,

H. Yu, Z. Liu, Y . Liu, T. Chen, M. Cong, X. Weng, D. Niyato, and Q. Yang, “A fairness-aware incentive scheme for federated learning,” inProceedings of the AAAI/ACM Conference on AI, Ethics, and Society, 2020, pp. 393–399

work page 2020
[18]

Counter- factual fairness,

M. J. Kusner, J. Loftus, C. Russell, and R. Silva, “Counter- factual fairness,”Advances in neural information processing systems, vol. 30, 2017

work page 2017
[19]

Advances and open problems in federated learning,

P. Kairouz, H. B. McMahan, B. Avent, A. Bellet, M. Bennis, A. N. Bhagoji, K. Bonawitz, Z. Charles, G. Cormode, R. Cum- mingset al., “Advances and open problems in federated learning,”Foundations and Trends® in Machine Learning, vol. 14, no. 1–2, pp. 1–210, 2021

work page 2021
[20]

Towards fair federated learning with zero- shot data augmentation,

W. Hao, M. El-Khamy, J. Lee, J. Zhang, K. J. Liang, C. Chen, and L. C. Duke, “Towards fair federated learning with zero- shot data augmentation,” inProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2021, pp. 3310–3319

work page 2021
[21]

Self-balancing federated learning with global imbalanced data in mobile systems,

M. Duan, D. Liu, X. Chen, R. Liu, Y . Tan, and L. Liang, “Self-balancing federated learning with global imbalanced data in mobile systems,”IEEE Transactions on Parallel and Distributed Systems, vol. 32, no. 1, pp. 59–71, 2020

work page 2020
[22]

Privacy-preserving ma- chine learning: Methods, challenges and directions,

R. Xu, N. Baracaldo, and J. Joshi, “Privacy-preserving ma- chine learning: Methods, challenges and directions,”arXiv preprint arXiv:2108.04417, 2021

work page arXiv 2021
[23]

Neither private nor fair: Impact of data imbalance on utility and fairness in differential privacy,

T. Farrand, F. Mireshghallah, S. Singh, and A. Trask, “Neither private nor fair: Impact of data imbalance on utility and fairness in differential privacy,” inProceedings of the 2020 workshop on privacy-preserving machine learning in practice, 2020, pp. 15–19

work page 2020
[24]

Robin hood and matthew effects: Differential privacy has disparate impact on synthetic data,

G. Ganev, B. Oprisanu, and E. De Cristofaro, “Robin hood and matthew effects: Differential privacy has disparate impact on synthetic data,” inInternational Conference on Machine Learning. PMLR, 2022, pp. 6944–6959

work page 2022
[25]

Differential privacy has disparate impact on model accuracy,

E. Bagdasaryan, O. Poursaeed, and V . Shmatikov, “Differential privacy has disparate impact on model accuracy,”Advances in neural information processing systems, vol. 32, 2019

work page 2019
[26]

Disparate impact in differential privacy from gradient mis- alignment,

M. S. Esipova, A. A. Ghomi, Y . Luo, and J. C. Cresswell, “Disparate impact in differential privacy from gradient mis- alignment,”arXiv preprint arXiv:2206.07737, 2022

work page arXiv 2022
[27]

Fairness in criminal justice risk assessments: The state of the art,

R. Berk, H. Heidari, S. Jabbari, M. Kearns, and A. Roth, “Fairness in criminal justice risk assessments: The state of the art,”Sociological Methods & Research, vol. 50, no. 1, pp. 3–44, 2021

work page 2021
[28]

A reductions approach to fair classification,

A. Agarwal, A. Beygelzimer, M. Dudík, J. Langford, and H. Wallach, “A reductions approach to fair classification,” in International conference on machine learning. PMLR, 2018, pp. 60–69

work page 2018
[29]

Fair learning with private demographic data,

H. Mozannar, M. Ohannessian, and N. Srebro, “Fair learning with private demographic data,” inInternational Conference on Machine Learning. PMLR, 2020, pp. 7066–7075

work page 2020
[30]

On the kantorovich–rubinstein theorem,

D. A. Edwards, “On the kantorovich–rubinstein theorem,” Expositiones Mathematicae, vol. 29, no. 4, pp. 387–398, 2011

work page 2011