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REVIEW 4 major objections 5 minor 52 references

Incentive-Compatible Federated Learning with Stackelberg Game Modeling

T0 review · 4 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read FLamma, an adaptive gamma-based Stackelberg game, claims to make federated learning fairer and more accurate by decaying dominant clients' influence while clients choose local epochs to maximize utility.

desk verdict Nice empirical recipe for a gamma-scaled FedAvg, but the Stackelberg theory that is supposed to justify it collapses on inspection, and the experiments never test the mechanism they analyze. read the letter →

arxiv 2501.02662 v1 pith:BD6ZEP3M submitted 2025-01-05 cs.LG cs.DC

Simin Javaherian , Bryce Turney , Li Chen , Nian-Feng Tzeng This is my paper · ORCID
classification cs.LGcs.DC
keywords federatedlearningStackelberggameincentivemechanismfairnessnon-IIDdatadecayfactorconvergenceanalysisaccuracyvariance
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Federated learning breaks down when a few clients dominate the global model, especially when data is non-IID, because accuracy varies sharply across participants. FLamma attacks this by modeling the server–client interaction as a Stackelberg game: the server leads with a decay factor $\gamma$ that shrinks the influence of high-contributing clients as training progresses, and each client follows by choosing the number of local epochs $\tau_i$ that maximizes its own utility $U_i$. The paper claims this restores fairness—measured as lower variance of per-client accuracy—while keeping global accuracy and convergence at or above the level of FedAvg, FedProx, q-FFL, and a contribution-based incentive baseline, reporting gains such as a 120.93% accuracy improvement over q-FFL on non-IID CIFAR-10 and variance reductions of 85–99% relative to FedAvg. A convergence theorem (Eq. (2)) is provided to argue that the decay mechanism tightens the error bound instead of loosening it.

What carries the argument

The load-bearing object is the Stackelberg game with decay factor $\gamma$: the server leads by setting $\gamma$, each client follower replies with the best response $\tau_i^* = \gamma \omega_i / (2 c_i)$ that maximizes the concave utility $\gamma \omega_i \tau_i - c_i \tau_i^2$, and the server's utility, after substitution, is concave in $\gamma$ with a closed-form maximizer. Repeated play drives the system toward the equilibrium, and the same $\gamma$ scales the local gradient updates ($w_k^t \leftarrow w_k^t - \eta \gamma \nabla F_k(w_k^t)$), which is what lets the mechanism control both client influence and the divergence term in the convergence bound of Eq. (2). The contribution measure $\omega_i$ is the quantity that connects geometric closeness of local and global models to an economic "contribution."

What would settle it

Run FLamma on a non-IID split and measure $\omega_i$ for every selected client each round. If any client has $\|w_i^t - w^t\| > \|w^t\|$, the paper's best-response derivation and IR proof do not apply, so the reported equilibrium story fails for that client. A direct check would report the fraction of selected clients with negative $\omega_i$ during training.

Watch

Extended reading notes

Core claim

The paper's central claim is that fairness in federated learning can be engineered through the equilibrium of a two-level game rather than through a hand-designed reweighting rule. The server announces a decay factor $\gamma \in [0,1]$; client $i$ then chooses its local iteration count $\tau_i$ to maximize $\gamma\,\omega_i\,\tau_i - c_i \tau_i^2$, where $\omega_i = 1 - \|w_i^t - w^t\|/\|w^t\|$ measures how close the client's local model is to the global model. Concavity gives the unique best response $\tau_i^* = \gamma \omega_i / (2 c_i)$, and substituting these responses into the server's utility yields an optimal $\gamma^*$; iterating this play drives the system to a Stackelberg equilibrium in which each client is individually rational. As $\gamma$ decays over rounds, initially dominant clients lose influence, the accuracy distribution across clients flattens, and the global model improves or holds steady. Experiments on MNIST, FashionMNIST, and CIFAR-10 under both IID and non-IID splits show FLamma with lower accuracy variance than FedAvg, FedProx, q-FFL, and the incentive baseline, alongside higher or comparable accuracy.

Load-bearing premise

All of the game-theoretic guarantees assume the contribution $\omega_i = 1 - \|w_i^t - w^t\|/\|w^t\|$ is never negative; with the non-IID data the paper targets, a client's local model can easily be farther from the global model than the global model's own norm, making $\omega_i < 0$, the best response $\tau_i^*$ negative, and the individual-rationality guarantee in Lemma 5 void for that client.

Editorial extensions

If this is right

  • FLamma's Stackelberg design gives each client a rational, self-interested reason to choose a finite number of local epochs, so fairness emerges from incentives rather than from a fixed aggregation rule.
  • The variance reductions on non-IID datasets (99.09% on FMNIST, 85.03% on CIFAR-10 relative to FedAvg) suggest that a single server-side decay parameter can substantially flatten the accuracy distribution across heterogeneous clients.
  • The convergence bound of Eq. (2) implies that the decay factor does not sacrifice the FedAvg-style convergence rate; at $\gamma = 1$ the bound reduces to the standard setting, and smaller $\gamma$ only shrinks the divergence term.
  • Because the method only adds a server-side $\gamma$ update and a client-side epoch choice to standard FedAvg, it can be layered onto existing FL systems without changing the aggregation rule or communication protocol.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the contribution measure is clipped or rectified to be non-negative, the same Stackelberg construction could be extended to other client actions, such as participation probability or local batch size, with the server's $\gamma$ controlling the rate at which influence equalizes.
  • The reported gains may mix two effects: the game's epoch choice and the server's contribution-based client selection. An ablation that fixes client selection to uniform random while keeping the $\gamma$ mechanism would isolate the fairness effect of the decay factor itself.
  • A negative-$\omega_i$ case is not just a theoretical corner: it is likely to occur precisely in the non-IID regime the paper studies, so a practical deployment would need a projection or clipping rule to keep $\tau_i^*$ in the feasible interval.
  • The variance metric is computed across clients' test accuracies on their own local distributions; under extreme label skew, equalizing this variance may trade against worst-case per-class accuracy, which the paper does not report.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper proposes FLamma, a federated learning framework in which a server acts as a Stackelberg leader by setting a decay factor gamma, while clients act as followers who choose their number of local epochs tau_i to maximize a utility that combines contribution-dependent reward with a quadratic cost. The authors derive a closed-form client best response tau_i^* and a server-optimal gamma^*, state lemmas on concavity, Nash equilibrium, and individual rationality, and provide a FedAvg-style convergence bound. They evaluate FLamma on MNIST, FashionMNIST, and CIFAR-10 under IID and non-IID splits, comparing against FedAvg, FedProx, q-FFL, and an incentivization baseline, and report higher accuracy and substantially lower accuracy variance.

Significance. If the equilibrium analysis were correct, the paper would contribute a principled incentive mechanism for fairness in non-IID federated learning, with a falsifiable prediction about accuracy-variance reduction. The experimental results, taken at face value, show large variance reductions across three datasets. Credit is due for a clearly described experimental setup and for identifying limitations in Section VII. However, the significance is contingent on the game-theoretic derivation, and the central derivation does not survive scrutiny: the closed-form gamma^* is algebraically inconsistent with the stated server utility, the implemented algorithm does not specify the gamma update, and the experiments fix tau_i instead of using the derived equilibrium. The contribution is therefore not established in its current form.

major comments (4)
  1. [Section IV.C, server utility] The derivation of gamma^* drops the sum over clients. From the server utility in Section IV.B, substituting tau_i^* = gamma * omega_i / (2 c_i) gives U_server = gamma * sum_i omega_i + (gamma^2 / 2) * sum_i omega_i / c_i - t * gamma^2, whose maximizer is gamma^* = (sum_i omega_i) / (2t - sum_i omega_i / c_i), not the per-client expression gamma^* = omega_i * c_i / (2 t c_i - omega_i) displayed after the derivative. The displayed substitution also omits the summation sign. Consequently Lemma 3, the claimed Stackelberg equilibrium, and the incentive-compatible characterization in Section IV.C do not follow from the stated model except in the degenerate single-client case.
  2. [Section IV.C, Eq. (1) and Lemma 5] The best-response formula tau_i^* = gamma * omega_i / (2 c_i) is obtained as an unconstrained interior maximum, but omega_i = 1 - ||w_i^t - w^t|| / ||w^t|| is not guaranteed to be nonnegative under non-IID data. When omega_i < 0, the candidate tau_i^* is negative and outside any reasonable strategy set, the client utility is decreasing for tau_i >= 0, and the optimal strategy is a boundary point, not the interior solution. The IR guarantee in Lemma 5 is then not automatic: with a positive lower bound tau_min, a client with omega_i < 0 can have negative utility at tau_min, and the proof's deviation to tau_i = 0 is unavailable if 0 is not in the strategy space. The manuscript provides no clipping, projection, or alternative treatment of negative contributions.
  3. [Section V, Theorem and proof] The convergence analysis is internally inconsistent with Algorithm 1. Line 12 of Algorithm 1 uses the effective learning rate eta * gamma, but the recurrence in the proof is written for a plain eta step, with gamma appearing only as a multiplier of the gradient-divergence term. Assumption 5 bounds E[sum_k p_k ||w_t - w_t^k||^2] by 4 eta^2 (tau_max - 1)^2 G^2 without the gamma^2 factor that a gamma-scaled local update would introduce, and the final bound in Eq. (2) contains terms (e.g., rho * xi * gamma_max / 2 * M and the expression for B) that do not follow from the proof's algebra, which ends with eta^3 terms. Therefore the claimed FedAvg-comparable convergence rate is not established by the supplied argument.
  4. [Sections VI.B, VI.C, and Algorithm 1] The experimental evaluation does not exercise the proposed equilibrium. Section VI.B states that clients train for ten local iterations and that the contribution is updated every ten global rounds, while Algorithm 1 line 17 says only 'Update the decay factor gamma' with no rule, and no experimental values for gamma or tau_i^* are reported. Thus Table I and Figs. 2-3 can at most demonstrate properties of a gamma-scaled FedAvg variant, not of the Stackelberg mechanism whose gamma^* is derived in Section IV.C. Section VII's admission that 'the optimal tuning of this decay factor requires non-negligible experimentation' further confirms that the closed-form equilibrium is not what is implemented and evaluated.
minor comments (5)
  1. [Section IV.B] The server utility formula is displayed with ambiguous parentheses, making it unclear whether tau_i is inside or outside the factor gamma * (...); omega_i is also introduced parenthetically after the summation, so it should be defined before the utility expression.
  2. [Eq. (1)] The client utility is written as U_i(gamma, tau_i, tau_{-i}) but contains no dependence on tau_{-i}; either remove the redundant argument or explain how other clients' strategies enter the utility.
  3. [Section VI.B vs. Algorithm 1] The text says the contribution is updated every 10 global rounds, while Algorithm 1 recomputes contributions every round (lines 3-4); this discrepancy should be reconciled.
  4. [Section V] Assumption 3 appears to be stated but is not used in the proof; either use it explicitly or remove it to avoid confusing the reader about which assumptions are load-bearing.
  5. [Section VI.A and Table I] The experimental description reports only that each experiment was run 3 times and does not give hyperparameters such as batch size, learning rate schedule, local data partitioning details, or the gamma schedule used, which are necessary for reproducibility; the Table I caption also contains a grammatical typo ('across CIFAR10, and FMNIST, and MNIST').

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: FLamma's Stackelberg and convergence derivations are self-contained, and the paper's self-citations are background-only.

full rationale

The paper's central theoretical claims are derived from its own stated utility functions and from external, independently established results. The client best response tau_i^* is computed by differentiating the client utility in Eq. (1), and the server's gamma^* is obtained from the server utility by a first-order condition; these are internal derivations, not fitted parameters renamed as predictions. The convergence bound in Eq. (2) is obtained from the standard FedAvg-style assumptions (Assumptions 1-5) with the FedAvg convergence analysis [46] as an external anchor, and the proof does not rely on the paper's own prior results. The self-citations that appear (Refs. [2], [5], [41]) are used only in background enumerations of clustering and fairness work; they are not load-bearing for the equilibrium, convergence, or experimental claims. The empirical section fixes local epochs at ten and leaves the gamma update unspecified, and the server-utility algebra in Section IV.C drops the client sum when computing gamma*, but those are internal-consistency and soundness concerns rather than cases where a claimed prediction is equivalent to an input by construction. No fitted input is called a prediction, no uniqueness theorem is imported from the authors' prior work, and no ansatz is smuggled in through self-citation. Therefore no circular step is identified, and the circularity score is 0.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central equilibrium and convergence results rest on unverified assumptions. The gamma update rule, cost coefficients, and epoch bounds are free parameters that are never specified, and the non-negativity of the contribution measure is assumed without discussion.

free parameters (3)
  • gamma (decay factor) = not specified
    Central server strategy constrained to [0,1]; the paper gives a candidate optimum formula but no update rule for Algorithm 1 line 17, and experiments do not report the schedule.
  • c_i (client cost coefficient) = not reported
    Appears in client utility Eq. (1) and in tau_i* and gamma* formulas; no values or estimation method are given, and experiments fix local epochs so c_i is never used.
  • tau_min, tau_max (local epoch bounds) = not reported
    Introduced in Lemma 4 to ensure compact strategy space; experiments use a fixed 10 local epochs, so these bounds are unused and unspecified.
assumptions (5)
  • domain assumption Local losses F_i are rho-strongly convex and beta-smooth (Assumption 1)
    Used in the convergence theorem; not true for neural networks used in the experiments.
  • standard math Stochastic gradient variance and norm bounds (Assumption 2), including E||h_k||^2 <= G^2
    Standard bounded-variance assumption in FL convergence proofs, borrowed from Li et al. [46].
  • domain assumption Assumption 3: E||w_t - w_{t+1}||^2 <= (4/K) eta^2 tau^2 G^2
    Specific bound on round-to-round model movement; not derived for the gamma-scaled local update, so it may not hold for FLamma's algorithm.
  • ad hoc to paper The strategy space tau_i in [tau_min, tau_max] is compact and convex (Lemma 4)
    Introduced without values or connection to the unconstrained tau_i*; needed for the fixed-point existence argument.
  • domain assumption Contribution omega_i is non-negative
    Unstated; required for tau_i* and IR to be valid; may be violated in non-IID settings.

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Cite this review

Pith. "Pith review of Incentive-Compatible Federated Learning with Stackelberg Game Modeling." pith.science (2026). https://pith.science/paper/BD6ZEP3M

@misc{pith2026250102662,
  author       = {Pith},
  title        = {Pith review of: Incentive-Compatible Federated Learning with Stackelberg Game Modeling},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BD6ZEP3M}},
  note         = {Machine review of arXiv:2501.02662}
}
read the original abstract

Federated Learning (FL) has gained prominence as a decentralized machine learning paradigm, allowing clients to collaboratively train a global model while preserving data privacy. Despite its potential, FL faces significant challenges in heterogeneous environments, where varying client resources and capabilities can undermine overall system performance. Existing approaches primarily focus on maximizing global model accuracy, often at the expense of unfairness among clients and suboptimal system efficiency, particularly in non-IID (non-Independent and Identically Distributed) settings. In this paper, we introduce FLamma, a novel Federated Learning framework based on adaptive gamma-based Stackelberg game, designed to address the aforementioned limitations and promote fairness. Our approach allows the server to act as the leader, dynamically adjusting a decay factor while clients, acting as followers, optimally select their number of local epochs to maximize their utility. Over time, the server incrementally balances client influence, initially rewarding higher-contributing clients and gradually leveling their impact, driving the system toward a Stackelberg Equilibrium. Extensive simulations on both IID and non-IID datasets show that our method significantly improves fairness in accuracy distribution without compromising overall model performance or convergence speed, outperforming traditional FL baselines.

Figures

Figures reproduced from arXiv: 2501.02662 by the authors.

Figure 1
Figure 1. Overview of FLamma, an adaptive gamma-based game theoretic framework for fair federated learning. IV. DESIGN OF FLamma This section introduces the design of our game-theoretic framework for fair federated learning [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Comparison of the FLamma with the baselines including FedAvg, FedProx, q-FFL, and Incentivization in terms of accuracy, and accuracy variance on IID dataset. 0 20 40 60 80 100 Global Rounds 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Testing Accuracy MNIST Accuracy 0 20 40 60 80 100 Global Rounds 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Testing Accuracy FMNIST Accuracy 0 20 40 60 80 100 120 140 Global Rounds 0.1 0.2 0.3 0.4 0.5 … view at source ↗
Figure 3
Figure 3. Comparison of the FLamma with the baselines including FedAvg, FedProx, q-FFL, and Incentivization in terms of accuracy, and accuracy variance on non-IID dataset. each receives data that does not fully represent the overall distribution, mimicking real-world scenarios where client data varies significantly. We first divide the dataset into more shards than there are clients to maintain diversity. The data is sorted b… view at source ↗

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Reference graph

Works this paper leans on

52 extracted references · 35 canonical work pages

  1. [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,” in Artificial intelligence and statistics . PMLR, 2017, pp. 1273– 1282

    2017

  2. [2]

    Fedclust: Optimizing federated learning on non-iid data through weight-driven client clustering,

    M. S. Islam, S. Javaherian, F. Xu, X. Yuan, L. Chen, and N.-F. Tzeng, “Fedclust: Optimizing federated learning on non-iid data through weight-driven client clustering,” arXiv preprint arXiv:2403.04144, 2024

    arXiv 2024

  3. [3]

    An efficient frame- work for clustered federated learning,

    A. Ghosh, J. Chung, D. Yin, and K. Ramchandran, “An efficient frame- work for clustered federated learning,” Advances in Neural Information Processing Systems, vol. 33, pp. 19 586–19 597, 2020

    2020

  4. [4]

    Client selection in federated learning: Convergence analysis and power-of-choice selection strategies,

    Y . J. Cho, J. Wang, and G. Joshi, “Client selection in federated learning: Convergence analysis and power-of-choice selection strategies,” arXiv preprint arXiv:2010.01243, 2020

    arXiv 2010

  5. [5]

    Fedfairˆ 3: Unlocking threefold fairness in federated learning,

    S. Javaherian, S. Panta, S. Williams, M. S. Islam, and L. Chen, “Fedfairˆ 3: Unlocking threefold fairness in federated learning,” arXiv preprint arXiv:2401.16350, 2024

    arXiv 2024

  6. [6]

    Oort: Efficient federated learning via guided participant selection,

    F. Lai, X. Zhu, H. V . Madhyastha, and M. Chowdhury, “Oort: Efficient federated learning via guided participant selection,” in 15th {USENIX} Symposium on Operating Systems Design and Implementation ( {OSDI} 21), 2021, pp. 19–35

    2021

  7. [7]

    Fairfed: Enabling group fairness in federated learning,

    Y . H. Ezzeldin, S. Yan, C. He, E. Ferrara, and A. S. Avestimehr, “Fairfed: Enabling group fairness in federated learning,” in Proceedings of the AAAI Conference on Artificial Intelligence , vol. 37, no. 6, 2023, pp. 7494–7502

    work page 2023

  8. [8]

    Three approaches for personalization with applications to federated learning,

    Y . Mansour, M. Mohri, J. Ro, and A. T. Suresh, “Three approaches for personalization with applications to federated learning,” arXiv preprint arXiv:2002.10619, 2020

    arXiv 2002

Show all 52 references
  1. [9]

    Ditto: Fair and robust federated learning through personalization,

    T. Li, S. Hu, A. Beirami, and V . Smith, “Ditto: Fair and robust federated learning through personalization,” in International conference on machine learning . PMLR, 2021, pp. 6357–6368

    2021

  2. [10]

    One for one, or all for all: Equilibria and optimality of collaboration in federated learning,

    A. Blum, N. Haghtalab, R. L. Phillips, and H. Shao, “One for one, or all for all: Equilibria and optimality of collaboration in federated learning,” in International Conference on Machine Learning . PMLR, 2021, pp. 1005–1014

    2021

  3. [11]

    Maschler, S

    M. Maschler, S. Zamir, and E. Solan, Game theory . Cambridge University Press, 2020

    2020

  4. [12]

    Federated learning for edge networks: Resource opti- mization and incentive mechanism,

    L. U. Khan, S. R. Pandey, N. H. Tran, W. Saad, Z. Han, M. N. Nguyen, and C. S. Hong, “Federated learning for edge networks: Resource opti- mization and incentive mechanism,” IEEE Communications Magazine , vol. 58, no. 10, pp. 88–93, 2020

    2020

  5. [13]

    Motivating workers in federated learning: A stackelberg game perspective,

    Y . Sarikaya and O. Ercetin, “Motivating workers in federated learning: A stackelberg game perspective,” IEEE Networking Letters, vol. 2, no. 1, pp. 23–27, 2019

    2019

  6. [14]

    Stackelberg versus cournot equilibrium,

    R. Amir and I. Grilo, “Stackelberg versus cournot equilibrium,” Games and Economic Behavior , vol. 26, no. 1, pp. 1–21, 1999

    1999

  7. [15]

    Incentivizing quality contributions in federated learning: A stackelberg game approach,

    W. Zhang, Q. Wang, H. Zhao, W. Xia, and H. Zhu, “Incentivizing quality contributions in federated learning: A stackelberg game approach,” in 2024 IEEE 99th Vehicular Technology Conference (VTC2024-Spring) . IEEE, 2024, pp. 1–5

    2024

  8. [16]

    Incentive mechanism for federated learning with random client selection,

    H. Wu, X. Tang, Y .-J. A. Zhang, and L. Gao, “Incentive mechanism for federated learning with random client selection,” IEEE Transactions on Network Science and Engineering , 2023

    2023

  9. [17]

    In- centivizing honesty among competitors in collaborative learning and optimization,

    F. E. Dorner, N. Konstantinov, G. Pashaliev, and M. Vechev, “In- centivizing honesty among competitors in collaborative learning and optimization,” Advances in Neural Information Processing Systems , vol. 36, 2024

    2024

  10. [18]

    Non-cooperative edge server selection game for federated learning in iot,

    K. Khawam, H. Taleb, S. Lahoud, H. Fawaz, D. Quadri, and S. Martin, “Non-cooperative edge server selection game for federated learning in iot,” in NOMS 2024-2024 IEEE Network Operations and Management Symposium. IEEE, 2024, pp. 1–6

    2024

  11. [19]

    Model-sharing games: Analyzing fed- erated learning under voluntary participation,

    K. Donahue and J. Kleinberg, “Model-sharing games: Analyzing fed- erated learning under voluntary participation,” in Proceedings of the AAAI Conference on Artificial Intelligence , vol. 35, no. 6, 2021, pp. 5303–5311

    2021

  12. [20]

    Coalitional fl: Coalition formation and selection in federated learning with heterogeneous data,

    N. Zhang, Q. Ma, W. Mao, and X. Chen, “Coalitional fl: Coalition formation and selection in federated learning with heterogeneous data,” IEEE Transactions on Mobile Computing , 2024

    2024

  13. [21]

    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,” in Proceedings of the AAAI/ACM Conference on AI, Ethics, and Society , 2020, pp. 393–399

    2020

  14. [22]

    Game- theoretic design of quality-aware incentive mechanisms for hierarchical federated learning,

    G. Hu, J. Han, J. Lu, J. Yu, S. Qiu, H. Peng, D. Zhu, and T. Li, “Game- theoretic design of quality-aware incentive mechanisms for hierarchical federated learning,” IEEE Internet of Things Journal , 2024

    2024

  15. [23]

    Incentive-aware federated learning with training-time model rewards,

    Z. Wu, M. M. Amiri, R. Raskar, and B. K. H. Low, “Incentive-aware federated learning with training-time model rewards,” in The Twelfth International Conference on Learning Representations , 2024

    2024

  16. [24]

    Federated learning game in iot edge computing,

    S. Durand, K. Khawam, D. Quadri, S. Lahoud, and S. Martin, “Federated learning game in iot edge computing,” IEEE Access, 2024

    2024

  17. [25]

    Coalitional federated learning: Improving communication and training on non-iid data with selfish clients,

    S. Arisdakessian, O. A. Wahab, A. Mourad, and H. Otrok, “Coalitional federated learning: Improving communication and training on non-iid data with selfish clients,” IEEE Transactions on Services Computing , vol. 16, no. 4, pp. 2462–2476, 2023

    2023

  18. [26]

    Edge learning as a hedonic game in lorawan,

    K. Khawam, S. Lahoud, C. Adjih, S. Makhoul, R. Al Tawil, and S. Martin, “Edge learning as a hedonic game in lorawan,” in ICC 2023- IEEE International Conference on Communications . IEEE, 2023, pp. 3163–3168

    2023

  19. [27]

    Incentive mechanism design for federated learning: Hedonic game approach,

    C. Hasan, “Incentive mechanism design for federated learning: Hedonic game approach,” arXiv preprint arXiv:2101.09673 , 2021

    2021 arXiv

  20. [28]

    Incentives in federated learning: Equilibria, dynamics, and mechanisms for welfare maximization,

    A. Murhekar, Z. Yuan, B. Ray Chaudhury, B. Li, and R. Mehta, “Incentives in federated learning: Equilibria, dynamics, and mechanisms for welfare maximization,” Advances in Neural Information Processing Systems, vol. 36, 2024

    2024

  21. [29]

    To federate or not to federate: incentivizing client participation in federated learning,

    Y . J. Cho, D. Jhunjhunwala, T. Li, V . Smith, and G. Joshi, “To federate or not to federate: incentivizing client participation in federated learning,” in Workshop on Federated Learning: Recent Advances and New Challenges (in Conjunction with NeurIPS 2022) , 2022

    2022

  22. [30]

    A contract theory based incentive mechanism for federated learning,

    Y . Liu, M. Tian, Y . Chen, Z. Xiong, C. Leung, and C. Miao, “A contract theory based incentive mechanism for federated learning,” in Federated and Transfer Learning . Springer, 2022, pp. 117–137

    2022

  23. [31]

    Optimal contract design for efficient federated learning with multi-dimensional private information,

    N. Ding, Z. Fang, and J. Huang, “Optimal contract design for efficient federated learning with multi-dimensional private information,” IEEE Journal on Selected Areas in Communications , vol. 39, no. 1, pp. 186– 200, 2020

    2020

  24. [32]

    An incentive mechanism design for efficient edge learning by deep reinforcement learning approach,

    Y . Zhan and J. Zhang, “An incentive mechanism design for efficient edge learning by deep reinforcement learning approach,” in IEEE INFOCOM 2020-IEEE conference on computer communications . IEEE, 2020, pp. 2489–2498

    2020

  25. [33]

    Contract-based incentive mechanism for federated learning in edge computing system,

    L. Yu, Z. Chang, and Z. Zhao, “Contract-based incentive mechanism for federated learning in edge computing system,” in 2024 IEEE Wireless Communications and Networking Conference (WCNC) . IEEE, 2024, pp. 1–6

    2024

  26. [34]

    An incentive mechanism for cross-silo federated learning: A public goods perspective,

    M. Tang and V . W. Wong, “An incentive mechanism for cross-silo federated learning: A public goods perspective,” in IEEE INFOCOM 2021-IEEE Conference on Computer Communications . IEEE, 2021, pp. 1–10

    2021

  27. [35]

    Incentive mech- anism for reliable federated learning: A joint optimization approach to combining reputation and contract theory,

    J. Kang, Z. Xiong, D. Niyato, S. Xie, and J. Zhang, “Incentive mech- anism for reliable federated learning: A joint optimization approach to combining reputation and contract theory,” IEEE Internet of Things Journal, vol. 6, no. 6, pp. 10 700–10 714, 2019

    2019

  28. [36]

    A learning-based incentive mechanism for federated learning,

    Y . Zhan, P. Li, Z. Qu, D. Zeng, and S. Guo, “A learning-based incentive mechanism for federated learning,” IEEE Internet of Things Journal , vol. 7, no. 7, pp. 6360–6368, 2020

    2020

  29. [37]

    Federated learning with heterogeneous client expectations: A game theory approach,

    S. Shen, C. Liu, and T. J. Lim, “Federated learning with heterogeneous client expectations: A game theory approach,” IEEE Transactions on Knowledge and Data Engineering , 2024

    2024

  30. [38]

    Fairness in model-sharing games,

    K. Donahue and J. Kleinberg, “Fairness in model-sharing games,” in Proceedings of the ACM Web Conference 2023 , 2023, pp. 3775–3783

    2023

  31. [39]

    Fairness-aware client selection for federated learning,

    Y . Shi, Z. Liu, Z. Shi, and H. Yu, “Fairness-aware client selection for federated learning,” in 2023 IEEE International Conference on Multimedia and Expo (ICME) . IEEE, 2023, pp. 324–329

    2023

  32. [40]

    Adafl: Adaptive client selection and dynamic contribution evaluation for efficient federated learning,

    Q. Li, X. Li, L. Zhou, and X. Yan, “Adafl: Adaptive client selection and dynamic contribution evaluation for efficient federated learning,” in ICASSP 2024-2024 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) . IEEE, 2024, pp. 6645–6649

    2024

  33. [41]

    Fedfair3: Unlocking threefold fairness in federated learning,

    S. Javaherian, S. Panta, S. Williams, M. S. Islam, and L. Chen, “Fedfair3: Unlocking threefold fairness in federated learning,” in ICC 2024 - IEEE International Conference on Communications , 2024, pp. 3622–3627

    2024

  34. [42]

    Eiffel: Efficient and fair scheduling in adaptive federated learning,

    A. Sultana, M. M. Haque, L. Chen, F. Xu, and X. Yuan, “Eiffel: Efficient and fair scheduling in adaptive federated learning,” IEEE Transactions on Parallel and Distributed Systems , vol. 33, no. 12, pp. 4282–4294, 2022

    2022

  35. [43]

    Fair resource allocation in federated learning,

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

    1905 arXiv

  36. [44]

    Adafed: Fair federated learning via adaptive common descent direction,

    S. M. Hamidi and E.-H. Yang, “Adafed: Fair federated learning via adaptive common descent direction,” arXiv preprint arXiv:2401.04993 , 2024

    2024 arXiv

  37. [45]

    Existence and uniqueness of equilibrium points for concave n-person games,

    J. B. Rosen, “Existence and uniqueness of equilibrium points for concave n-person games,” Econometrica: Journal of the Econometric Society, pp. 520–534, 1965

    1965

  38. [46]

    On the convergence of fedavg on non-iid data,

    X. Li, K. Huang, W. Yang, S. Wang, and Z. Zhang, “On the convergence of fedavg on non-iid data,” arXiv preprint arXiv:1907.02189 , 2019

    1907 arXiv

  39. [47]

    Deep residual learning for image recognition,

    K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for image recognition,” in Proceedings of the IEEE conference on computer vision and pattern recognition , 2016, pp. 770–778

    2016

  40. [48]

    Backpropagation applied to handwritten zip code recognition,

    Y . LeCun, B. Boser, J. S. Denker, D. Henderson, R. E. Howard, W. Hubbard, and L. D. Jackel, “Backpropagation applied to handwritten zip code recognition,” Neural computation, vol. 1, no. 4, pp. 541–551, 1989

    1989

  41. [49]

    The mnist database of handwritten digit images for machine learning research [best of the web],

    L. Deng, “The mnist database of handwritten digit images for machine learning research [best of the web],” IEEE signal processing magazine , vol. 29, no. 6, pp. 141–142, 2012

    2012

  42. [50]

    Fashion-mnist: a novel image dataset for benchmarking machine learning algorithms,

    H. Xiao, K. Rasul, and R. V ollgraf, “Fashion-mnist: a novel image dataset for benchmarking machine learning algorithms,” arXiv preprint arXiv:1708.07747, 2017

    2017 arXiv

  43. [51]

    Learning multiple layers of features from tiny images,

    A. Krizhevsky, G. Hinton et al. , “Learning multiple layers of features from tiny images,” cs.utoronto.ca, 2009

    2009

  44. [52]

    Federated optimization in heterogeneous networks,

    T. Li, A. K. Sahu, M. Zaheer, M. Sanjabi, A. Talwalkar, and V . Smith, “Federated optimization in heterogeneous networks,” Proceedings of Machine learning and systems , vol. 2, pp. 429–450, 2020

    2020

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.