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REVIEW 4 major objections 5 minor 37 references

Fair Distributed Machine Learning with Imbalanced Data as a Stackelberg Evolutionary Game

T0 review · 4 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read By modeling distributed learning as a Stackelberg evolutionary game and reweighting each node's contribution every round, this paper claims that underrepresented nodes gain 2.713% average AUC while the largest node loses only 0.441%.

desk verdict The 2.713% AUC gain is an artifact of selecting weights on local test sets; the Stackelberg idea is plausible but the empirical claim is unsupported. read the letter →

arxiv 2412.16079 v1 pith:6EW5W5RG submitted 2024-12-20 cs.LG cs.CVcs.GTcs.NE

Sebastian Niehaus , Ingo Roeder , Nico Scherf This is my paper · ORCID
classification cs.LGcs.CVcs.GTcs.NE
keywords federatedlearningdecentralizedmachineStackelberggameevolutionarytheorydataimbalancenon-IIDcontributionweightingAUC
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

Distributed machine learning suffers when participants hold very unequal datasets: the node with the most data dominates the shared model, and smaller nodes end up with worse predictions. This paper argues that the imbalance is a strategic, sequential interaction and models it as a Stackelberg evolutionary game, with the large-data node as leader and smaller nodes as followers. It introduces two algorithms, DSWM and ASWM, that replace the usual data-size weights in federated averaging with per-round contribution weights chosen to minimize each player's loss. On three medical image datasets, the adaptive version raises the Area Under the Curve (AUC) of underrepresented nodes by an average of 2.713% compared to precision-weighted federated averaging, while the leader loses only 0.441% on average. If the result holds, dynamic game-theoretic weighting is a practical way to make distributed medical learning fairer without centralizing data.

What carries the argument

The load-bearing object is the contribution weight $C_k$ that replaces the data count $n_k$ in the federated averaging update, together with the Stackelberg equilibrium procedure that selects it: the leader minimizes $L_0(C_0,C_1^*(C_0),C_2^*(C_0))$ and each follower minimizes its own loss given earlier choices. DSWM implements this by brute-force grid search over ten weights; ASWM replaces the search with two neural networks whose inputs include previous contribution weights, previous global weights, and local test-set losses, trained through experience replay. This mechanism is what lets a small node amplify its own update when its loss is high, counterbalancing the leader's data advantage.

What would settle it

Split each node's data into training, validation, and a never-touched test set, and let ASWM select contribution weights using validation loss instead of test-set loss; if the held-out AUC improvement over PWFedAvg falls below the reported 2.713% or reverses, the central claim fails. A simpler check on DSWM: if the weight chosen by lowest test loss is not the weight with lowest held-out loss in repeated Dirichlet draws, the selection rule is overfitting the evaluation set.

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Extended reading notes

Core claim

The paper's central claim is that the performance gap between large- and small-data nodes in distributed learning is not fixed: it can be reshaped by letting each node strategically choose how much influence its update has on the global model. Formally, the authors rewrite federated averaging as $w_{t+1} = \sum_k C_k w^k_t / \sum_k C_k$, replacing dataset sizes $n_k$ with contribution weights $C_k$, and define a Stackelberg game where the leader picks weights first, anticipating the followers' best responses. DSWM searches a fixed grid $C = \{0.1, 0.2, \dots, 1.0\}$ each round and selects the weight with the lowest local loss; ASWM trains neural networks with experience replay to predict those weights. Across BreastMNIST, DermaMNIST, and BloodMNIST simulations with one leader and two followers, ASWM consistently yields the highest AUC on the smallest nodes, and the aggregate improvement over PWFedAvg is the reported 2.713% with a 0.441% average decrease for the large node.

Load-bearing premise

The protocol assumes that choosing contribution weights by minimizing each node's loss computed on its local test set does not leak evaluation information and that the chosen weights generalize to unseen data; if the weights are overfitted to those test sets, the reported AUC gains are artifacts.

Editorial extensions

If this is right

  • The smallest nodes gain most: Node 3 improves by roughly 5.97% on DermaMNIST, 2.02% on BloodMNIST, and 1.20% on BreastMNIST relative to PWFedAvg, so the method targets exactly the participants who are currently worst off.
  • The leader's cost is bounded: its AUC decreases by at most about 1.34% in these experiments, with an average drop of 0.441%, so adopting ASWM does not require sacrificing the large node's model.
  • Because the weighting replaces only the scalar coefficients in federated averaging, the scheme can be inserted into existing distributed training loops without centralizing data or changing local model architectures.
  • The Stackelberg formulation generalizes to $n$ leaders and $m$ followers, so the same per-round weighting logic is not limited to the three-node simulations tested here.

Reading between the lines

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

  • A deployment-grade version would need a privacy-safe source for the utility losses; if nodes cannot reveal local test-set losses without leaking information, the mechanism may require secure aggregation or a trusted coordinator.
  • The average 2.713% gain is uneven across datasets and nodes, so per-seed intervals and worst-case analysis would show whether the benefit is reliable or driven by one favorable configuration.
  • The sequential leader-follower updates likely incur extra synchronization compared with simultaneous FedAvg; a wall-clock and communication-cost comparison would test whether the fairness gain survives efficiency constraints.
  • A natural stress test is to vary the number of followers and the Dirichlet concentration parameter to map where ASWM's advantage over PWFedAvg disappears; the paper's data-generation setup makes this a direct next experiment.
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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 frames distributed machine learning with imbalanced data as a three-player Stackelberg evolutionary game, with a leader node and two follower nodes. It proposes two algorithms, DSWM and ASWM, which set per-round contribution weights in the federated averaging update. The methods are evaluated on BreastMNIST, DermaMNIST, and BloodMNIST in a simulated three-node setup, and the authors report that ASWM improves underrepresented (follower) nodes by about 2.713% AUC on average over PWFedAvg while decreasing the leader node's AUC by only about 0.441%. The central quantitative claim is that ASWM improves fairness for small-data nodes with only a modest cost to the large-data node.

Significance. If the reported results were obtained with an unbiased evaluation protocol, the paper would offer a practical and useful mechanism for improving fairness in federated learning with imbalanced medical data. The idea of treating contribution-weight selection as a Stackelberg game is reasonable, and the use of three public medical datasets with simulated imbalance is a strength. However, the central empirical claim is currently undermined by a direct leakage of test-set information into the weight-selection and policy-training procedures, and the paper does not report any uncertainty estimates despite stating that experiments were repeated ten times. With the protocol as written, the 2.713% improvement cannot be interpreted as an unbiased estimate of the method's performance on unseen data. The paper would need a corrected evaluation protocol and substantially more statistical rigor before its claims can be accepted.

major comments (4)
  1. [Section 2, Section 3.2, Algorithm 1] The paper's central quantitative claim is invalidated by test-set leakage. The loss functions in Eqs. (1)-(3) are explicitly defined as losses on the local test sets of the leader and followers. DSWM is described in Section 3.2 as selecting the contribution weight c that yields the lowest loss, and Algorithm 1 lines 8 and 15-16 compute UL and UFi on the local datasets DL and DFi and then store them in the experience replay buffer used to train the policy networks at line 19. The reported AUCs in Tables 2-4 are measured on those same test sets. Therefore, both DSWM and ASWM directly optimize the evaluation metric during weight selection and policy training, so the reported 2.713% average improvement is a fitted quantity rather than an unbiased estimate of performance on unseen data. The experiments must be redone with a separate validation split for weight selection and policy training, with the test sets used exactly once at the end.
  2. [Section 3.2, Algorithm 1] There is an internal contradiction about which data are used for loss evaluation. The paragraph after Algorithm 1 says that 'the leader applies this weight to the model updates and then evaluates the resulting performance on a validation set,' but Section 2 and the algorithm's input and data-flow description identify the losses as being computed on local test sets. If a validation split was in fact used, the algorithm description is incorrect and must be corrected; if not, the test-set leakage is confirmed. Either way, the current text does not support a valid evaluation protocol.
  3. [Section 4, Tables 2-4] The claim that ASWM 'significantly' favors underrepresented nodes is not supported by any statistical evidence. The experiments are stated to be repeated ten times in Section 3.3, but Tables 2-4 report only point estimates of AUC with no standard deviations, confidence intervals, or paired tests. Differences of 0.01-0.03 AUC could easily be within run-to-run variability, especially given the small number of repetitions. The paper must report mean and variance across runs and, preferably, paired comparisons against PWFedAvg.
  4. [Section 2, Eqs. (2)-(3), Section 3.2] The game-theoretic formulation is asserted but not actually used. The followers' problems in Eqs. (2) and (3) are mutually recursive, and no existence, uniqueness, or computation of the claimed Stackelberg equilibrium is provided. Algorithm 1 is described as an actor-critic method with experience replay, but no connection is shown between the algorithm's weight updates and the Stackelberg equilibrium defined in Section 2. This mismatch weakens the central framing of the paper; the authors should either provide a formal analysis of the game or substantially soften the claims that the algorithm implements a Stackelberg equilibrium.
minor comments (5)
  1. [Abstract, Section 5] There are grammatical errors such as 'an Stackelberg evolutionary game' in the abstract and 'a inspiration' in the conclusion; these should be corrected before resubmission.
  2. [Section 3.1] The notation for contribution weights is inconsistent: Section 2 introduces C0, C1, C2, while Section 3.1 uses Ck and Algorithm 1 uses C = {cF1, cF2}. The leader's own contribution weight is never clearly specified in the global update formula, so it is unclear how the leader's weight is set.
  3. [Section 3.3] The experimental setup omits many details needed for reproducibility, including model architectures, local training epochs, learning rates, number of communication rounds T, the Dirichlet concentration parameter, and the Gaussian noise parameters. The authors state that class distributions were generated using a Dirichlet model, but no code or data-generation script is provided.
  4. [Figure 1] Figure 1 is described in the text only briefly; panels (c) and (d) are said to show contribution-weight selection for ASWM and DSWM, but the axes and the meaning of individual curves are not explained in the caption or the text.
  5. [References] Some references appear to be cited for claims they do not directly support, such as a course note on the Dirichlet distribution [19] being used as the methodological basis for the data-generation model; a more standard statistics textbook reference would be appropriate.

Circularity Check

2 steps flagged · score 7.0 of 10

Reported ASWM AUC gains are fitted to the same local test sets used for evaluation, because DSWM and ASWM select contribution weights by minimizing loss on those test sets (Section 2, Section 3.2, Algorithm 1).

  1. fitted input called prediction [Section 2 (Eqs. 1–3) and Section 3.2 (DSWM description); Algorithm 1 lines 8 and 15–16; abstract claims 2.713% AUC improvement.]
    "L0(C0, C1, C2) be the loss function for the leader (Player 0) on its local test set. ... The objective in DSWM is to select the weight c from this set that minimizes the loss of the leader or the followers."

    The contribution weights are defined as minimizers of loss on each node's local test set, and the reported AUC values are measured on those same local test sets. Thus the 'optimal' weighting is fitted to the evaluation data, so the claimed 2.713% improvement is a fitted outcome rather than an unbiased prediction on unseen data. A single mention of a 'validation set' in Section 3.2 does not undo the formal definitions or the algorithm pseudocode, which consistently use local test sets.

  2. fitted input called prediction [Section 3.2 (ASWM input vectors; experience replay) and Algorithm 1 lines 8, 15–16, 18–19.]
    "These input vectors incorporate local strategies, previous contribution weights C (t−1), previous iteration weights W (t−1), and utility functions UL or UFi as loss functions on local test sets. ... Compute the follower’s loss UFi = LFi (WFi ; DFi ); Store the predicted cFi and resulting loss UFi in the experience replay buffer."

    ASWM trains its policy networks on exactly the losses that are used to evaluate the method. The experience replay buffer stores losses computed on local test sets, and the networks are trained to predict weights minimizing those same losses. Therefore the reported ASWM AUC values in Tables 2–4 are not independent test results; they are the result of optimizing against the test sets themselves.

full rationale

The paper's central empirical claim is that ASWM improves underrepresented nodes by 2.713% AUC. Tracing the derivation chain, the contribution weights in DSWM are chosen from C = {0.1,...,1.0} by minimizing the node's loss, and Section 2 explicitly defines L0, L1, L2 as losses on local test sets. Algorithm 1 stores these test-set losses in the experience replay buffer, and ASWM is trained to predict weights that minimize them. The AUC tables in Section 4 are reported on the same node-level test data. The selection and policy training are therefore directly optimizing the evaluation metric, so the headline improvement is a fitted quantity, not a prediction on held-out data. Repeating the experiment 10 times does not remove this bias, since every run leaks the same test-set information into weight selection. The one sentence in Section 3.2 mentioning a 'validation set' contradicts the formal definitions and algorithm description; as written, the method uses local test sets. No self-citation chain or imported uniqueness theorem is involved. The game-theoretic framing itself is not circular, but the key quantitative result reduces by construction to fitting the evaluation loss, so the paper is substantially circular on its central claim.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central result depends on a small set of fitted contribution weights that are chosen by test-set loss minimization, on unspecified data-synthesis parameters, and on a Stackelberg framing that is asserted rather than derived. No new entities are introduced.

free parameters (4)
  • Contribution weights c_F1, c_F2 per round = learned (not reported)
    Core mechanism: DSWM selects the weight from a fixed set that minimizes local test loss; ASWM predicts weights with neural networks. These weights directly determine the global model and the reported AUC.
  • ASWM policy network parameters theta_L and theta_F = trained via actor-critic with experience replay
    The neural networks that predict contribution weights are fitted on local loss experiences; their training details are not specified.
  • Dirichlet concentration and Gaussian noise parameters = not reported
    Section 3.3 uses a Dirichlet model and node-specific Gaussian noise to synthesize data splits, but no parameter values are given, so the data-generation process is not reproducible.
  • Fixed candidate weight set C = 0.1 to 1.0 in steps of 0.1
    Chosen by hand as the DSWM search space.
assumptions (5)
  • domain assumption A distributed learning setup with one large-data node and two small-data nodes can be modeled as a three-player Stackelberg game in which the large node is the leader and sets the followers' contribution weights.
    Section 2 models the setup as a three-player Stackelberg game; this assumes a hierarchy that real federated learning does not impose, since nodes normally choose their own updates.
  • domain assumption Each node's loss computed on its local test set is a valid signal for choosing contribution weights.
    Section 3.2 and Algorithm 1 use local test-set losses as utilities; this assumes no overfitting to the evaluation data and that test sets are available during training.
  • domain assumption The Dirichlet distribution and per-node Gaussian noise generate realistic medical data imbalance.
    Section 3.3 uses a Dirichlet model for class distributions and Gaussian noise without specifying parameters or validating the surrogate against real distributions.
  • ad hoc to paper The candidate weight set C = {0.1, 0.2, ..., 1.0} is an adequate search space for optimal contribution weights.
    Section 3.2 fixes this set without justification.
  • standard math Stackelberg equilibrium definitions and sequential best-response logic apply to iterative neural network training.
    Section 2 invokes standard game-theoretic equilibrium but no equilibrium is computed; the connection is asserted.

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Cite this review

Pith. "Pith review of Fair Distributed Machine Learning with Imbalanced Data as a Stackelberg Evolutionary Game." pith.science (2026). https://pith.science/paper/6EW5W5RG

@misc{pith2026241216079,
  author       = {Pith},
  title        = {Pith review of: Fair Distributed Machine Learning with Imbalanced Data as a Stackelberg Evolutionary Game},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6EW5W5RG}},
  note         = {Machine review of arXiv:2412.16079}
}
read the original abstract

Decentralised learning enables the training of deep learning algorithms without centralising data sets, resulting in benefits such as improved data privacy, operational efficiency and the fostering of data ownership policies. However, significant data imbalances pose a challenge in this framework. Participants with smaller datasets in distributed learning environments often achieve poorer results than participants with larger datasets. Data imbalances are particularly pronounced in medical fields and are caused by different patient populations, technological inequalities and divergent data collection practices. In this paper, we consider distributed learning as an Stackelberg evolutionary game. We present two algorithms for setting the weights of each node's contribution to the global model in each training round: the Deterministic Stackelberg Weighting Model (DSWM) and the Adaptive Stackelberg Weighting Model (ASWM). We use three medical datasets to highlight the impact of dynamic weighting on underrepresented nodes in distributed learning. Our results show that the ASWM significantly favours underrepresented nodes by improving their performance by 2.713% in AUC. Meanwhile, nodes with larger datasets experience only a modest average performance decrease of 0.441%.

Figures

Figures reproduced from arXiv: 2412.16079 by the authors.

Figure 1
Figure 1. This figure provides a detailed overview of the estimation of contribution weights for model updates and [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗

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Reference graph

Works this paper leans on

37 extracted references · 31 canonical work pages

  1. [1]

    Decentralized machine learning governance: Overview, opportunities, and challenges

    Dana Alsagheer, Lei Xu, and Weidong Shi. Decentralized machine learning governance: Overview, opportunities, and challenges. IEEE Access, 2023. 9 A PREPRINT - D ECEMBER 23, 2024

    work page 2023

  2. [2]

    A game theory competitive intelligence solution stimulated from a stackelberg game: A three players scenario

    Dhekra Ben Sassi and Marouene Chaieb. A game theory competitive intelligence solution stimulated from a stackelberg game: A three players scenario. Engineering Applications of Artificial Intelligence, 135:108825, 2024

    work page 2024

  3. [3]

    Practical secure aggregation for privacy-preserving machine learning

    Keith Bonawitz, Vladimir Ivanov, Ben Kreuter, Antonio Marcedone, H Brendan McMahan, Sarvar Patel, Daniel Ramage, Aaron Segal, and Karn Seth. Practical secure aggregation for privacy-preserving machine learning. In proceedings of the 2017 ACM SIGSAC Conference on Computer and Communications Security, pages 1175–1191, 2017

    work page 2017

  4. [4]

    Non-cooperative game algorithms for computation offloading in mobile edge computing environments

    Jianguo Chen, Qingying Deng, and Xulei Yang. Non-cooperative game algorithms for computation offloading in mobile edge computing environments. Journal of Parallel and Distributed Computing, 172:18–31, 2023

    work page 2023

  5. [5]

    Sex and gender differences and biases in artificial intelligence for biomedicine and healthcare

    Davide Cirillo, Silvina Catuara-Solarz, Czuee Morey, Emre Guney, Laia Subirats, Simona Mellino, Annalisa Gigante, Alfonso Valencia, María José Rementeria, Antonella Santuccione Chadha, et al. Sex and gender differences and biases in artificial intelligence for biomedicine and healthcare. NPJ digital medicine, 3(1):1–11, 2020

    work page 2020

  6. [6]

    Towards scalable and efficient deep-rl in edge computing: A game-based partition approach

    Hao Dai, Jiashu Wu, Yang Wang, and Chengzhong Xu. Towards scalable and efficient deep-rl in edge computing: A game-based partition approach. Journal of Parallel and Distributed Computing, 168:108–119, 2022

    work page 2022

  7. [7]

    Improving federated learning with quality-aware user incentive and auto-weighted model aggregation

    Yongheng Deng, Feng Lyu, Ju Ren, Yi-Chao Chen, Peng Yang, Yuezhi Zhou, and Yaoxue Zhang. Improving federated learning with quality-aware user incentive and auto-weighted model aggregation. IEEE Transactions on Parallel and Distributed Systems, 33(12):4515–4529, 2022

    work page 2022

  8. [8]

    Revisiting fundamentals of experience replay

    William Fedus, Prajit Ramachandran, Rishabh Agarwal, Yoshua Bengio, Hugo Larochelle, Mark Rowland, and Will Dabney. Revisiting fundamentals of experience replay. CoRR, abs/2007.06700, 2020

    arXiv 2007

Show all 37 references
  1. [9]

    Prevalence, age distribution, and gender of patients with atrial fibrillation: analysis and implications

    William M Feinberg, Joseph L Blackshear, Andreas Laupacis, Richard Kronmal, and Robert G Hart. Prevalence, age distribution, and gender of patients with atrial fibrillation: analysis and implications. Archives of internal medicine, 155(5):469–473, 1995

    1995

  2. [10]

    Game theory

    Drew Fudenberg and Jean Tirole. Game theory. MIT Press, 1993

    1993

  3. [11]

    The non-iid data quagmire of decentralized machine learning

    Kevin Hsieh, Amar Phanishayee, Onur Mutlu, and Phillip Gibbons. The non-iid data quagmire of decentralized machine learning. In International Conference on Machine Learning, pages 4387–4398. PMLR, 2020

    2020

  4. [12]

    Online task scheduling for edge computing based on repeated stackelberg game

    Yingmo Jie, Xinyu Tang, Kim-Kwang Raymond Choo, Shenghao Su, Mingchu Li, and Cheng Guo. Online task scheduling for edge computing based on repeated stackelberg game. Journal of Parallel and Distributed Computing, 122:159–172, 2018

    2018

  5. [13]

    Key challenges for delivering clinical impact with artificial intelligence

    Christopher J Kelly, Alan Karthikesalingam, Mustafa Suleyman, Greg Corrado, and Dominic King. Key challenges for delivering clinical impact with artificial intelligence. BMC medicine, 17:1–9, 2019

    2019

  6. [14]

    Hierarchical aerial offload computing algorithm based on the stackelberg-evolutionary game model

    Sungwook Kim. Hierarchical aerial offload computing algorithm based on the stackelberg-evolutionary game model. Computer Networks, 245:110348, 2024

    2024

  7. [15]

    Federated learning: Strategies for improving communication efficiency

    Jakub Koneˇcn`y, H Brendan McMahan, Felix X Yu, Peter Richtárik, Ananda Theertha Suresh, and Dave Bacon. Federated learning: Strategies for improving communication efficiency. arXiv preprint arXiv:1610.05492, 2016

    2016 arXiv

  8. [16]

    Federated learning based on stackelberg game in unmanned- aerial-vehicle-enabled mobile edge computing

    Chunlin Li, Mingyang Song, and Youlong Luo. Federated learning based on stackelberg game in unmanned- aerial-vehicle-enabled mobile edge computing. Expert Systems with Applications, 235:121023, 2024

    2024

  9. [17]

    On the convergence of fedavg on non-iid data

    Xiang Li, Kaixuan Huang, Wenhao Yang, Shusen Wang, and Zhihua Zhang. On the convergence of fedavg on non-iid data. arXiv preprint arXiv:1907.02189, 2019

    1907 arXiv

  10. [18]

    Robust and scalable federated learning framework for client data heterogeneity based on optimal clustering

    Zihan Li, Shuai Yuan, and Zhitao Guan. Robust and scalable federated learning framework for client data heterogeneity based on optimal clustering. Journal of Parallel and Distributed Computing, 195:104990, 2025

    2025

  11. [19]

    On the dirichlet distribution

    Jiayu Lin. On the dirichlet distribution. Department of Mathematics and Statistics, Queens University, 40, 2016

    2016

  12. [20]

    No fear of heterogeneity: Classifier calibration for federated learning with non-iid data

    Mi Luo, Fei Chen, Dapeng Hu, Yifan Zhang, Jian Liang, and Jiashi Feng. No fear of heterogeneity: Classifier calibration for federated learning with non-iid data. Advances in Neural Information Processing Systems, 34:5972– 5984, 2021

    2021

  13. [21]

    Addressing bias in artificial intelligence in health care

    Ravi B Parikh, Stephanie Teeple, and Amol S Navathe. Addressing bias in artificial intelligence in health care. Jama, 322(24):2377–2378, 2019

    2019

  14. [22]

    Rural–urban distribution of the us geriatrics physician workforce

    Lars E Peterson, Andrew Bazemore, Elizabeth J Bragg, Imam Xierali, and Gregg A Warshaw. Rural–urban distribution of the us geriatrics physician workforce. Journal of the American Geriatrics Society, 59(4):699–703, 2011

    2011

  15. [23]

    Precision-weighted federated learning

    Jonatan Reyes, Lisa Di-Jorio, Cécile Low-Kam, and Marta Kersten-Oertel. Precision-weighted federated learning. CoRR, abs/2107.09627, 2021. 10 A PREPRINT - D ECEMBER 23, 2024

    2021 arXiv

  16. [24]

    Simaan and J

    M. Simaan and J. B. Cruz. Additional aspects of the stackelberg strategy in nonzero-sum games. Journal of Optimization Theory and Applications, 11(6):613–626, June 1973

    1973

  17. [25]

    Simaan and J

    M. Simaan and J. B. Cruz. On the stackelberg strategy in nonzero-sum games. Journal of Optimization Theory and Applications, 11(5):533–555, 1973

    1973

  18. [26]

    Stackelberg evolutionary game theory: how to manage evolving systems

    Alexander Stein, Monica Salvioli, Hasti Garjani, Johan Dubbeldam, Yannick Viossat, Joel S Brown, and Kateˇrina Staˇnková. Stackelberg evolutionary game theory: how to manage evolving systems. Philosophical Transactions of the Royal Society B, 378(1876):20210495, 2023

    2023

  19. [27]

    Knowledge gap regarding osteoporosis among medical professionals in southern india.Journal of Evaluation in Clinical Practice, 26(1):272–280, 2020

    Preyander Thakur, Cijoy Kuriakose, Kripa Elizabeth Cherian, Hesarghatta S Asha, Nitin Kapoor, and Thomas V Paul. Knowledge gap regarding osteoporosis among medical professionals in southern india.Journal of Evaluation in Clinical Practice, 26(1):272–280, 2020

    2020

  20. [28]

    Theory of games and economic behavior

    John von Neumann and Oskar Morgenstern. Theory of games and economic behavior. Princeton University Press, 1944

    1944

  21. [29]

    Optimizing federated learning on non-iid data with reinforcement learning

    Hao Wang, Zakhary Kaplan, Di Niu, and Baochun Li. Optimizing federated learning on non-iid data with reinforcement learning. In IEEE INFOCOM 2020-IEEE conference on computer communications, pages 1698–

    2020

  22. [30]

    Understanding shortages of sufficient health care in rural areas

    Ines Weinhold and Sebastian Gurtner. Understanding shortages of sufficient health care in rural areas. Health Policy, 118(2):201–214, 2014

    2014

  23. [31]

    Fast-convergent federated learning with adaptive weighting

    Hongda Wu and Ping Wang. Fast-convergent federated learning with adaptive weighting. IEEE Transactions on Cognitive Communications and Networking, 7(4):1078–1088, 2021

    2021

  24. [32]

    Node selection toward faster convergence for federated learning on non-iid data

    Hongda Wu and Ping Wang. Node selection toward faster convergence for federated learning on non-iid data. IEEE Transactions on Network Science and Engineering, 9(5):3099–3111, 2022

    2022

  25. [33]

    Supply–demand balancing for power management in smart grid: A stackelberg game approach

    Mengmeng Yu and Seung Ho Hong. Supply–demand balancing for power management in smart grid: A stackelberg game approach. Applied energy, 164:702–710, 2016

    2016

  26. [34]

    Towards value-sensitive and poisoning-proof model aggregation for federated learning on heterogeneous data

    Hui Zeng, Tongqing Zhou, Yeting Guo, Zhiping Cai, and Fang Liu. Towards value-sensitive and poisoning-proof model aggregation for federated learning on heterogeneous data. Journal of Parallel and Distributed Computing, 196:104994, 2025

    2025

  27. [35]

    Fedsw: Federated learning with adaptive sample weights

    Xingying Zhao and Dong Shen. Fedsw: Federated learning with adaptive sample weights. Information Sciences, 654:119873, 2024

    2024

  28. [36]

    Federated learning with non-iid data

    Yue Zhao, Meng Li, Liangzhen Lai, Naveen Suda, Damon Civin, and Vikas Chandra. Federated learning with non-iid data. arXiv preprint arXiv:1806.00582, 2018

    2018 arXiv

  29. [37]

    Modeling demand response in electricity retail markets as a stackelberg game

    Marco Zugno, Juan Miguel Morales González, Pierre Pinson, and Henrik Madsen. Modeling demand response in electricity retail markets as a stackelberg game. In 12th IAEE European Energy Conference: Energy challenge and environmental sustainability, 2012. 11

    2012

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