A Game-Theoretic Approach for Robust Federated Learning

Document Type : Special Issue on BDCPSI


Faculty of Computer Engineering, Shahrood University of Technology, Shahrood, Iran


Federated Learning enables aggregating models trained over a large number of clients by sending these models to a central server, while data privacy is preserved since only the models are sent. Federated learning techniques are considerably vulnerable to poisoning attacks. In this paper, we explore the threat of poisoning attacks and introduce a game-based robust federated averaging algorithm to detect and discard bad updates provided by the clients. We model the aggregating process with a mixed-strategy game that is played between the server and each client. The valid actions of the clients are to send good or bad updates while the server can accept or ignore these updates as its valid actions. By employing the Nash Equilibrium property, the server determines the probability of providing good updates by each client. The experimental results show that our proposed game-based aggregation algorithm is significantly more robust to faulty and noisy clients in comparison with the most recently presented methods. According to these results, our algorithm converges after a maximum of 30 iterations and can detect 100% of the bad clients for all the investigated scenarios. In addition, the accuracy of the proposed algorithm is at least 15.8% and 2.3% better than state of the art for flipping and noisy scenarios, respectively.


1.     McMahan, B., Moore, E., Ramage, D., Hampson, S. and y Arcas, B.A., "Communication-efficient learning of deep networks from decentralized data", in Artificial Intelligence and Statistics, PMLR. 1273-1282.
2.     Konečný, J., McMahan, H.B., Ramage, D. and Richtárik, P., "Federated optimization: Distributed machine learning for on-device intelligence", arXiv preprint arXiv:1610.02527,  Vol., No., (2016).
3.     Bagdasaryan, E., Veit, A., Hua, Y., Estrin, D. and Shmatikov, V., "How to backdoor federated learning", in International Conference on Artificial Intelligence and Statistics, PMLR., 2938-2948.
4.     Yang, Q., Liu, Y., Chen, T. and Tong, Y., "Federated machine learning: Concept and applications", ACM Transactions on Intelligent Systems and Technology (TIST),  Vol. 10, No. 2, (2019), 1-19. Doi: 10.1145/3298981
5.     Bhagoji, A.N., Chakraborty, S., Mittal, P. and Calo, S., "Analyzing federated learning through an adversarial lens", in International Conference on Machine Learning, PMLR. 634-643.
6.     Li, T., Sahu, A.K., Talwalkar, A. and Smith, V., "Federated learning: Challenges, methods, and future directions", IEEE Signal Processing Magazine,  Vol. 37, No. 3, (2020), 50-60. Doi: 10.1109/msp.2020.2975749
7.     Sattler, F., Wiedemann, S., Müller, K.-R. and Samek, W., "Robust and communication-efficient federated learning from non-iid data", IEEE Transactions on Neural Networks and Learning Systems,  Vol. 31, No. 9, (2019), 3400-3413. Doi: 10.1109/tnnls.2019.2944481
8.     Blanchard, P., El Mhamdi, E.M., Guerraoui, R. and Stainer, J., "Machine learning with adversaries: Byzantine tolerant gradient descent", in Proceedings of the 31st International Conference on Neural Information Processing Systems. Vol., No., (Year), 118-128.
9.     Damaskinos, G., El Mhamdi, E.M., Guerraoui, R., Guirguis, A.H.A. and Rouault, S.L.A., "Aggregathor: Byzantine machine learning via robust gradient aggregation", in The Conference on Systems and Machine Learning (SysML), 2019. Vol., No. CONF, (Year).
10.   Mhamdi, E.M.E., Guerraoui, R. and Rouault, S., "The hidden vulnerability of distributed learning in byzantium", arXiv preprint arXiv:1802.07927,  (2018).
11.   Nash, J., "Non-cooperative games", Annals of Mathematics,  (1951), 286-295.
12.   Konečný, J., McMahan, H.B., Yu, F.X., Richtárik, P., Suresh, A.T. and Bacon, D., "Federated learning: Strategies for improving communication efficiency", arXiv preprint arXiv:1610.05492,  (2016).
13.   McMahan, H.B., Moore, E., Ramage, D. and y Arcas, B.A., "Federated learning of deep networks using model averaging", arXiv preprint arXiv:1602.05629,  (2016).
14.   Chen, M., Mathews, R., Ouyang, T. and Beaufays, F., "Federated learning of out-of-vocabulary words", arXiv preprint arXiv:1903.10635,  (2019).
15.   Hard, A., Rao, K., Mathews, R., Ramaswamy, S., Beaufays, F., Augenstein, S., Eichner, H., Kiddon, C. and Ramage, D., "Federated learning for mobile keyboard prediction", arXiv preprint arXiv:1811.03604,  (2018).
16.   Wang, Y., "Co-op: Cooperative machine learning from mobile devices",  , (2017).
17.   Yin, D., Chen, Y., Kannan, R. and Bartlett, P., "Byzantine-robust distributed learning: Towards optimal statistical rates", in International Conference on Machine Learning, PMLR., 5650-5659.
18.   Xie, C., Koyejo, S. and Gupta, I., "Zeno: Distributed stochastic gradient descent with suspicion-based fault-tolerance", in International Conference on Machine Learning, PMLR., 6893-6901.
19.   Sun, Z., Kairouz, P., Suresh, A.T. and McMahan, H.B., "Can you really backdoor federated learning?", arXiv preprint arXiv:1911.07963,  (2019).
20.   Kang, J., Xiong, Z., Niyato, D., Yu, H., Liang, Y.-C. and Kim, D.I., "Incentive design for efficient federated learning in mobile networks: A contract theory approach", in 2019 IEEE VTS Asia Pacific Wireless Communications Symposium (APWCS), IEEE., 1-5. Doi: 10.1109/vts-apwcs.2019.8851649
21.   Feng, S., Niyato, D., Wang, P., Kim, D.I. and Liang, Y.-C., "Joint service pricing and cooperative relay communication for federated learning", in 2019 International Conference on Internet of Things (iThings) and IEEE Green Computing and Communications (GreenCom) and IEEE Cyber, Physical and Social Computing (CPSCom) and IEEE Smart Data (SmartData), IEEE., 815-820. Doi: 10.1109/ithings/greencom/cpscom/smartdata.2019.00148
22.   Zou, Y., Feng, S., Niyato, D., Jiao, Y., Gong, S. and Cheng, W., "Mobile device training strategies in federated learning: An evolutionary game approach", in 2019 International Conference on Internet of Things (iThings) and IEEE Green Computing and Communications (GreenCom) and IEEE Cyber, Physical and Social Computing (CPSCom) and IEEE Smart Data (SmartData), IEEE., 874-879. Doi: 10.1109/ithings/greencom/cpscom/smartdata.2019.00157
23.   Limam, N. and Boutaba, R., "Assessing software service quality and trustworthiness at selection time", IEEE Transactions on Software Engineering,  Vol. 36, No. 4, (2010), 559-574. Doi: 10.1109/tse.2010.2
24.   Rehman, A.U., Jiang, A., Rehman, A. and Paul, A., "Weighted based trustworthiness ranking in social internet of things by using soft set theory", in 2019 IEEE 5th International Conference on Computer and Communications (ICCC), IEEE., 1644-1648. Doi: 10.1109/iccc47050.2019.9064242
25.   De Kerchove, C. and Van Dooren, P., "Iterative filtering in reputation systems", SIAM Journal on Matrix Analysis and Applications,  Vol. 31, No. 4, (2010), 1812-1834. Doi: 10.1137/090748196
26.   Myerson, R.B., "Game theory, Harvard university press,  (2013). Doi: 10.1002/9781118547168
27.   Krizhevsky, A. and Hinton, G., "Learning multiple layers of features from tiny images",  Vol., No., (2009).
28.   LeCun, Y., Bottou, L., Bengio, Y. and Haffner, P., "Gradient-based learning applied to document recognition", Proceedings of the IEEE,  Vol. 86, No. 11, (1998), 2278-2324. Doi: 10.1109/5.726791
29.   Liu, S. and Deng, W., "Very deep convolutional neural network based image classification using small training sample size", in 2015 3rd IAPR Asian conference on pattern recognition (ACPR), IEEE., 730-734. Doi: 10.1109/acpr.2015.7486599