本篇論文研究了在多模型空中傳輸聯邦學習在多時間區間傳輸情況下用戶的傳輸排程及波束成型設計。在相關空中傳輸研究中，多是透過利用多重接取傳輸技術中訊號疊加的特性，達成傳輸與計算結合的聯邦學習單一模型上傳。但在多模型空中傳輸情境下，不同模型之間同步傳輸可能會有極大的交互傳輸干擾，進而影響空中傳輸在聯邦學習的效率。因此在此篇研究我們考慮了透過多時間區間傳輸進行用戶的傳輸排程及波束成型設計，降低收斂分析在每個訓練週期加權後的多模型傳輸錯誤，以提升傳輸品質。基於對通道資訊的不同假設，我們提出了線上與線下的演算法，優化用戶傳輸排程與波束成型設計。
線上演算法是基於所有傳輸時間區的通道資訊都是已知的情況下，所有時間區間通道透過疊代優化共同優化用戶傳輸排成與波束成型，在固定接收或傳輸波束成型情況下，優化另一個波束成型。線下演算法則是基於只有當前通道訊息是已知情況下，將每時間區間分成用戶傳輸排程與波束成型設計兩階段，受到收斂分析啟發，我們提出一個基於用戶通道之間得相關性與過去傳輸狀態的優化問題式子進行用戶排程優化，並基於用戶排程透過疊代法求得波束成型。我們透過線性規劃模型模擬驗證提出的線上與縣下演算法，並比較隨機用戶排程與在無用戶排程下時間區間獨立波束成型設計，結果顯示提出的線下演算法表現可以優於其餘演算法，線上演算法則只能優於隨機用戶排程。

We study a multi-model Federated learning (FL) framework deployed over a wireless network, where multiple models are collaboratively trained and updated over the wireless channel by multiple edge users. With limited wireless resources, edge users transmit their local updates through a wireless transmission framework that merges transmission and computation, over-the-air computation (AirComp), to achieve time-efficient model updates. In previous works, they fully leveraged all user data aggregation for constructing a single model update.
This, however, is not the case in multi-model FL via AirComp. The multi-model FL via AirComp requires the concurrent reconstruction of each unrelated model. The retrieving process of each model will view others as interference and make efforts to rule out them to assuring the FL performance. In this work, we first propose a multi-time slot transmission framework, which jointly optimizes multi-time slot transceiver beamformer in an offline fashion based on the convergence analysis, to mitigate inter-model interference. Then, based on the interference-avoidance and update staleness characteristic, we propose a sequential user scheduling and beamformer design algorithm in an online fashion, in which user selection makes the decision in view of the current CSI of users and their transmission state in the past.
Since locality and propagation environment plays a key role in the characteristic of wireless channel, certain users may be deprived of model updates if user scheduling merely considers their CSI. This, however, may objectively represent the training data, which harms the convergence rate and leads to a biased FL model.
Therefore, we propose a heuristic formulation, which takes both the CSI and the staleness of users into account, for user selection optimization. We conduct our experiments on synthetic linear regression datasets, and characterize the performance between the offline beamformer design and the online counterpart. Experiments show that the proposed offline beamformer design can outperform other algorithms, and the proposed online user scheduling can only outperform random user scheduling.

[1] B. McMahan, E. Moore, D. Ramage, S. Hampson, and B. A. y Arcas, “Communicationefficient learning of deep networks from decentralized data,” in Artificial intelligence and statistics, PMLR, 2017.
[2] M. Chen, Z. Yang, W. Saad, C. Yin, H. V. Poor, and S. Cui, “A joint learning and communications framework for federated learning over wireless networks,” IEEE Transactions on Wireless Communications, vol. 20, no. 1, 2021.
[3] M. M. Amiri, D. Gund ¨ uz, S. R. Kulkarni, and H. V. Poor, “Convergence of update aware device scheduling for federated learning at the wireless edge,” IEEE Transactions on Wireless Communications, vol. 20, no. 6, 2021.
[4] H. H. Yang, Z. Liu, T. Q. S. Quek, and H. V. Poor, “Scheduling policies for federated learning in wireless networks,” IEEE Transactions on Communications, vol. 68, no. 1, 2020.
[5] L. Chen, X. Qin, and G. Wei, “A uniform-forcing transceiver design for over-the-air function computation,” IEEE Wireless Communications Letters, vol. 7, no. 6, 2018.
[6] X. Wei and C. Shen, “Federated learning over noisy channels: Convergence analysis and design examples,” IEEE Transactions on Cognitive Communications and Networking, 2022.
[7] K. Yang, T. Jiang, Y. Shi, and Z. Ding, “Federated learning via over-the-air computation,” IEEE Transactions on Wireless Communications, vol. 19, no. 3, 2020.
[8] W. Guo, R. Li, C. Huang, X. Qin, K. Shen, and W. Zhang, “Joint device selection and power control for wireless federated learning,” IEEE Journal on Selected Areas in Communications, vol. 40, no. 8, 2022.
[9] Y. Sun, S. Zhou, Z. Niu, and D. Gund ¨ uz, “Dynamic scheduling for over-the-air federated edge learning with energy constraints,” IEEE Journal on Selected Areas in Communications, vol. 40, no. 1, 2022.
[10] V. Smith, C.-K. Chiang, M. Sanjabi, and A. S. Talwalkar, “Federated multi-task learning,” Advances in neural information processing systems, vol. 30, 2017.
[11] C. Zhong, H. Yang, and X. Yuan, “Multi-task federated learning with over-the-air computation for mimo interference channels,” in 2022 International Symposium on Networks, Computers and Communications (ISNCC), 2022.
[12] H. Ma, X. Yuan, Z. Ding, D. Fan, and J. Fang, “Over-the-air federated multi-task learning via
model sparsification and turbo compressed sensing,” arXiv preprint arXiv:2205.03810, 2022.
[13] S. Zheng, C. Shen, and X. Chen, “Design and analysis of uplink and downlink communications for federated learning,” IEEE Journal on Selected Areas in Communications, vol. 39, no. 7, 2021.
[14] A. Reisizadeh, A. Mokhtari, H. Hassani, A. Jadbabaie, and R. Pedarsani, “Fedpaq: A
communication-efficient federated learning method with periodic averaging and quantization,” in International Conference on Artificial Intelligence and Statistics, PMLR, 2020.
[15] M. M. Amiri, D. Gunduz, S. R. Kulkarni, and H. V. Poor, “Federated learning with quantized
global model updates,” arXiv preprint arXiv:2006.10672, 2020.
[16] H. Gao, A. Xu, and H. Huang, “On the convergence of communication-efficient local sgd for federated learning,” in Proceedings of the AAAI Conference on Artificial Intelligence, vol. 35, 2021.
[17] D. Alistarh, T. Hoefler, M. Johansson, N. Konstantinov, S. Khirirat, and C. Renggli, “The convergence of sparsified gradient methods,” Advances in Neural Information Processing Systems, vol. 31, 2018.
[18] S. U. Stich, J.-B. Cordonnier, and M. Jaggi, “Sparsified sgd with memory,” Advances in Neural Information Processing Systems, 2018.
[19] C. Li, G. Li, and P. K. Varshney, “Communication-efficient federated learning based on compressed sensing,” IEEE Internet of Things Journal, vol. 8, no. 20, 2021.
[20] Z. Wang, Z. Zhang, Y. Tian, Q. Yang, H. Shan, W. Wang, and T. Q. S. Quek, “Asynchronous federated learning over wireless communication networks,” IEEE Transactions on Wireless Communications, vol. 21, no. 9, 2022.
[21] Z. Wang, J. Qiu, Y. Zhou, Y. Shi, L. Fu, W. Chen, and K. B. Letaief, “Federated learning via intelligent reflecting surface,” IEEE Transactions on Wireless Communications, vol. 21, no. 2, 2022.
[22] H. Yang, P. Qiu, J. Liu, and A. Yener, “Over-the-air federated learning with joint adaptive computation and power control,” in 2022 IEEE International Symposium on Information Theory (ISIT), 2022.
[23] S. Park and W. Choi, “Byzantine fault tolerant distributed stochastic gradient descent based on over-the-air computation,” IEEE Transactions on Communications, vol. 70, no. 5, 2022.
[24] N. Zhang and M. Tao, “Gradient statistics aware power control for over-the-air federated learning,” IEEE Transactions on Wireless Communications, vol. 20, no. 8, 2021.
[25] G. Zhu, Y. Wang, and K. Huang, “Broadband analog aggregation for low-latency federated edge learning,” IEEE Transactions on Wireless Communications, vol. 19, no. 1, 2020.
[26] J. Mao, H. Yang, P. Qiu, J. Liu, and A. Yener, “Charles: Channel-quality-adaptive over-theair federated learning over wireless networks,” in 2022 IEEE 23rd International Workshop on Signal Processing Advances in Wireless Communication (SPAWC), pp. 1–5, 2022.
[27] G. Zhu, Y. Du, D. Gund ¨ uz, and K. Huang, “One-bit over-the-air aggregation for communication-efficient federated edge learning: Design and convergence analysis,” IEEE Transactions on Wireless Communications, vol. 20, no. 3, 2021.
[28] T. Sery and K. Cohen, “On analog gradient descent learning over multiple access fading
channels,” IEEE Transactions on Signal Processing, vol. 68, 2020.
[29] S. Xia, J. Zhu, Y. Yang, Y. Zhou, Y. Shi, and W. Chen, “Fast convergence algorithm for analog federated learning,” in ICC 2021-IEEE International Conference on Communications, IEEE.
[30] H. Hellstrom, V. Fodor, and C. Fischione, “Over-the-air federated learning with retransmissions,” in 2021 IEEE 22nd International Workshop on Signal Processing Advances in Wireless Communications (SPAWC), 2021.
[31] M. P. Friedlander and M. Schmidt, “Hybrid deterministic-stochastic methods for data fitting,” SIAM Journal on Scientific Computing, vol. 34, no. 3, pp. A1380–A1405, 2012.
[32] H. H. Yang, A. Arafa, T. Q. S. Quek, and H. Vincent Poor, “Age-based scheduling policy for federated learning in mobile edge networks,” in ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 8743–8747, 2020.
[33] Y. Ma, S. Lao, E. Takikawa, and M. Kawade, “Discriminant analysis in correlation similarity measure space,” in Proceedings of the 24th International Conference on Machine Learning, ICML ’07, (New York, NY, USA), Association for Computing Machinery, 2007.