Wireless federated learning (WFL) undergoes a communication bottleneck in uplink, limiting the number of users that can upload their local models in each global aggregation round. This paper presents a new multi-carrier non-orthogonal multiple-access (MC-NOMA)-empowered WFL system under an adaptive learning setting of Flexible Aggregation. Since a WFL round accommodates both local model training and uploading for each user, the use of Flexible Aggregation allows the users to train different numbers of iterations per round, adapting to their channel conditions and computing resources. The key idea is to use MC-NOMA to concurrently upload the local models of the users, thereby extending the local model training times of the users and increasing participating users. A new metric, namely, Weighted Global Proportion of Trained Mini-batches (WGPTM), is analytically established to measure the convergence of the new system. Another important aspect is that we maximize the WGPTM to harness the convergence of the new system by jointly optimizing the transmit powers and subchannel bandwidths. This nonconvex problem is converted equivalently to a tractable convex problem and solved efficiently using variable substitution and Cauchy's inequality. As corroborated experimentally using a convolutional neural network and an 18-layer residential network, the proposed MC-NOMA WFL can efficiently reduce communication delay, increase local model training times, and accelerate the convergence by over 40%, compared to its existing alternative.

翻译：无线联邦学习在上行链路面临通信瓶颈，限制了每轮全局聚合中能够上传本地模型的用户数量。本文提出了一种新型多载波非正交多址赋能的无线联邦学习系统，采用自适应学习框架中的柔性聚合策略。由于每轮联邦学习需要兼顾每个用户的本地模型训练与上传，柔性聚合允许用户根据自身信道条件与计算资源，每轮训练不同数量的迭代次数。其核心思想是利用多载波非正交多址技术实现用户本地模型的并发上传，从而延长用户的本地模型训练时间并增加参与用户数量。本文分析建立了衡量新系统收敛性的新型指标——加权全局训练小批量比例。另一重要方面是，我们通过联合优化发射功率与子信道带宽来最大化加权全局训练小批量比例，以提升系统收敛性能。该非凸问题通过变量代换和柯西不等式等价转化为可解凸问题，并实现了高效求解。基于卷积神经网络和18层残差网络的实验验证表明，与现有方案相比，本文提出的多载波非正交多址无线联邦学习可有效降低通信延迟，增加本地模型训练时间，并将收敛速度提升超过40%。