This paper considers improving wireless communication and computation efficiency in federated learning (FL) via model quantization. In the proposed bitwidth FL scheme, edge devices train and transmit quantized versions of their local FL model parameters to a coordinating server, which aggregates them into a quantized global model and synchronizes the devices. The goal is to jointly determine the bitwidths employed for local FL model quantization and the set of devices participating in FL training at each iteration. We pose this as an optimization problem that aims to minimize the training loss of quantized FL under a per-iteration device sampling budget and delay requirement. However, the formulated problem is difficult to solve without (i) a concrete understanding of how quantization impacts global ML performance and (ii) the ability of the server to construct estimates of this process efficiently. To address the first challenge, we analytically characterize how limited wireless resources and induced quantization errors affect the performance of the proposed FL method. Our results quantify how the improvement of FL training loss between two consecutive iterations depends on the device selection and quantization scheme as well as on several parameters inherent to the model being learned. Then, we show that the FL training process can be described as a Markov decision process and propose a model-based reinforcement learning (RL) method to optimize action selection over iterations. Compared to model-free RL, this model-based RL approach leverages the derived mathematical characterization of the FL training process to discover an effective device selection and quantization scheme without imposing additional device communication overhead. Simulation results show that the proposed FL algorithm can reduce the convergence time.

翻译：本文考虑通过模型量化提升联邦学习中的无线通信与计算效率。在所提出的比特宽度联邦学习方案中，边缘设备对其本地联邦学习模型参数进行量化后传输至协调服务器，服务器将量化后的全局模型聚合后同步各设备。目标在于联合确定每次迭代中用于本地联邦学习模型量化的比特宽度及参与联邦训练的设备集合。我们将此构建为优化问题，旨在满足每迭代设备采样预算与延迟约束条件下最小化量化联邦学习的训练损失。然而，该问题难以求解，原因在于：(i) 缺乏对量化如何影响全局机器学习性能的具体理解；(ii) 服务器无法高效构建该过程的估计。针对第一个挑战，我们从解析角度刻画有限无线资源与引入的量化误差如何影响所提联邦学习方法的性能。研究结果定量揭示了相邻两次迭代间联邦学习训练损失的改进幅度与设备选择、量化方案及被学习模型固有参数之间的关系。进一步表明，联邦学习训练过程可描述为马尔可夫决策过程，并提出基于模型的强化学习方法以优化迭代间动作选择。相较于无模型强化学习，该基于模型的强化学习方法利用联邦学习训练过程的导出数学特性，在不增加额外设备通信开销的情况下发掘有效的设备选择与量化方案。仿真结果显示，所提联邦学习算法可缩短收敛时间。