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（FL）中的无线通信与计算效率。在所提出的位宽联邦学习方案中，边缘设备对其本地FL模型参数进行量化并传输至协调服务器，该服务器将其聚合为量化全局模型并同步各设备。目标是在每次迭代中联合确定本地FL模型量化所用的位宽以及参与FL训练的设备集合。我们将此建模为一个优化问题，旨在最小化量化FL的训练损失，同时满足每次迭代的设备采样预算与延迟约束。然而，该问题难以直接求解，其原因在于：（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，我们通过理论分析刻画了有限无线资源与引入的量化误差对所提FL方法性能的影响。结果表明，FL训练损失在连续两次迭代间的改善程度取决于设备选择与量化方案，以及被学习模型固有的若干参数。随后，我们将FL训练过程描述为马尔可夫决策过程，并提出一种基于模型的强化学习（RL）方法来优化迭代间的动作选择。与无模型RL相比，这种基于模型的RL方法利用对FL训练过程推导的数学表征，可在不增加设备额外通信开销的情况下发现有效的设备选择与量化方案。仿真结果表明，所提FL算法可缩短收敛时间。