In this paper, we take an information-theoretic approach to understand the robustness in wireless distributed learning. Upon measuring the difference in loss functions, we provide an upper bound of the performance deterioration due to imperfect wireless channels. Moreover, we characterize the transmission rate under task performance guarantees and propose the channel capacity gain resulting from the inherent robustness in wireless distributed learning. An efficient algorithm for approximating the derived upper bound is established for practical use. The effectiveness of our results is illustrated by the numerical simulations.

翻译：本文采用信息论方法研究无线分布式学习中的鲁棒性。通过测量损失函数差异，我们给出了因无线信道不完美导致的性能退化上界。进一步地，我们刻画了在任务性能保障下的传输速率，并提出了无线分布式学习中固有鲁棒性所带来的信道容量增益。为便于实际应用，我们建立了一种高效算法以逼近所推导的上界。数值仿真结果验证了本文方法的有效性。