  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.
