Power Allocation and Data Assignment for Over-The-Air Distributed Learning

Recently, over-the-air computation is considered an efficient scheme for enormous data transmission in distributed learning and computing systems. Its performance is limited by the aggregation errors, which may be caused by noise, channel fading, and insufficient device power budgets. Inspired by gradient coding, this paper considers to leverage the computing abilities of the edge devices to reap a diversity gain and alleviate the effects of inadequate transmit power. The edge server divides the whole dataset into subsets and distributes them to edge devices by some data assignment scheme. The edge devices send the computation results simultaneously back to the edge server by over-the-air transmission. This paper jointly optimizes the data assignment and power allocation problems in over-the-air distributed learning systems to minimize the mean square error (MSE) of the aggregation data. Given the data assignment scheme, the power allocation problem is solved optimally by block coordinate descent (BCD) and grid search. Besides, some optimality conditions for data assignment are proved. Accordingly, a heuristic data assignment scheme is proposed. Numerical results show our proposed scheme outperforms existing works in terms of MSE and learning metrics.