Convergence of Update Aware Device Scheduling for Federated Learning at\n the Wireless Edge

We study federated learning (FL) at the wireless edge, where power-limited\ndevices with local datasets collaboratively train a joint model with the help\nof a remote parameter server (PS). We assume that the devices are connected to\nthe PS through a bandwidth-limited shared wireless channel. At each iteration\nof FL, a subset of the devices are scheduled to transmit their local model\nupdates to the PS over orthogonal channel resources, while each participating\ndevice must compress its model update to accommodate to its link capacity. We\ndesign novel scheduling and resource allocation policies that decide on the\nsubset of the devices to transmit at each round, and how the resources should\nbe allocated among the participating devices, not only based on their channel\nconditions, but also on the significance of their local model updates. We then\nestablish convergence of a wireless FL algorithm with device scheduling, where\ndevices have limited capacity to convey their messages. The results of\nnumerical experiments show that the proposed scheduling policy, based on both\nthe channel conditions and the significance of the local model updates,\nprovides a better long-term performance than scheduling policies based only on\neither of the two metrics individually. Furthermore, we observe that when the\ndata is independent and identically distributed (i.i.d.) across devices,\nselecting a single device at each round provides the best performance, while\nwhen the data distribution is non-i.i.d., scheduling multiple devices at each\nround improves the performance. This observation is verified by the convergence\nresult, which shows that the number of scheduled devices should increase for a\nless diverse and more biased data distribution.\n