InModel generalization thisModel update chapterTask migration, weConstrained optimization aim to make the best joint decision of device selectionDevice selection and computing and spectrum resource allocation for optimizing federated learning performance in distributed industrial Internet of Things networks. To implement efficient FLFederated Learning (FL) over geographically dispersed data, we introduce a three-layer collaborative FL architecture to support DNN training. Specifically, using the data dispersed in IIoT devices, the industrial gatewaysGateway locally train the DNN model and the local models can be aggregated by their associated edge servers every FL epoch or by a cloud server every a few FL epochs for obtaining the global modelGlobal model. To optimally select participating devices and allocate computing and spectrum resources for training and transmitting the model parameters, we formulate a stochastic optimization problem with the objective of minimizing FL evaluating loss while satisfying delay and long-term energy consumption requirements. Since the objective function of the FL evaluating loss is implicit and the energy consumption is temporally correlated, it is difficult to solve the problem via traditional optimization methods. Thus, we propose a “reinforcement on federated” (RoF) scheme, based on deep multi-agent reinforcement learning, to solve the problem. Specifically, the RoF scheme is executed decentralizedly at edge servers, which can cooperatively make the optimal device selection and resource allocation decisions. Moreover, a device refinement subroutine is embedded into the RoF scheme to accelerate convergence while effectively saving the on-device energy. Simulation results demonstrate that the RoF scheme can facilitate efficient FL and achieve better performance compared with state-of-the-art benchmarks.