In the above article [1], this shows a corrected statement and proof of Theorem 1. The analysis in [1] incorrectly treated subsets of scheduled devices independently, overlooking that global iterates depend on all subsets. In addition, in the proof of Lemma 2 (now Lemma 3 in this document), the expectation over the randomness in the gradient sparsification was inaccurate.

Federated learning (FL) has received significant attention in recent years for its advantages in efficient training of machine learning models across distributed clients without disclosing user-sensitive data. Specifically, in federated edge learning (FEEL) systems, the time-varying nature of wireless channels introduces inevitable system dynamics in the communication process, thereby affecting training latency and energy consumption. In this work, we further consider a streaming data scenario where new training data samples are randomly generated over time at edge devices. Our goal is to develop a dynamic scheduling and resource allocation algorithm to address the inherent randomness in data arrivals and resource availability under long-term energy constraints. To achieve this, we formulate a stochastic network optimization problem and use the Lyapunov drift-plus-penalty framework to obtain a dynamic resource management design. Our proposed algorithm makes adaptive decisions on device scheduling, computational capacity adjustment, and allocation of bandwidth and transmit power in every round. We provide convergence analysis for the considered setting with heterogeneous data and time-varying objective functions, which supports the rationale behind our proposed scheduling design. The effectiveness of our scheme is verified through simulation results, demonstrating improved learning performance and energy efficiency as compared to baseline schemes.

Federated Learning (FL) is a collaborative machine learning (ML) framework that combines on-device training and server-based aggregation to train a common ML model among distributed agents. In this work, we propose an asynchronous FL design with periodic aggregation to tackle the straggler issue in FL systems. Considering limited wireless communication resources, we investigate the effect of different scheduling policies and aggregation designs on the convergence performance. Driven by the importance of reducing the bias and variance of the aggregated model updates, we propose a scheduling policy that jointly considers the channel quality and training data representation of user devices. The effectiveness of our channel-aware data-importance-based scheduling policy, compared with state-of-the-art methods proposed for synchronous FL, is validated through simulations. Moreover, we show that an “age-aware” aggregation weighting design can significantly improve the learning performance in an asynchronous FL setting.