Optimizing Asynchronous Federated Learning: A Delicate Trade-Off Between Model-Parameter Staleness and Update Frequency

Synchronous federated learning (FL) scales poorly with the number of clients due to the straggler effect. Algorithms like FedAsync and GeneralizedFedAsync address this limitation by enabling asynchronous communication between clients and the central server. In this work, we rely on stochastic modeling and analysis to better understand the impact of design choices in asynchronous FL algorithms, such as the concurrency level and routing probabilities, and we leverage this knowledge to optimize loss. Compared to most existing studies, we account for the joint impact of heterogeneous and variable service speeds and heterogeneous datasets at the clients. We characterize in particular a fundamental trade-off for optimizing asynchronous FL: minimizing gradient estimation errors by avoiding model parameter staleness, while also speeding up the system by increasing the throughput of model updates. Our two main contributions can be summarized as follows. First, we prove a discrete variant of Little's law to derive a closed-form expression for relative delay, a metric that quantifies staleness. This allows us to efficiently minimize the average loss per model update, which has been the gold standard in literature to date, using the upper-bound of Leconte et al. as a proxy. Second, we observe that naively optimizing this metric drastically slows down the system by overemphasizing staleness at the expense of throughput. This motivates us to introduce an alternative metric that also accounts for speed, for which we derive a tractable upper-bound that can be minimized numerically. Extensive numerical results show these optimizations enhance accuracy by 10% to 30%.