pFedCal: Lightweight Personalized Federated Learning With Adaptive Calibration Strategy

Federated learning (FL) is a promising artificial intelligence framework that enables clients to collectively train models with data privacy. However, in real-world scenarios, to construct practical FL frameworks, several challenges have to be addressed, including statistical heterogeneity, constrained resources, and fairness. Therefore, we first investigate an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">aggregation gap</i> caused by statistical heterogeneity during local model initialization, which not only causes additional computational overhead for clients but also leads to the degradation of fairness. To bridge this gap, we propose <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">pFedCal</i>, a novel <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</u>ersonalized <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">fed</u>erated learning with lightweight adaptive <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">cal</u>ibration strategy that performs calibration compensation through the prior knowledge of clients. Specifically, we introduce compensation for each client at the model initialization, with the compensation derived from the global gradient and the latest gradient bias. To enhance the calibration effect, we introduce a smoothing-based calibration strategy, and we design an adaptive calibration strategy. A representative example demonstrates that the proposed calibration and smoothing strategies improve fairness for clients. The theoretical analysis indicates that with an appropriate learning rate, pFedCal converges to a first-order stationary point for non-convex loss functions. Comprehensive experimental results show that pFedCal achieves faster convergence, higher accuracy, and improved fairness than the state-of-the-art methods.