Non-Convex Over-the-Air Heterogeneous Federated Learning: A Bias-Variance Trade-off
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| Format: | Preprint |
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2025
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| author | Abrar, Muhammad Faraz Ul Michelusi, Nicolò |
| author_facet | Abrar, Muhammad Faraz Ul Michelusi, Nicolò |
| contents | Over-the-air (OTA) federated learning (FL) has been well recognized as a scalable paradigm that exploits the waveform superposition of the wireless multiple-access channel to aggregate model updates in a single use. Existing OTA-FL designs largely enforce zero-bias model updates by either assuming \emph{homogeneous} wireless conditions (equal path loss across devices) or forcing zero-bias updates to guarantee convergence. Under \emph{heterogeneous} wireless scenarios, however, such designs are constrained by the weakest device and inflate the update variance. Moreover, prior analyses of biased OTA-FL largely address convex objectives, while most modern AI models are highly non-convex. Motivated by these gaps, we study OTA-FL with stochastic gradient descent (SGD) for general smooth non-convex objectives under wireless heterogeneity. We develop novel OTA-FL SGD updates that allow a structured, time-invariant model bias while facilitating reduced variance updates. We derive a finite-time stationarity bound (expected time average squared gradient norm) that explicitly reveals a bias-variance trade-off. To optimize this trade-off, we pose a non-convex joint OTA power-control design and develop an efficient successive convex approximation (SCA) algorithm that requires only statistical CSI at the base station. Experiments on a non-convex image classification task validate the approach: the SCA-based design accelerates convergence via an optimized bias and improves generalization over prior OTA-FL baselines. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_26722 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-Convex Over-the-Air Heterogeneous Federated Learning: A Bias-Variance Trade-off Abrar, Muhammad Faraz Ul Michelusi, Nicolò Machine Learning Artificial Intelligence Distributed, Parallel, and Cluster Computing Systems and Control Signal Processing Over-the-air (OTA) federated learning (FL) has been well recognized as a scalable paradigm that exploits the waveform superposition of the wireless multiple-access channel to aggregate model updates in a single use. Existing OTA-FL designs largely enforce zero-bias model updates by either assuming \emph{homogeneous} wireless conditions (equal path loss across devices) or forcing zero-bias updates to guarantee convergence. Under \emph{heterogeneous} wireless scenarios, however, such designs are constrained by the weakest device and inflate the update variance. Moreover, prior analyses of biased OTA-FL largely address convex objectives, while most modern AI models are highly non-convex. Motivated by these gaps, we study OTA-FL with stochastic gradient descent (SGD) for general smooth non-convex objectives under wireless heterogeneity. We develop novel OTA-FL SGD updates that allow a structured, time-invariant model bias while facilitating reduced variance updates. We derive a finite-time stationarity bound (expected time average squared gradient norm) that explicitly reveals a bias-variance trade-off. To optimize this trade-off, we pose a non-convex joint OTA power-control design and develop an efficient successive convex approximation (SCA) algorithm that requires only statistical CSI at the base station. Experiments on a non-convex image classification task validate the approach: the SCA-based design accelerates convergence via an optimized bias and improves generalization over prior OTA-FL baselines. |
| title | Non-Convex Over-the-Air Heterogeneous Federated Learning: A Bias-Variance Trade-off |
| topic | Machine Learning Artificial Intelligence Distributed, Parallel, and Cluster Computing Systems and Control Signal Processing |
| url | https://arxiv.org/abs/2510.26722 |