Performative prediction (PP) is a framework that captures distribution shifts that occur during the training of machine learning models due to their deployment. As the trained model is used, its generated data could cause the model to evolve, leading to deviations from the original data distribution. The impact of such model-induced distribution shifts in the federated learning (FL) setup remains unexplored despite being increasingly likely to transpire in real-life use cases. Although Jin et al. (2024) recently extended PP to FL in a straightforward manner, the resulting model only converges to a performative stable point, which may be far from optimal. The methods in Izzo et al. (2021); Miller et al. (2021) can find a performative optimal point in centralized settings, but they require the performative risk to be convex and the training data to be noiseless, assumptions often violated in realistic FL systems. This paper overcomes all of these shortcomings and proposes Performative robust optimal Federated Learning (ProFL), an algorithm that finds performative optimal points in FL from noisy and contaminated data. We present the convergence analysis under the Polyak-Lojasiewicz condition, which applies to non-convex objectives. Extensive experiments on multiple datasets validate our proposed algorithms' efficiency.

翻译：性能预测（Performative Prediction, PP）是一个用于捕捉机器学习模型在训练过程中因其部署而产生的分布偏移的框架。随着训练模型的使用，其生成的数据可能导致模型演化，从而偏离原始数据分布。尽管在现实应用场景中此类模型引发的分布偏移日益可能发生，但联邦学习（Federated Learning, FL）设置下这种偏移的影响尚未得到探索。尽管 Jin 等人（2024）最近以直接方式将 PP 扩展到 FL，但所得模型仅收敛至一个性能稳定点，该点可能远离最优解。Izzo 等人（2021）和 Miller 等人（2021）的方法能够在集中式设置中找到性能最优点，但这些方法要求性能风险为凸函数且训练数据无噪声，这些假设在实际的 FL 系统中常被违反。本文克服了所有这些缺陷，提出了性能鲁棒最优联邦学习（ProFL），一种能够从噪声和污染数据中在 FL 中找到性能最优点的算法。我们在 Polyak-Lojasiewicz 条件下给出了收敛性分析，该条件适用于非凸目标函数。在多个数据集上的大量实验验证了我们所提出算法的高效性。