In this paper, we studied the federated bilevel optimization problem, which has widespread applications in machine learning. In particular, we developed two momentum-based algorithms for optimizing this kind of problem and established the convergence rate of our two algorithms, providing the sample and communication complexities. Importantly, to the best of our knowledge, our convergence rate is the first one achieving the linear speedup with respect to the number of devices for federated bilevel optimization algorithms. At last, our extensive experimental results confirm the effectiveness of our two algorithms.

翻译：在本文中,我们研究了联合双级优化问题,这在机器学习中具有广泛的应用性。特别是,我们开发了两种基于动力的算法来优化这类问题,并确定了我们两种算法的趋同率,提供了样本和通信的复杂性。重要的是,根据我们所知,我们的趋同率是第一个在联合双级优化算法设备数量方面实现线性加速的组合率。最后,我们的广泛实验结果证实了我们两种算法的有效性。