Federated bilevel optimization has received increasing attention in various emerging machine learning and communication applications. Recently, several Hessian-vector-based algorithms have been proposed to solve the federated bilevel optimization problem. However, several important properties in federated learning such as the partial client participation and the linear speedup for convergence (i.e., the convergence rate and complexity are improved linearly with respect to the number of sampled clients) in the presence of non-i.i.d.~datasets, still remain open. In this paper, we fill these gaps by proposing a new federated bilevel algorithm named FedMBO with a novel client sampling scheme in the federated hypergradient estimation. We show that FedMBO achieves a convergence rate of $\mathcal{O}\big(\frac{1}{\sqrt{nK}}+\frac{1}{K}+\frac{\sqrt{n}}{K^{3/2}}\big)$ on non-i.i.d.~datasets, where $n$ is the number of participating clients in each round, and $K$ is the total number of iteration. This is the first theoretical linear speedup result for non-i.i.d.~federated bilevel optimization. Extensive experiments validate our theoretical results and demonstrate the effectiveness of our proposed method.
Fully First-Order Methods for Decentralized Bilevel Optimization
The Hong Kong University of Science and Technology（香港科技大学）；University of California Davis（加州大学戴维斯分校）；Rice University（莱斯大学）；University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
STL-SGD: Speeding Up Local SGD with Stagewise Communication Period
University of Science and Technology of China（中国科学技术大学）；Ant Financial Services Group（蚂蚁集团）；IFLYTEK Co., Ltd.（科大讯飞股份有限公司）；Hong Kong University of Science and Technology（香港科技大学）
Bandwidth-Aware and Overlap-Weighted Compression for Communication-Efficient Federated Learning
The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））；Hong Kong Baptist University（香港浸会大学）；Harbin Institute of Technology, Shenzhen（哈尔滨工业大学（深圳））
