Fast Adaptive Federated Bilevel Optimization

Bilevel optimization is a popular hierarchical model in machine learning, and has been widely applied to many machine learning tasks such as meta learning, hyperparameter learning and policy optimization. Although many bilevel optimization algorithms recently have been developed, few adaptive algorithm focuses on the bilevel optimization under the distributed setting. It is well known that the adaptive gradient methods show superior performances on both distributed and non-distributed optimization. In the paper, thus, we propose a novel adaptive federated bilevel optimization algorithm (i.e.,AdaFBiO) to solve the distributed bilevel optimization problems, where the objective function of Upper-Level (UL) problem is possibly nonconvex, and that of Lower-Level (LL) problem is strongly convex. Specifically, our AdaFBiO algorithm builds on the momentum-based variance reduced technique and local-SGD to obtain the best known sample and communication complexities simultaneously. In particular, our AdaFBiO algorithm uses the unified adaptive matrices to flexibly incorporate various adaptive learning rates to update variables in both UL and LL problems. Moreover, we provide a convergence analysis framework for our AdaFBiO algorithm, and prove it needs the sample complexity of $\tilde{O}(\epsilon^{-3})$ with communication complexity of $\tilde{O}(\epsilon^{-2})$ to obtain an $\epsilon$-stationary point. Experimental results on federated hyper-representation learning and federated data hyper-cleaning tasks verify efficiency of our algorithm.