Decentralized bilevel optimization

Bilevel optimization has been successfully applied to many important machine learning problems. Algorithms for solving bilevel optimization have been studied under various settings. In this paper, we study the nonconvex-strongly-convex bilevel optimization under a decentralized setting. We design decentralized algorithms for both deterministic and stochastic bilevel optimization problems. Moreover, we analyze the convergence rates of the proposed algorithms in difference scenarios including the case where data heterogeneity is observed across agents. Numerical experiments on both synthetic and real data demonstrate that the proposed methods are efficient.