  Bilevel optimization has gained significant attention in recent years due to
its broad applications in machine learning. This paper focuses on bilevel
optimization in decentralized networks and proposes a novel single-loop
algorithm for solving decentralized bilevel optimization with a strongly convex
lower-level problem. Our approach is a fully single-loop method that
approximates the hypergradient using only two matrix-vector multiplications per
iteration. Importantly, our algorithm does not require any gradient
heterogeneity assumption, distinguishing it from existing methods for
decentralized bilevel optimization and federated bilevel optimization. Our
analysis demonstrates that the proposed algorithm achieves the best-known
convergence rate for bilevel optimization algorithms. We also present
experimental results on hyperparameter optimization problems using both
synthetic and MNIST datasets, which demonstrate the efficiency of our proposed
algorithm.
