Part of Advances in Neural Information Processing Systems 37 (NeurIPS 2024) Main Conference Track
Andi Han, Bamdev Mishra, Pratik Kumar Jawanpuria, Akiko Takeda
Bilevel optimization has gained prominence in various applications. In this study, we introduce a framework for solving bilevel optimization problems, where the variables in both the lower and upper levels are constrained on Riemannian manifolds. We present several hypergradient estimation strategies on manifolds and analyze their estimation errors. Furthermore, we provide comprehensive convergence and complexity analyses for the proposed hypergradient descent algorithm on manifolds. We also extend our framework to encompass stochastic bilevel optimization and incorporate the use of general retraction. The efficacy of the proposed framework is demonstrated through several applications.