{"ID":2853892,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.15305","arxiv_id":"2510.15305","title":"Riemannian Bilevel Optimization with Gradient Aggregation","abstract":"Bilevel optimization (BLO) offers a principled framework for hierarchical decision-making and has been widely applied in machine learning tasks such as hyperparameter optimization and meta-learning. While existing BLO methods are mostly developed in Euclidean spaces, many real-world problems involve structural constraints. In this paper, we propose a Riemannian bilevel optimization (RBLO) algorithm that incorporates a bilevel descent aggregation (BDA) scheme to jointly coordinate upper- and lower-level updates. Concretely, first we abstract the constraints in the BLO to a manifold structure and then transform the constrained BLO be a unconstrained RBLO problem. Second, to address limitations of existing RBLO methods, particularly the restrictive assumptions required for convergence, we reformulate the bilevel problem using smooth manifold mappings and provide a convergence analysis under the conditions of geodesic convexity and Lipschitz smoothness. Finally, we recall the multi-view hypergraph spectral clustering task, and evaluate the proposed approach on 3sources data sets. The numerical results validate the superior performance over Euclidean and manifold-based baselines.","short_abstract":"Bilevel optimization (BLO) offers a principled framework for hierarchical decision-making and has been widely applied in machine learning tasks such as hyperparameter optimization and meta-learning. While existing BLO methods are mostly developed in Euclidean spaces, many real-world problems involve structural constrai...","url_abs":"https://arxiv.org/abs/2510.15305","url_pdf":"https://arxiv.org/pdf/2510.15305v1","authors":"[\"Zhuo Chen\",\"Xinjian Xu\",\"Shihui Ying\",\"Tieyong Zeng\"]","published":"2025-10-17T04:30:44Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"math.NA\"]","methods":"[]","has_code":false}