6 papers
On Second-Order Methods for Bilevel Optimization
Jiawen Bi, Jiaxiang Li, Mingyi Hong +1
Bilevel optimization is an indispensable modeling tool for modern machine learning and engineering design. However, the theory and practice for finding second order stationary poin…
On the Nature of Regularity Assumptions in Bilevel Optimization with Constrained Lower-level Problem
Xiaotian Jiang, Chang He, Mingyi Hong +1
In this paper, we study the regularity assumptions commonly adopted in bilevel optimization with constrained lower-level problems, including the linear independence constraint qual…
Natural Hypergradient Descent: Algorithm Design, Convergence Analysis, and Parallel Implementation
Deyi Kong, Zaiwei Chen, Shuzhong Zhang +1
In this work, we propose Natural Hypergradient Descent (NHGD), a new method for solving bilevel optimization problems. To address the computational bottleneck in hypergradient esti…
A Correspondence-Driven Approach for Bilevel Decision-making with Nonconvex Lower-Level Problems
Xiaotian Jiang, Jiaxiang Li, Jiawen Bi +2
We consider bilevel optimization problems with general nonconvex lower-level objectives and show that the classical hyperfunction-based formulation is unsettled, since the global m…
General Constrained Matrix Optimization
Casey Garner, Gilad Lerman, Shuzhong Zhang
This paper presents and analyzes the first matrix optimization model which allows general coordinate and spectral constraints. The breadth of problems our model covers is exemplifi…
A Barrier Function Approach for Bilevel Optimization with Coupled Lower-Level Constraints: Formulation, Approximation and Algorithms
Xiaotian Jiang, Jiaxiang Li, Mingyi Hong +1
In this paper, we consider bilevel optimization problem where the lower-level has coupled constraints, i.e. the constraints depend both on the upper- and lower-level variables. In…