171. Alternating Gradient-Type Algorithm for Bilevel Optimization with Inexact Lower-Level Solutions via Moreau Envelope-based Reformulation
Invited abstract in session TB-7: Nonsmooth Bilevel Optimization, stream Bilevel and multilevel optimization.
Tuesday, 10:30-12:30Room: B100/5015
Authors (first author is the speaker)
| 1. | Shangzhi Zeng
|
| Southern University of Science and Technology |
Abstract
In this work, we study a class of bilevel optimization problems where the lower-level problem is a convex composite optimization model, which arises in various applications, including bilevel hyperparameter selection for regularized regression models. To solve these problems, we propose an Alternating Gradient-type algorithm with Inexact Lower-level Solutions (AGILS) based on a Moreau envelope-based reformulation of the bilevel optimization problem. The proposed algorithm does not require exact solutions of the lower-level problem at each iteration, improving computational efficiency. We prove the convergence of AGILS to stationary points and, under the Kurdyka-Lojasiewicz (KL) property, establish its sequential convergence. Numerical experiments, including a toy example and a bilevel hyperparameter selection problem for the sparse group Lasso model, demonstrate the effectiveness of the proposed AGILS.
Keywords
- Multi-level optimization
- First-order optimization
Status: accepted
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