Computer Science > Machine Learning
[Submitted on 10 Feb 2023 (v1), last revised 12 Sep 2023 (this version, v4)]
Title:On Penalty-based Bilevel Gradient Descent Method
View PDFAbstract:Bilevel optimization enjoys a wide range of applications in hyper-parameter optimization, meta-learning and reinforcement learning. However, bilevel optimization problems are difficult to solve. Recent progress on scalable bilevel algorithms mainly focuses on bilevel optimization problems where the lower-level objective is either strongly convex or unconstrained. In this work, we tackle the bilevel problem through the lens of the penalty method. We show that under certain conditions, the penalty reformulation recovers the solutions of the original bilevel problem. Further, we propose the penalty-based bilevel gradient descent (PBGD) algorithm and establish its finite-time convergence for the constrained bilevel problem without lower-level strong convexity. Experiments showcase the efficiency of the proposed PBGD algorithm.
Submission history
From: Quan Xiao [view email][v1] Fri, 10 Feb 2023 11:30:19 UTC (694 KB)
[v2] Sat, 11 Mar 2023 20:29:49 UTC (1,015 KB)
[v3] Tue, 21 Mar 2023 19:25:54 UTC (1,015 KB)
[v4] Tue, 12 Sep 2023 20:09:08 UTC (1,021 KB)
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