On Penalty-based Bilevel Gradient Descent Method

Autor:	Shen, Han, Xiao, Quan, Chen, Tianyi
Rok vydání:	2023
Předmět:	Computer Science - Machine Learning Mathematics - Optimization and Control Statistics - Machine Learning
Druh dokumentu:	Working Paper
Popis:	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. Comment: Improved Section 4 by removing a critical assumption; Added Section 5 and citations
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2302.05185 Zobrazit plný text záznamu View this record from Arxiv