首页|Gradient-based algorithms for multi-objective bi-level optimization

Gradient-based algorithms for multi-objective bi-level optimization

扫码查看
原文链接
  • 万方数据
  • 维普
Multi-objective bi-level optimization(MOBLO)addresses nested multi-objective optimization problems common in a range of applications.However,its multi-objective and hierarchical bi-level nature makes it notably complex.Gradient-based MOBLO algorithms have recently grown in popularity,as they effectively solve crucial machine learning problems like meta-learning,neural architecture search,and reinforcement learning.Unfortunately,these algorithms depend on solving a sequence of approximation subproblems with high accuracy,resulting in adverse time and memory complexity that lowers their numerical efficiency.To address this issue,we propose a gradient-based algorithm for MOBLO,called gMOBA,which has fewer hyperparameters to tune,making it both simple and efficient.Additionally,we demonstrate the theoretical validity by accomplishing the desirable Pareto stationarity.Numerical experiments confirm the practical efficiency of the proposed method and verify the theoretical results.To accelerate the convergence of gMOBA,we introduce a beneficial L2O(learning to optimize)neural network(called L2O-gMOBA)implemented as the initialization phase of our gMOBA algorithm.Comparative results of numerical experiments are presented to illustrate the performance of L2O-gMOBA.

multi-objectivebi-level optimizationconvergence analysisPareto stationarylearning to optimize

Xinmin Yang、Wei Yao、Haian Yin、Shangzhi Zeng、Jin Zhang

展开 >

National Center for Applied Mathematics in Chongqing,Chongqing 401331,China

School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China

Department of Mathematics,Southern University of Science and Technology,Shenzhen 518055,China

National Center for Applied Mathematics Shenzhen,Shenzhen 518000,China

Department of Mathematics and Statistics,University of Victoria,Victoria,BC V8W 2Y2,Canada

展开 >

Major Program of National Natural Science Foundation of ChinaMajor Program of National Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaGuangdong Basic and Applied Basic Research FoundationShenzhen Science and Technology Program

119910201199102412371305122221062022B1515020082RCYX20200714114700072

2024

10.1007/s11425-023-2302-9

中国科学:数学(英文版)
中国科学院

中国科学:数学(英文版)

CSTPCD
影响因子：0.36
ISSN：1674-7283
年,卷(期)：2024.67(6)