Gradient-based algorithms for multi-objective bi-level optimization
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 e...
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| Published in: | Science China. Mathematics Vol. 67; no. 6; pp. 1419 - 1438 |
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| Main Authors: | , , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Beijing
Science China Press
01.06.2024
Springer Nature B.V |
| Subjects: | |
| ISSN: | 1674-7283, 1869-1862 |
| Online Access: | Get full text |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Yang, Xinmin Zeng, Shangzhi Zhang, Jin Yao, Wei Yin, Haian |
| Author_xml | – sequence: 1 givenname: Xinmin surname: Yang fullname: Yang, Xinmin organization: National Center for Applied Mathematics in Chongqing, School of Mathematical Sciences, Chongqing Normal University – sequence: 2 givenname: Wei surname: Yao fullname: Yao, Wei organization: Department of Mathematics, Southern University of Science and Technology, National Center for Applied Mathematics Shenzhen – sequence: 3 givenname: Haian surname: Yin fullname: Yin, Haian organization: Department of Mathematics, Southern University of Science and Technology – sequence: 4 givenname: Shangzhi surname: Zeng fullname: Zeng, Shangzhi organization: Department of Mathematics and Statistics, University of Victoria – sequence: 5 givenname: Jin surname: Zhang fullname: Zhang, Jin email: zhangj9@sustech.edu.cn organization: Department of Mathematics, Southern University of Science and Technology, National Center for Applied Mathematics Shenzhen |
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| Cites_doi | 10.1109/TPAMI.2021.3132674 10.1080/02331934.2019.1625900 10.1109/TNSE.2022.3169117 10.1007/s10994-010-5232-5 10.1109/TEVC.2018.2855411 10.1137/10079731X 10.1007/s10957-012-0161-z 10.1137/S1052623403429093 10.1137/1.9781611974997 10.1007/s11075-018-0576-1 10.1016/j.ejor.2023.04.022 10.1109/GlobalSIP.2013.6737048 10.1007/s10589-018-0043-x 10.1109/4235.996017 10.1109/TSMCB.2004.834438 10.1007/s10957-006-9150-4 10.1109/TSMCC.2008.919172 10.1016/j.crma.2012.03.014 10.1109/MSP.2020.3016905 10.1007/s001860000043 10.1007/s10589-012-9494-7 10.1109/TEVC.2013.2281534 |
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