Adaptive multi-gradient methods for quasiconvex vector optimization and applications to multi-task learning
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909099439947776 |
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| author | Minh, Nguyen Anh Muu, Le Dung Thang, Tran Ngoc |
| author_facet | Minh, Nguyen Anh Muu, Le Dung Thang, Tran Ngoc |
| contents | We present an adaptive step-size method, which does not include line-search techniques, for solving a wide class of nonconvex multiobjective programming problems on an unbounded constraint set. We also prove convergence of a general approach under modest assumptions. More specifically, the convexity criterion might not be satisfied by the objective function. Unlike descent line-search algorithms, it does not require an initial step-size to be determined by a previously determined Lipschitz constant. The process's primary characteristic is its gradual step-size reduction up until a predetermined condition is met. It can be specifically applied to offer an innovative multi-gradient projection method for unbounded constrained optimization issues. Preliminary findings from a few computational examples confirm the accuracy of the strategy. We apply the proposed technique to some multi-task learning experiments to show its efficacy for large-scale challenges. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_06224 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Adaptive multi-gradient methods for quasiconvex vector optimization and applications to multi-task learning Minh, Nguyen Anh Muu, Le Dung Thang, Tran Ngoc Optimization and Control Machine Learning We present an adaptive step-size method, which does not include line-search techniques, for solving a wide class of nonconvex multiobjective programming problems on an unbounded constraint set. We also prove convergence of a general approach under modest assumptions. More specifically, the convexity criterion might not be satisfied by the objective function. Unlike descent line-search algorithms, it does not require an initial step-size to be determined by a previously determined Lipschitz constant. The process's primary characteristic is its gradual step-size reduction up until a predetermined condition is met. It can be specifically applied to offer an innovative multi-gradient projection method for unbounded constrained optimization issues. Preliminary findings from a few computational examples confirm the accuracy of the strategy. We apply the proposed technique to some multi-task learning experiments to show its efficacy for large-scale challenges. |
| title | Adaptive multi-gradient methods for quasiconvex vector optimization and applications to multi-task learning |
| topic | Optimization and Control Machine Learning |
| url | https://arxiv.org/abs/2402.06224 |