Revisiting norm optimization for multi-objective black-box problems : a finite-time analysis
The complexity of Pareto fronts imposes a great challenge on the convergence analysis of multi-objective optimization methods. While most theoretical convergence studies have addressed finite-set and/or discrete problems, others have provided probabilistic guarantees, assumed a total order on the so...
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| Format: | Journal Article |
| Language: | English |
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2020
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| Online Access: | https://hdl.handle.net/10356/143267 |
| _version_ | 1811687144680325120 |
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| author | Al-Dujaili, Abdullah Suresh, Sundaram |
| author2 | School of Computer Science and Engineering |
| author_facet | School of Computer Science and Engineering Al-Dujaili, Abdullah Suresh, Sundaram |
| author_sort | Al-Dujaili, Abdullah |
| collection | NTU |
| description | The complexity of Pareto fronts imposes a great challenge on the convergence analysis of multi-objective optimization methods. While most theoretical convergence studies have addressed finite-set and/or discrete problems, others have provided probabilistic guarantees, assumed a total order on the solutions, or studied their asymptotic behaviour. In this paper, we revisit the Tchebycheff weighted method in a hierarchical bandits setting and provide a finite-time bound on the Pareto-compliant additive ϵ-indicator. To the best of our knowledge, this paper is one of few that establish a link between weighted sum methods and quality indicators in finite time. |
| first_indexed | 2024-10-01T05:11:39Z |
| format | Journal Article |
| id | ntu-10356/143267 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T05:11:39Z |
| publishDate | 2020 |
| record_format | dspace |
| spelling | ntu-10356/1432672020-08-18T04:34:11Z Revisiting norm optimization for multi-objective black-box problems : a finite-time analysis Al-Dujaili, Abdullah Suresh, Sundaram School of Computer Science and Engineering Engineering::Computer science and engineering Multi-objective Optimization Black-box Optimization The complexity of Pareto fronts imposes a great challenge on the convergence analysis of multi-objective optimization methods. While most theoretical convergence studies have addressed finite-set and/or discrete problems, others have provided probabilistic guarantees, assumed a total order on the solutions, or studied their asymptotic behaviour. In this paper, we revisit the Tchebycheff weighted method in a hierarchical bandits setting and provide a finite-time bound on the Pareto-compliant additive ϵ-indicator. To the best of our knowledge, this paper is one of few that establish a link between weighted sum methods and quality indicators in finite time. Accepted version 2020-08-18T04:34:11Z 2020-08-18T04:34:11Z 2018 Journal Article Al-Dujaili, A., & Suresh, S. (2019). Revisiting norm optimization for multi-objective black-box problems : a finite-time analysis. Journal of Global Optimization, 73(3), 659-673. doi:10.1007/s10898-018-0709-z 0925-5001 https://hdl.handle.net/10356/143267 10.1007/s10898-018-0709-z 2-s2.0-85054316678 3 73 659 673 en Journal of Global Optimization © 2018 Springer. This is a post-peer-review, pre-copyedit version of an article published in Journal of Global Optimization. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10898-018-0709-z. application/pdf |
| spellingShingle | Engineering::Computer science and engineering Multi-objective Optimization Black-box Optimization Al-Dujaili, Abdullah Suresh, Sundaram Revisiting norm optimization for multi-objective black-box problems : a finite-time analysis |
| title | Revisiting norm optimization for multi-objective black-box problems : a finite-time analysis |
| title_full | Revisiting norm optimization for multi-objective black-box problems : a finite-time analysis |
| title_fullStr | Revisiting norm optimization for multi-objective black-box problems : a finite-time analysis |
| title_full_unstemmed | Revisiting norm optimization for multi-objective black-box problems : a finite-time analysis |
| title_short | Revisiting norm optimization for multi-objective black-box problems : a finite-time analysis |
| title_sort | revisiting norm optimization for multi objective black box problems a finite time analysis |
| topic | Engineering::Computer science and engineering Multi-objective Optimization Black-box Optimization |
| url | https://hdl.handle.net/10356/143267 |
| work_keys_str_mv | AT aldujailiabdullah revisitingnormoptimizationformultiobjectiveblackboxproblemsafinitetimeanalysis AT sureshsundaram revisitingnormoptimizationformultiobjectiveblackboxproblemsafinitetimeanalysis |