Pseudoconvex Problems in Operational Decision Systems: Algorithms for Joint Learning and Optimization
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917401769017344 |
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| author | Li, Zijun Kannan, Aswin |
| author_facet | Li, Zijun Kannan, Aswin |
| contents | We consider joint optimization and learning problems arising in real-time decision systems. While most existing work focuses primarily on convex, revenue-based objectives, we extend this line of research to multi-objective formulations. In energy systems, for instance, we incorporate metrics such as renewable penetration and generation costs. Our key focus, however, is on a class of problems with a pseudoconvex structure - a natural relaxation of convexity. Representative examples include fractional objectives in energy management and logit-based revenue models in retail. The outer-level problem optimizes these pseudoconvex objectives, while the inner-level problem involves training a machine learning model using historical data. Our contributions are twofold. First, we propose a simultaneous learning-and-optimization framework that iteratively updates both inner- and outer-level variables. Second, we develop convergent algorithms for these problem classes under realistic mathematical assumptions. Using real-world datasets, we evaluate the computational performance of our methods and highlight an important observation: there exist clear trade-offs between inexact learning and computational time when assessing final solution quality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_10778 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Pseudoconvex Problems in Operational Decision Systems: Algorithms for Joint Learning and Optimization Li, Zijun Kannan, Aswin Optimization and Control 90C26, 90C30, 49M27 F.2.1; G.1.6; I.2.6 We consider joint optimization and learning problems arising in real-time decision systems. While most existing work focuses primarily on convex, revenue-based objectives, we extend this line of research to multi-objective formulations. In energy systems, for instance, we incorporate metrics such as renewable penetration and generation costs. Our key focus, however, is on a class of problems with a pseudoconvex structure - a natural relaxation of convexity. Representative examples include fractional objectives in energy management and logit-based revenue models in retail. The outer-level problem optimizes these pseudoconvex objectives, while the inner-level problem involves training a machine learning model using historical data. Our contributions are twofold. First, we propose a simultaneous learning-and-optimization framework that iteratively updates both inner- and outer-level variables. Second, we develop convergent algorithms for these problem classes under realistic mathematical assumptions. Using real-world datasets, we evaluate the computational performance of our methods and highlight an important observation: there exist clear trade-offs between inexact learning and computational time when assessing final solution quality. |
| title | Pseudoconvex Problems in Operational Decision Systems: Algorithms for Joint Learning and Optimization |
| topic | Optimization and Control 90C26, 90C30, 49M27 F.2.1; G.1.6; I.2.6 |
| url | https://arxiv.org/abs/2604.10778 |