A kernel-based stochastic approximation framework for contextual optimization
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916041877094400 |
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| author | Cao, Hao Hu, Jian-Qiang Hu, Jiaqiao |
| author_facet | Cao, Hao Hu, Jian-Qiang Hu, Jiaqiao |
| contents | We present a kernel-based stochastic approximation (KBSA) framework for solving contextual stochastic optimization problems with differentiable objective functions. The framework only relies on system output estimates and can be applied to address a large class of contextual measures, including conditional expectations, conditional quantiles, CoVaR, and conditional expected shortfalls.Under appropriate conditions, we show the strong convergence of KBSA and characterize its finite-time performance in terms of bounds on the mean squared errors of the sequences of iterates produced. In addition, we discuss variants of the framework, including a version based on high-order kernels for further enhancing the convergence rate of the method and an extension of KBSA for handling contextual measures involving multiple conditioning events.Simulation experiments are also carried out to illustrate the framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_24033 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A kernel-based stochastic approximation framework for contextual optimization Cao, Hao Hu, Jian-Qiang Hu, Jiaqiao Optimization and Control We present a kernel-based stochastic approximation (KBSA) framework for solving contextual stochastic optimization problems with differentiable objective functions. The framework only relies on system output estimates and can be applied to address a large class of contextual measures, including conditional expectations, conditional quantiles, CoVaR, and conditional expected shortfalls.Under appropriate conditions, we show the strong convergence of KBSA and characterize its finite-time performance in terms of bounds on the mean squared errors of the sequences of iterates produced. In addition, we discuss variants of the framework, including a version based on high-order kernels for further enhancing the convergence rate of the method and an extension of KBSA for handling contextual measures involving multiple conditioning events.Simulation experiments are also carried out to illustrate the framework. |
| title | A kernel-based stochastic approximation framework for contextual optimization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2510.24033 |