Stratified adaptive sampling for derivative-free stochastic trust-region optimization
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866911558626443264 |
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| author | Amici, Giovanni Shashaani, Sara Jain, Pranav |
| author_facet | Amici, Giovanni Shashaani, Sara Jain, Pranav |
| contents | There is emerging evidence that trust-region (TR) algorithms are very effective at solving derivative-free nonconvex stochastic optimization problems in which the objective function is a Monte Carlo (MC) estimate. A recent strand of methodologies adaptively adjusts the sample size of the MC estimates by keeping the estimation error below a measure of stationarity induced from the TR radius. In this work we explore stratified adaptive sampling strategies to equip the TR framework with accurate estimates of the objective function, thus optimizing the required number of MC samples to reach a given ε-accuracy of the solution. We prove a reduced sample complexity, confirm a superior efficiency via numerical tests and applications, and explore inexpensive implementations in high dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_00178 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stratified adaptive sampling for derivative-free stochastic trust-region optimization Amici, Giovanni Shashaani, Sara Jain, Pranav Optimization and Control Mathematical Finance There is emerging evidence that trust-region (TR) algorithms are very effective at solving derivative-free nonconvex stochastic optimization problems in which the objective function is a Monte Carlo (MC) estimate. A recent strand of methodologies adaptively adjusts the sample size of the MC estimates by keeping the estimation error below a measure of stationarity induced from the TR radius. In this work we explore stratified adaptive sampling strategies to equip the TR framework with accurate estimates of the objective function, thus optimizing the required number of MC samples to reach a given ε-accuracy of the solution. We prove a reduced sample complexity, confirm a superior efficiency via numerical tests and applications, and explore inexpensive implementations in high dimension. |
| title | Stratified adaptive sampling for derivative-free stochastic trust-region optimization |
| topic | Optimization and Control Mathematical Finance |
| url | https://arxiv.org/abs/2604.00178 |