Optimizing Shortfall Risk Metric for Learning Regression Models
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918054346096640 |
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| author | Ramaswamy, Harish G. Prashanth, L. A. |
| author_facet | Ramaswamy, Harish G. Prashanth, L. A. |
| contents | We consider the problem of estimating and optimizing utility-based shortfall risk (UBSR) of a loss, say $(Y - \hat Y)^2$, in the context of a regression problem. Empirical risk minimization with a UBSR objective is challenging since UBSR is a non-linear function of the underlying distribution. We first derive a concentration bound for UBSR estimation using independent and identically distributed (i.i.d.) samples. We then frame the UBSR optimization problem as minimization of a pseudo-linear function in the space of achievable distributions $\mathcal D$ of the loss $(Y- \hat Y)^2$. We construct a gradient oracle for the UBSR objective and a linear minimization oracle (LMO) for the set $\mathcal D$. Using these oracles, we devise a bisection-type algorithm, and establish convergence to the UBSR-optimal solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_17777 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimizing Shortfall Risk Metric for Learning Regression Models Ramaswamy, Harish G. Prashanth, L. A. Machine Learning We consider the problem of estimating and optimizing utility-based shortfall risk (UBSR) of a loss, say $(Y - \hat Y)^2$, in the context of a regression problem. Empirical risk minimization with a UBSR objective is challenging since UBSR is a non-linear function of the underlying distribution. We first derive a concentration bound for UBSR estimation using independent and identically distributed (i.i.d.) samples. We then frame the UBSR optimization problem as minimization of a pseudo-linear function in the space of achievable distributions $\mathcal D$ of the loss $(Y- \hat Y)^2$. We construct a gradient oracle for the UBSR objective and a linear minimization oracle (LMO) for the set $\mathcal D$. Using these oracles, we devise a bisection-type algorithm, and establish convergence to the UBSR-optimal solution. |
| title | Optimizing Shortfall Risk Metric for Learning Regression Models |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2505.17777 |