Optimizing Shortfall Risk Metric for Learning Regression Models

• URL: http://arxiv.org/abs/2505.17777v3
• Date: Wed, 11 Jun 2025 12:47:35 GMT
• Title: Optimizing Shortfall Risk Metric for Learning Regression Models
• Authors: Harish G. Ramaswamy, L. A. Prashanth,
• Abstract summary: Empirical risk minimization with a UBSR objective is challenging since UBSR is a non-linear function of the underlying distribution.<n>We devise a bisection-type algorithm, and establish convergence to the UBSR-optimal solution.
• Score: 0.6445605125467572
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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