Year: 2025
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Ramaswamy, Harish G., Prashanth, L. A.
Institution: Indian Institute of Technology Madras
Language: English
Field: Decision Sciences
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W6947953032
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