提出优化回归模型风险的新方法，提升对极端损失的控制能力。
Optimizing Shortfall Risk Metric for Learning Regression Models
- 将非线性风险度量转化为可优化的伪线性形式
- 构建梯度与线性最小化算子，实现收敛优化
- 适合关注鲁棒回归和风险敏感建模的研究者
本文研究回归问题中基于效用的短缺风险（UBSR）的估计与优化，针对损失函数 $(Y - ilde Y)^2$ 展开。由于UBSR是非线性函数，基于经验风险最小化的优化面临挑战。首先，我们基于独立同分布（i.i.d.）样本推导出UBSR估计的集中界。随后，将UBSR优化问题转化为在损失分布可达集 $\ extcal{D}$ 上对伪线性函数的最小化。我们构造了UBSR目标的梯度代理和集合 $\ extcal{D}$ 的线性最小化算子（LMO），并设计一种分治型算法，证明其能收敛至最优解。
原文摘要 · Abstract (English)
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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