Optimizing Shortfall Risk Metric for Learning Regression Models
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Abstract (arXiv)
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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References · 8
- 2017Learning with Average Top-k Losscited by 52
- 2020Learning Bounds for Risk-sensitive Learningcited by 33
- 2019A Wasserstein distance approach for concentration of empirical risk estimatescited by 18
- 2022Consistent Multiclass Algorithms for Complex Metrics and Constraintscited by 13
- 2022Risk Measures and Upper Probabilities: Coherence and Stratificationcited by 9
- 2021Spectral risk-based learning using unbounded lossescited by 8
- 2022Stochastic Optimization for Spectral Risk Measurescited by 7
- 2021Online Estimation and Optimization of Utility-Based Shortfall Riskcited by 5
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