Stochastic Optimization for Spectral Risk Measures

• URL: http://arxiv.org/abs/2212.05149v1
• Date: Sat, 10 Dec 2022 00:03:12 GMT
• Title: Stochastic Optimization for Spectral Risk Measures
• Authors: Ronak Mehta, Vincent Roulet, Krishna Pillutla, Lang Liu, Zaid Harchaoui
• Abstract summary: Spectral risk objectives allow learning systems to interpolate between optimizing average-case performance (as in empirical risk minimization) and worst-case performance on a task. We develop algorithms to optimize these quantities by characterizing their subdifferential and addressing challenges such as biasedness of subgradient estimates and non-smoothness of the objective.
• Score: 5.55979411072702
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Spectral risk objectives - also called $L$-risks - allow for learning systems to interpolate between optimizing average-case performance (as in empirical risk minimization) and worst-case performance on a task. We develop stochastic algorithms to optimize these quantities by characterizing their subdifferential and addressing challenges such as biasedness of subgradient estimates and non-smoothness of the objective. We show theoretically and experimentally that out-of-the-box approaches such as stochastic subgradient and dual averaging are hindered by bias and that our approach outperforms them.

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