Stochastic Optimization for Spectral Risk Measures

Ronak Mehta; Vincent Roulet; Krishna Pillutla; Lang Liu; Zaid Harchaoui

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arXiv · 2212.05149

Stochastic Optimization for Spectral Risk Measures

Ronak Mehta·Vincent Roulet·Krishna Pillutla·Lang Liu·Zaid Harchaoui

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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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BibTeX RIS

Ronak Mehta, Vincent Roulet, Krishna Pillutla, Lang Liu, Zaid Harchaoui. 2022-12-10. Stochastic Optimization for Spectral Risk Measures. https://arxiv.org/abs/2212.05149

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