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.
@article{arxiv.2212.05149,
title = {Stochastic Optimization for Spectral Risk Measures},
author = {Ronak Mehta and Vincent Roulet and Krishna Pillutla and Lang Liu and Zaid Harchaoui},
journal= {arXiv preprint arXiv:2212.05149},
year = {2022}
}