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Mathematics > Optimization and Control

arXiv:2305.17498 (math)
[Submitted on 27 May 2023]

Title:A Model-Based Method for Minimizing CVaR and Beyond

Authors:Si Yi Meng, Robert M. Gower
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Abstract:We develop a variant of the stochastic prox-linear method for minimizing the Conditional Value-at-Risk (CVaR) objective. CVaR is a risk measure focused on minimizing worst-case performance, defined as the average of the top quantile of the losses. In machine learning, such a risk measure is useful to train more robust models. Although the stochastic subgradient method (SGM) is a natural choice for minimizing the CVaR objective, we show that our stochastic prox-linear (SPL+) algorithm can better exploit the structure of the objective, while still providing a convenient closed form update. Our SPL+ method also adapts to the scaling of the loss function, which allows for easier tuning. We then specialize a general convergence theorem for SPL+ to our setting, and show that it allows for a wider selection of step sizes compared to SGM. We support this theoretical finding experimentally.
Subjects: Optimization and Control (math.OC); Machine Learning (cs.LG)
Cite as: arXiv:2305.17498 [math.OC]
  (or arXiv:2305.17498v1 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2305.17498

Submission history

From: Si Yi Meng [view email]
[v1] Sat, 27 May 2023 15:38:53 UTC (3,694 KB)
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