A Model-Based Method for Minimizing CVaR and Beyond

Si Yi Meng, Robert M. Gower
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:24436-24456, 2023.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-meng23a, title = {A Model-Based Method for Minimizing {CV}a{R} and Beyond}, author = {Meng, Si Yi and Gower, Robert M.}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {24436--24456}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/meng23a/meng23a.pdf}, url = {https://proceedings.mlr.press/v202/meng23a.html}, 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.} }
Endnote
%0 Conference Paper %T A Model-Based Method for Minimizing CVaR and Beyond %A Si Yi Meng %A Robert M. Gower %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-meng23a %I PMLR %P 24436--24456 %U https://proceedings.mlr.press/v202/meng23a.html %V 202 %X 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.
APA
Meng, S.Y. & Gower, R.M.. (2023). A Model-Based Method for Minimizing CVaR and Beyond. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:24436-24456 Available from https://proceedings.mlr.press/v202/meng23a.html.

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