# A Model-Based Method for Minimizing CVaR and Beyond

arXiv: https://arxiv.org/abs/2305.17498 · HTML: https://mlsanity.com/paper/2305.17498/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 40 references that are in the map.
- First posted on arXiv 27 May 2023.

## Builds on (most cited first, 16 of 16)

- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [Risk-Constrained Reinforcement Learning with Percentile Risk Criteria](https://mlsanity.com/paper/1512.01629/) (2015)
- [Learning Models with Uniform Performance via Distributionally Robust Optimization](https://mlsanity.com/paper/1810.08750/) (2018)
- [Risk-Sensitive and Robust Decision-Making: a CVaR Optimization Approach](https://mlsanity.com/paper/1506.02188/) (2015)
- [Stochastic model-based minimization of weakly convex functions](https://mlsanity.com/paper/1803.06523/) (2018)
- [Algorithms for CVaR Optimization in MDPs](https://mlsanity.com/paper/1406.3339/) (2014)
- [Fairness risk measures](https://mlsanity.com/paper/1901.08665/) (2019)
- [Stochastic (Approximate) Proximal Point Methods: Convergence, Optimality, and Adaptivity](https://mlsanity.com/paper/1810.05633/) (2018)
- [Stochastic Methods for Composite and Weakly Convex Optimization Problems](https://mlsanity.com/paper/1703.08570/) (2017)
- [Adaptive Sampling for Stochastic Risk-Averse Learning](https://mlsanity.com/paper/1910.12511/) (2019)
- [The importance of better models in stochastic optimization](https://mlsanity.com/paper/1903.08619/) (2019)
- [Minimizing the Maximal Loss: How and Why?](https://mlsanity.com/paper/1602.01690/) (2016)
- [Statistical Learning with Conditional Value at Risk](https://mlsanity.com/paper/2002.05826/) (2020)
- [Cutting Some Slack for SGD with Adaptive Polyak Stepsizes](https://mlsanity.com/paper/2202.12328/) (2022)
- [Risk-Averse Stochastic Convex Bandit](https://mlsanity.com/paper/1810.00737/) (2018)
- [Superquantiles at Work: Machine Learning Applications and Efficient Subgradient Computation](https://mlsanity.com/paper/2201.00508/) (2022)

## Built on by (most cited first, 5 of 5)

- [An Exploration of Non-Euclidean Gradient Descent: Muon and its Many Variants](https://mlsanity.com/paper/2510.09827/) (2025)
- [Function Value Learning: Adaptive Learning Rates Based on the Polyak Stepsize and Function Splitting in ERM](https://mlsanity.com/paper/2307.14528/) (2023)
- [A Near-Optimal Single-Loop Stochastic Algorithm for Convex Finite-Sum Coupled Compositional Optimization](https://mlsanity.com/paper/2312.02277/) (2023)
- [Multi-Group Fairness Evaluation via Conditional Value-at-Risk Testing](https://mlsanity.com/paper/2312.03867/) (2023)
- [On Calibration in Multi-Distribution Learning](https://mlsanity.com/paper/2412.14142/) (2024)

## Abstract (arXiv)

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.