# Diametrical Risk Minimization: Theory and Computations

arXiv: https://arxiv.org/abs/1910.10844 · HTML: https://mlsanity.com/paper/1910.10844/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Oct 2019.

## Built on by (most cited first, 15 of 15)

- [SWAD: Domain Generalization by Seeking Flat Minima](https://mlsanity.com/paper/2102.08604/) (2021)
- [Same Pre-training Loss, Better Downstream: Implicit Bias Matters for Language Models](https://mlsanity.com/paper/2210.14199/) (2022)
- [Sharpness Minimization Algorithms Do Not Only Minimize Sharpness To Achieve Better Generalization](https://mlsanity.com/paper/2307.11007/) (2023)
- [Flat minima generalize for low-rank matrix recovery](https://mlsanity.com/paper/2203.03756/) (2022)
- [Formalizing Generalization and Robustness of Neural Networks to Weight Perturbations](https://mlsanity.com/paper/2103.02200/) (2021)
- [How to escape sharp minima with random perturbations](https://mlsanity.com/paper/2305.15659/) (2023)
- [Domain-Inspired Sharpness-Aware Minimization Under Domain Shifts](https://mlsanity.com/paper/2405.18861/) (2024)
- [The Inductive Bias of Flatness Regularization for Deep Matrix Factorization](https://mlsanity.com/paper/2306.13239/) (2023)
- [Identity Curvature Laplace Approximation for Improved Out-of-Distribution Detection](https://mlsanity.com/paper/2312.10464/) (2023)
- [Simplicity Bias via Global Convergence of Sharpness Minimization](https://mlsanity.com/paper/2410.16401/) (2024)
- [Flat Minima and Generalization: Insights from Stochastic Convex Optimization](https://mlsanity.com/paper/2511.03548/) (2025)
- [Rockafellian Relaxation and Stochastic Optimization under Perturbations](https://mlsanity.com/paper/2204.04762/) (2022)
- [Membership Privacy Risks of Sharpness Aware Minimization](https://mlsanity.com/paper/2310.00488/) (2023)
- [On Robustness in Nonconvex Optimization with Application to Defense Planning](https://mlsanity.com/paper/2208.09725/) (2022)
- [Revisiting Video Quality Assessment from the Perspective of Generalization](https://mlsanity.com/paper/2409.14847/) (2024)

## Abstract (arXiv)

The theoretical and empirical performance of Empirical Risk Minimization (ERM) often suffers when loss functions are poorly behaved with large Lipschitz moduli and spurious sharp minimizers. We propose and analyze a counterpart to ERM called Diametrical Risk Minimization (DRM), which accounts for worst-case empirical risks within neighborhoods in parameter space. DRM has generalization bounds that are independent of Lipschitz moduli for convex as well as nonconvex problems and it can be implemented using a practical algorithm based on stochastic gradient descent. Numerical results illustrate the ability of DRM to find quality solutions with low generalization error in sharp empirical risk landscapes from benchmark neural network classification problems with corrupted labels.