# Modeling the Second Player in Distributionally Robust Optimization

arXiv: https://arxiv.org/abs/2103.10282 · HTML: https://mlsanity.com/paper/2103.10282/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 47 references that are in the map.
- First posted on arXiv 18 Mar 2021.

## Builds on (most cited first, 21 of 21)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Don't Stop Pretraining: Adapt Language Models to Domains and Tasks](https://mlsanity.com/paper/2004.10964/) (2020)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [Automated Hate Speech Detection and the Problem of Offensive Language](https://mlsanity.com/paper/1703.04009/) (2017)
- [Deep Speech 2: End-to-End Speech Recognition in English and Mandarin](https://mlsanity.com/paper/1512.02595/) (2015)
- [Certifying Some Distributional Robustness with Principled Adversarial Training](https://mlsanity.com/paper/1710.10571/) (2017)
- [Learning Models with Uniform Performance via Distributionally Robust Optimization](https://mlsanity.com/paper/1810.08750/) (2018)
- [Large Scale Crowdsourcing and Characterization of Twitter Abusive Behavior](https://mlsanity.com/paper/1802.00393/) (2018)
- [Demographic Dialectal Variation in Social Media: A Case Study of African-American English](https://mlsanity.com/paper/1608.08868/) (2016)
- [Statistics of Robust Optimization: A Generalized Empirical Likelihood Approach](https://mlsanity.com/paper/1610.03425/) (2016)
- [Distributionally Robust Language Modeling](https://mlsanity.com/paper/1909.02060/) (2019)
- [The Mechanics of n-Player Differentiable Games](https://mlsanity.com/paper/1802.05642/) (2018)
- [Towards Debiasing NLU Models from Unknown Biases](https://mlsanity.com/paper/2009.12303/) (2020)
- [Reward Augmented Maximum Likelihood for Neural Structured Prediction](https://mlsanity.com/paper/1609.00150/) (2016)
- [Demoting Racial Bias in Hate Speech Detection](https://mlsanity.com/paper/2005.12246/) (2020)
- [Distributionally Robust Counterfactual Risk Minimization](https://mlsanity.com/paper/1906.06211/) (2019)
- [Nash Convergence of Gradient Dynamics in Iterated General-Sum Games](https://mlsanity.com/paper/1301.3892/) (2013)
- [Distributional Robustness with IPMs and links to Regularization and GANs](https://mlsanity.com/paper/2006.04349/) (2020)
- [Robust Bayesian Classification Using an Optimistic Score Ratio](https://mlsanity.com/paper/2007.04458/) (2020)

## Built on by (most cited first, 29 of 29)

- [Examining and Combating Spurious Features under Distribution Shift](https://mlsanity.com/paper/2106.07171/) (2021)
- [DORO: Distributional and Outlier Robust Optimization](https://mlsanity.com/paper/2106.06142/) (2021)
- [Towards Robust Alignment of Language Models: Distributionally Robustifying Direct Preference Optimization](https://mlsanity.com/paper/2407.07880/) (2024)
- [Learning to Augment Distributions for Out-of-Distribution Detection](https://mlsanity.com/paper/2311.01796/) (2023)
- [UMIX: Improving Importance Weighting for Subpopulation Shift via Uncertainty-Aware Mixup](https://mlsanity.com/paper/2209.08928/) (2022)
- [Understanding Contrastive Learning via Distributionally Robust Optimization](https://mlsanity.com/paper/2310.11048/) (2023)
- [Adaptive Preference Scaling for Reinforcement Learning with Human Feedback](https://mlsanity.com/paper/2406.02764/) (2024)
- [Distributionally Robust Models with Parametric Likelihood Ratios](https://mlsanity.com/paper/2204.06340/) (2022)
- [Domain-Specific Risk Minimization for Out-of-Distribution Generalization](https://mlsanity.com/paper/2208.08661/) (2022)
- [Boosted CVaR Classification](https://mlsanity.com/paper/2110.13948/) (2021)
- [Moderately Distributional Exploration for Domain Generalization](https://mlsanity.com/paper/2304.13976/) (2023)
- [Diffusion Theory as a Scalpel: Detecting and Purifying Poisonous Dimensions in Pre-trained Language Models Caused by Backdoor or Bias](https://mlsanity.com/paper/2305.04547/) (2023)
- [Prompt Disentanglement via Language Guidance and Representation Alignment for Domain Generalization](https://mlsanity.com/paper/2507.02288/) (2025)
- [Worst-case generation via minimax optimization in Wasserstein space](https://mlsanity.com/paper/2512.08176/) (2025)
- [A Tale of Two Models: Constructing Evasive Attacks on Edge Models](https://mlsanity.com/paper/2204.10933/) (2022)
- [A survey of Identification and mitigation of Machine Learning algorithmic biases in Image Analysis](https://mlsanity.com/paper/2210.04491/) (2022)
- [Decision Making under the Exponential Family: Distributionally Robust Optimisation with Bayesian Ambiguity Sets](https://mlsanity.com/paper/2411.16829/) (2024)
- [Distributionally Robust Optimization via Generative Ambiguity Modeling](https://mlsanity.com/paper/2602.08976/) (2026)
- [Reweighted Mixup for Subpopulation Shift](https://mlsanity.com/paper/2304.04148/) (2023)
- [Class-attribute Priors: Adapting Optimization to Heterogeneity and Fairness Objective](https://mlsanity.com/paper/2401.14343/) (2024)
- [Decision Making under Model Misspecification: DRO with Robust Bayesian Ambiguity Sets](https://mlsanity.com/paper/2505.03585/) (2025)
- [Out-of-Distribution Generalization in Text Classification: Past, Present, and Future](https://mlsanity.com/paper/2305.14104/) (2023)
- [Distributionally Robust Optimisation with Bayesian Ambiguity Sets](https://mlsanity.com/paper/2409.03492/) (2024)
- [Learning Neural Models for Natural Language Processing in the Face of Distributional Shift](https://mlsanity.com/paper/2109.01558/) (2021)
- [Imagine Beyond! Distributionally Robust Auto-Encoding for State Space Coverage in Online Reinforcement Learning](https://mlsanity.com/paper/2505.17830/) (2025)
- [Adaptive Sample-Level Framework Motivated by Distributionally Robust Optimization with Variance-Based Radius Assignment for Enhanced Neural Network Generalization Under Distribution Shift](https://mlsanity.com/paper/2511.05568/) (2025)
- [3D-Learning: Diffusion-Augmented Distributionally Robust Decision-Focused Learning](https://mlsanity.com/paper/2602.02943/) (2026)
- [Sampler-Robust Optimization under Generative Models](https://mlsanity.com/paper/2604.27447/) (2026)
- [Generative Distributionally Robust Optimization](https://mlsanity.com/paper/2607.24983/) (2026)

## Abstract (arXiv)

Distributionally robust optimization (DRO) provides a framework for training machine learning models that are able to perform well on a collection of related data distributions (the "uncertainty set"). This is done by solving a min-max game: the model is trained to minimize its maximum expected loss among all distributions in the uncertainty set. While careful design of the uncertainty set is critical to the success of the DRO procedure, previous work has been limited to relatively simple alternatives that keep the min-max optimization problem exactly tractable, such as f-divergence balls. In this paper, we argue instead for the use of neural generative models to characterize the worst-case distribution, allowing for more flexible and problem-specific selection of the uncertainty set. However, while simple conceptually, this approach poses a number of implementation and optimization challenges. To circumvent these issues, we propose a relaxation of the KL-constrained inner maximization objective that makes the DRO problem more amenable to gradient-based optimization of large scale generative models, and develop model selection heuristics to guide hyper-parameter search. On both toy settings and realistic NLP tasks, we find that the proposed approach yields models that are more robust than comparable baselines.