# Distributionally Robust Games: f-Divergence and Learning

arXiv: https://arxiv.org/abs/1702.05371 · HTML: https://mlsanity.com/paper/1702.05371/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Feb 2017.

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

- [f-divergences and their applications in lossy compression and bounding generalization error](https://mlsanity.com/paper/2206.11042/) (2022)
- [Neural network algorithm and its application in temperature control of distillation tower](https://mlsanity.com/paper/2101.00582/) (2021)
- [Study on the simulation control of neural network algorithm in thermally coupled distillation](https://mlsanity.com/paper/2102.03506/) (2021)
- [Artificial Neural Network and its Application Research Progress in Distillation](https://mlsanity.com/paper/2110.01449/) (2021)
- [PeTeR: Post-Training Robustification of Probabilistic Circuits](https://mlsanity.com/paper/2607.07671/) (2026)

## Abstract (arXiv)

In this paper we introduce the novel framework of distributionally robust games. These are multi-player games where each player models the state of nature using a worst-case distribution, also called adversarial distribution. Thus each player's payoff depends on the other players' decisions and on the decision of a virtual player (nature) who selects an adversarial distribution of scenarios. This paper provides three main contributions. Firstly, the distributionally robust game is formulated using the statistical notions of f-divergence between two distributions, here represented by the adversarial distribution, and the exact distribution. Secondly, the complexity of the problem is significantly reduced by means of triality theory. Thirdly, stochastic Bregman learning algorithms are proposed to speedup the computation of robust equilibria. Finally, the theoretical findings are illustrated in a convex setting and its limitations are tested with a non-convex non-concave function.