# Tropical linear regression and mean payoff games: or, how to measure the distance to equilibria

arXiv: https://arxiv.org/abs/2106.01930 · HTML: https://mlsanity.com/paper/2106.01930/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jun 2021.

## Built on by (most cited first, 1 of 1)

- [Tropical Geometric Tools for Machine Learning: the TML package](https://mlsanity.com/paper/2309.01082/) (2023)

## Abstract (arXiv)

We study a tropical linear regression problem consisting in finding the best approximation of a set of points by a tropical hyperplane. We establish a strong duality theorem, showing that the value of this problem coincides with the maximal radius of a Hilbert's ball included in a tropical polyhedron. We also show that this regression problem is polynomial-time equivalent to mean payoff games. We illustrate our results by solving an inverse problem from auction theory. In this setting, a tropical hyperplane represents the set of equilibrium prices. Tropical linear regression allows us to quantify the distance of a market to the set of equilibria, and infer secret preferences of a decision maker.