# Approximate Solutions to a Class of Reachability Games

arXiv: https://arxiv.org/abs/2011.00601 · HTML: https://mlsanity.com/paper/2011.00601/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Nov 2020.

## Built on by (most cited first, 2 of 2)

- [The Safety Filter: A Unified View of Safety-Critical Control in Autonomous Systems](https://mlsanity.com/paper/2309.05837/) (2023)
- [Fail-Safe Adversarial Generative Imitation Learning](https://mlsanity.com/paper/2203.01696/) (2022)

## Abstract (arXiv)

In this paper, we present a method for finding approximate Nash equilibria in a broad class of reachability games. These games are often used to formulate both collision avoidance and goal satisfaction. Our method is computationally efficient, running in real-time for scenarios involving multiple players and more than ten state dimensions. The proposed approach forms a family of increasingly exact approximations to the original game. Our results characterize the quality of these approximations and show operation in a receding horizon, minimally-invasive control context. Additionally, as a special case, our method reduces to local gradient-based optimization in the single-player (optimal control) setting, for which a wide variety of efficient algorithms exist.