# Reinforcement Learning with Wasserstein Distance Regularisation, with Applications to Multipolicy Learning

arXiv: https://arxiv.org/abs/1802.03976 · HTML: https://mlsanity.com/paper/1802.03976/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Feb 2018.

## Built on by (most cited first, 3 of 3)

- [Primal Wasserstein Imitation Learning](https://mlsanity.com/paper/2006.04678/) (2020)
- [Wasserstein Unsupervised Reinforcement Learning](https://mlsanity.com/paper/2110.07940/) (2021)
- [Wasserstein Adaptive Value Estimation for Actor-Critic Reinforcement Learning](https://mlsanity.com/paper/2501.10605/) (2025)

## Abstract (arXiv)

We describe an application of Wasserstein distance to Reinforcement Learning. The Wasserstein distance in question is between the distribution of mappings of trajectories of a policy into some metric space, and some other fixed distribution (which may, for example, come from another policy). Different policies induce different distributions, so given an underlying metric, the Wasserstein distance quantifies how different policies are. This can be used to learn multiple polices which are different in terms of such Wasserstein distances by using a Wasserstein regulariser. Changing the sign of the regularisation parameter, one can learn a policy for which its trajectory mapping distribution is attracted to a given fixed distribution.