# A Cantor-Kantorovich Metric Between Markov Decision Processes with Application to Transfer Learning

arXiv: https://arxiv.org/abs/2407.08324 · HTML: https://mlsanity.com/paper/2407.08324/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 17 references that are in the map.
- First posted on arXiv 11 Jul 2024.

## Builds on (most cited first, 8 of 8)

- [Transfer Learning in Deep Reinforcement Learning: A Survey](https://mlsanity.com/paper/2009.07888/) (2020)
- [Reinforcement learning](https://mlsanity.com/paper/2405.10369/) (2024)
- [Quantifying Differences in Reward Functions](https://mlsanity.com/paper/2006.13900/) (2020)
- [REPAINT: Knowledge Transfer in Deep Reinforcement Learning](https://mlsanity.com/paper/2011.11827/) (2020)
- [On Computing the Total Variation Distance of Hidden Markov Models](https://mlsanity.com/paper/1804.06170/) (2018)
- [Target Transfer Q-Learning and Its Convergence Analysis](https://mlsanity.com/paper/1809.08923/) (2018)
- [On the Total Variation Distance of Labelled Markov Chains](https://mlsanity.com/paper/1405.2852/) (2014)
- [Data-driven abstractions via adaptive refinements and a Kantorovich metric [extended version]](https://mlsanity.com/paper/2303.17618/) (2023)

## Abstract (arXiv)

We extend the notion of Cantor-Kantorovich distance between Markov chains introduced by (Banse et al., 2023) in the context of Markov Decision Processes (MDPs). The proposed metric is well-defined and can be efficiently approximated given a finite horizon. Then, we provide numerical evidences that the latter metric can lead to interesting applications in the field of reinforcement learning. In particular, we show that it could be used for forecasting the performance of transfer learning algorithms.