# Reversible Markov decision processes and the Gaussian free field

arXiv: https://arxiv.org/abs/2207.05217 · HTML: https://mlsanity.com/paper/2207.05217/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jul 2022.

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

- [Optimizing Predictive Maintenance in Intelligent Manufacturing: An Integrated FNO-DAE-GNN-PPO MDP Framework](https://mlsanity.com/paper/2511.05594/) (2025)

## Abstract (arXiv)

A Markov decision problem is called reversible if the stationary controlled Markov chain is reversible under every stationary Markovian strategy. A natural application in which such problems arise is in the control of Metropolis-Hastings type dynamics. We characterize all discrete time reversible Markov decision processes with finite state and actions spaces. We show that policy iteration algorithm for finding an optimal policy can be significantly simplified Markov decision problems of this type. We also highlight the relation between the finite time evolution of the accrual of reward and the Gaussian free field associated to the controlled Markov chain.