# On Policy Evaluation Algorithms in Distributional Reinforcement Learning

arXiv: https://arxiv.org/abs/2407.14175 · HTML: https://mlsanity.com/paper/2407.14175/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods.
- Builds on 5 of its 23 references that are in the map.
- First posted on arXiv 19 Jul 2024.

## Placed in

- Deep reinforcement learning methods / [RL theory and sample complexity](https://mlsanity.com/deeprl/rl-theory-and-sample-complexity/)

## Builds on (most cited first, 5 of 5)

- [Distributional Reinforcement Learning with Quantile Regression](https://mlsanity.com/paper/1710.10044/) (2017)
- [Recent Advances in Reinforcement Learning in Finance](https://mlsanity.com/paper/2112.04553/) (2021)
- [An Analysis of Categorical Distributional Reinforcement Learning](https://mlsanity.com/paper/1802.08163/) (2018)
- [Particle Value Functions](https://mlsanity.com/paper/1703.05820/) (2017)
- [On solutions of the distributional Bellman equation](https://mlsanity.com/paper/2202.00081/) (2022)

## Abstract (arXiv)

We introduce a novel class of algorithms to efficiently approximate the unknown return distributions in policy evaluation problems from distributional reinforcement learning (DRL). The proposed distributional dynamic programming algorithms are suitable for underlying Markov decision processes (MDPs) having an arbitrary probabilistic reward mechanism, including continuous reward distributions with unbounded support being potentially heavy-tailed. For a plain instance of our proposed class of algorithms we prove error bounds, both within Wasserstein and Kolmogorov--Smirnov distances. Furthermore, for return distributions having probability density functions the algorithms yield approximations for these densities; error bounds are given within supremum norm. We introduce the concept of quantile-spline discretizations to come up with algorithms showing promising results in simulation experiments. While the performance of our algorithms can rigorously be analysed they can be seen as universal black box algorithms applicable to a large class of MDPs. We also derive new properties of probability metrics commonly used in DRL on which our quantitative analysis is based.