# Variance Control for Distributional Reinforcement Learning

arXiv: https://arxiv.org/abs/2307.16152 · HTML: https://mlsanity.com/paper/2307.16152/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 32 references that are in the map.
- First posted on arXiv 30 Jul 2023.

## Builds on (most cited first, 18 of 18)

- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [OpenAI Gym](https://mlsanity.com/paper/1606.01540/) (2016)
- [A Distributional Perspective on Reinforcement Learning](https://mlsanity.com/paper/1707.06887/) (2017)
- [Deep Exploration via Bootstrapped DQN](https://mlsanity.com/paper/1602.04621/) (2016)
- [Distributional Reinforcement Learning with Quantile Regression](https://mlsanity.com/paper/1710.10044/) (2017)
- [Implicit Quantile Networks for Distributional Reinforcement Learning](https://mlsanity.com/paper/1806.06923/) (2018)
- [Count-Based Exploration with Neural Density Models](https://mlsanity.com/paper/1703.01310/) (2017)
- [Controlling Overestimation Bias with Truncated Mixture of Continuous Distributional Quantile Critics](https://mlsanity.com/paper/2005.04269/) (2020)
- [Averaged-DQN: Variance Reduction and Stabilization for Deep Reinforcement Learning](https://mlsanity.com/paper/1611.01929/) (2016)
- [Fully Parameterized Quantile Function for Distributional Reinforcement Learning](https://mlsanity.com/paper/1911.02140/) (2019)
- [An Analysis of Categorical Distributional Reinforcement Learning](https://mlsanity.com/paper/1802.08163/) (2018)
- [Statistics and Samples in Distributional Reinforcement Learning](https://mlsanity.com/paper/1902.08102/) (2019)
- [Distributional Reinforcement Learning for Efficient Exploration](https://mlsanity.com/paper/1905.06125/) (2019)
- [A Comparative Analysis of Expected and Distributional Reinforcement Learning](https://mlsanity.com/paper/1901.11084/) (2019)
- [An Analysis of Quantile Temporal-Difference Learning](https://mlsanity.com/paper/2301.04462/) (2023)
- [Non-decreasing Quantile Function Network with Efficient Exploration for Distributional Reinforcement Learning](https://mlsanity.com/paper/2105.06696/) (2021)
- [The Statistical Benefits of Quantile Temporal-Difference Learning for Value Estimation](https://mlsanity.com/paper/2305.18388/) (2023)
- [Quantiled conditional variance, skewness, and kurtosis by Cornish-Fisher expansion](https://mlsanity.com/paper/2302.06799/) (2023)

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

- [MAD-TD: Model-Augmented Data stabilizes High Update Ratio RL](https://mlsanity.com/paper/2410.08896/) (2024)
- [Absolute Policy Optimization](https://mlsanity.com/paper/2310.13230/) (2023)

## Abstract (arXiv)

Although distributional reinforcement learning (DRL) has been widely examined in the past few years, very few studies investigate the validity of the obtained Q-function estimator in the distributional setting. To fully understand how the approximation errors of the Q-function affect the whole training process, we do some error analysis and theoretically show how to reduce both the bias and the variance of the error terms. With this new understanding, we construct a new estimator Quantiled Expansion Mean (QEM) and introduce a new DRL algorithm (QEMRL) from the statistical perspective. We extensively evaluate our QEMRL algorithm on a variety of Atari and Mujoco benchmark tasks and demonstrate that QEMRL achieves significant improvement over baseline algorithms in terms of sample efficiency and convergence performance.