# Conjugated Discrete Distributions for Distributional Reinforcement Learning

arXiv: https://arxiv.org/abs/2112.07424 · HTML: https://mlsanity.com/paper/2112.07424/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 26 references that are in the map.
- First posted on arXiv 14 Dec 2021.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model](https://mlsanity.com/paper/1911.08265/) (2019)
- [Deep Reinforcement Learning at the Edge of the Statistical Precipice](https://mlsanity.com/paper/2108.13264/) (2021)
- [Rainbow: Combining Improvements in Deep Reinforcement Learning](https://mlsanity.com/paper/1710.02298/) (2017)
- [A Distributional Perspective on Reinforcement Learning](https://mlsanity.com/paper/1707.06887/) (2017)
- [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)
- [Agent57: Outperforming the Atari Human Benchmark](https://mlsanity.com/paper/2003.13350/) (2020)
- [Revisiting the Arcade Learning Environment: Evaluation Protocols and Open Problems for General Agents](https://mlsanity.com/paper/1709.06009/) (2017)
- [Dopamine: A Research Framework for Deep Reinforcement Learning](https://mlsanity.com/paper/1812.06110/) (2018)
- [The Cramer Distance as a Solution to Biased Wasserstein Gradients](https://mlsanity.com/paper/1705.10743/) (2017)
- [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)
- [A Comparative Analysis of Expected and Distributional Reinforcement Learning](https://mlsanity.com/paper/1901.11084/) (2019)
- [Observe and Look Further: Achieving Consistent Performance on Atari](https://mlsanity.com/paper/1805.11593/) (2018)
- [Distributional reinforcement learning with linear function approximation](https://mlsanity.com/paper/1902.03149/) (2019)
- [General non-linear Bellman equations](https://mlsanity.com/paper/1907.03687/) (2019)

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

- [Atari-5: Distilling the Arcade Learning Environment down to Five Games](https://mlsanity.com/paper/2210.02019/) (2022)
- [PACER: A Fully Push-forward-based Distributional Reinforcement Learning Algorithm](https://mlsanity.com/paper/2306.06637/) (2023)

## Abstract (arXiv)

In this work we continue to build upon recent advances in reinforcement learning for finite Markov processes. A common approach among previous existing algorithms, both single-actor and distributed, is to either clip rewards or to apply a transformation method on Q-functions to handle a large variety of magnitudes in real discounted returns. We theoretically show that one of the most successful methods may not yield an optimal policy if we have a non-deterministic process. As a solution, we argue that distributional reinforcement learning lends itself to remedy this situation completely. By the introduction of a conjugated distributional operator we may handle a large class of transformations for real returns with guaranteed theoretical convergence. We propose an approximating single-actor algorithm based on this operator that trains agents directly on unaltered rewards using a proper distributional metric given by the Cram'er distance. To evaluate its performance in a stochastic setting we train agents on a suite of 55 Atari 2600 games using sticky-actions and obtain state-of-the-art performance compared to other well-known algorithms in the Dopamine framework.