# Distributional Reinforcement Learning with Quantile Regression

arXiv: https://arxiv.org/abs/1710.10044 · HTML: https://mlsanity.com/paper/1710.10044/

## Key facts

- Cited by 474 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Oct 2017.

## Built on by (most cited first, 30 of 474)

- [Conservative Q-Learning for Offline Reinforcement Learning](https://mlsanity.com/paper/2006.04779/) (2020)
- [Decision Transformer: Reinforcement Learning via Sequence Modeling](https://mlsanity.com/paper/2106.01345/) (2021)
- [Offline Reinforcement Learning with Implicit Q-Learning](https://mlsanity.com/paper/2110.06169/) (2021)
- [Deep Reinforcement Learning at the Edge of the Statistical Precipice](https://mlsanity.com/paper/2108.13264/) (2021)
- [IDQL: Implicit Q-Learning as an Actor-Critic Method with Diffusion Policies](https://mlsanity.com/paper/2304.10573/) (2023)
- [Reward learning from human preferences and demonstrations in Atari](https://mlsanity.com/paper/1811.06521/) (2018)
- [Uncertainty Weighted Actor-Critic for Offline Reinforcement Learning](https://mlsanity.com/paper/2105.08140/) (2021)
- [Understanding and Preventing Capacity Loss in Reinforcement Learning](https://mlsanity.com/paper/2204.09560/) (2022)
- [Benchmarking Batch Deep Reinforcement Learning Algorithms](https://mlsanity.com/paper/1910.01708/) (2019)
- [Generalized Decision Transformer for Offline Hindsight Information Matching](https://mlsanity.com/paper/2111.10364/) (2021)
- [Online and Offline Reinforcement Learning by Planning with a Learned Model](https://mlsanity.com/paper/2104.06294/) (2021)
- [d3rlpy: An Offline Deep Reinforcement Learning Library](https://mlsanity.com/paper/2111.03788/) (2021)
- [A Survey on Uncertainty Quantification Methods for Deep Learning](https://mlsanity.com/paper/2302.13425/) (2023)
- [Conservative Offline Distributional Reinforcement Learning](https://mlsanity.com/paper/2107.06106/) (2021)
- [BOND: Aligning LLMs with Best-of-N Distillation](https://mlsanity.com/paper/2407.14622/) (2024)
- [SimBa: Simplicity Bias for Scaling Up Parameters in Deep Reinforcement Learning](https://mlsanity.com/paper/2410.09754/) (2024)
- [Recent Advances in Optimal Transport for Machine Learning](https://mlsanity.com/paper/2306.16156/) (2023)
- [Reincarnating Reinforcement Learning: Reusing Prior Computation to Accelerate Progress](https://mlsanity.com/paper/2206.01626/) (2022)
- [A Survey of Deep RL and IL for Autonomous Driving Policy Learning](https://mlsanity.com/paper/2101.01993/) (2021)
- [Quantile Regression for Distributional Reward Models in RLHF](https://mlsanity.com/paper/2409.10164/) (2024)
- [Exploration in Deep Reinforcement Learning: From Single-Agent to Multiagent Domain](https://mlsanity.com/paper/2109.06668/) (2021)
- [On The Effect of Auxiliary Tasks on Representation Dynamics](https://mlsanity.com/paper/2102.13089/) (2021)
- [Tactical Optimism and Pessimism for Deep Reinforcement Learning](https://mlsanity.com/paper/2102.03765/) (2021)
- [A Survey on Quantum Reinforcement Learning](https://mlsanity.com/paper/2211.03464/) (2022)
- [The Difficulty of Passive Learning in Deep Reinforcement Learning](https://mlsanity.com/paper/2110.14020/) (2021)
- [Invariance in Policy Optimisation and Partial Identifiability in Reward Learning](https://mlsanity.com/paper/2203.07475/) (2022)
- [Universal Off-Policy Evaluation](https://mlsanity.com/paper/2104.12820/) (2021)
- [MICo: Improved representations via sampling-based state similarity for Markov decision processes](https://mlsanity.com/paper/2106.08229/) (2021)
- [Exponential Bellman Equation and Improved Regret Bounds for Risk-Sensitive Reinforcement Learning](https://mlsanity.com/paper/2111.03947/) (2021)
- [Efficient Risk-Averse Reinforcement Learning](https://mlsanity.com/paper/2205.05138/) (2022)

## Abstract (arXiv)

In reinforcement learning an agent interacts with the environment by taking actions and observing the next state and reward. When sampled probabilistically, these state transitions, rewards, and actions can all induce randomness in the observed long-term return. Traditionally, reinforcement learning algorithms average over this randomness to estimate the value function. In this paper, we build on recent work advocating a distributional approach to reinforcement learning in which the distribution over returns is modeled explicitly instead of only estimating the mean. That is, we examine methods of learning the value distribution instead of the value function. We give results that close a number of gaps between the theoretical and algorithmic results given by Bellemare, Dabney, and Munos (2017). First, we extend existing results to the approximate distribution setting. Second, we present a novel distributional reinforcement learning algorithm consistent with our theoretical formulation. Finally, we evaluate this new algorithm on the Atari 2600 games, observing that it significantly outperforms many of the recent improvements on DQN, including the related distributional algorithm C51.