# Safe Distributional Reinforcement Learning

arXiv: https://arxiv.org/abs/2102.13446 · HTML: https://mlsanity.com/paper/2102.13446/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 40 references that are in the map.
- First posted on arXiv 26 Feb 2021.

## Builds on (most cited first, 22 of 22)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Constrained Policy Optimization](https://mlsanity.com/paper/1705.10528/) (2017)
- [A Distributional Perspective on Reinforcement Learning](https://mlsanity.com/paper/1707.06887/) (2017)
- [Safe Reinforcement Learning via Shielding](https://mlsanity.com/paper/1708.08611/) (2017)
- [Reward Constrained Policy Optimization](https://mlsanity.com/paper/1805.11074/) (2018)
- [Implicit Quantile Networks for Distributional Reinforcement Learning](https://mlsanity.com/paper/1806.06923/) (2018)
- [Safe Model-based Reinforcement Learning with Stability Guarantees](https://mlsanity.com/paper/1705.08551/) (2017)
- [Risk-Constrained Reinforcement Learning with Percentile Risk Criteria](https://mlsanity.com/paper/1512.01629/) (2015)
- [End-to-End Safe Reinforcement Learning through Barrier Functions for Safety-Critical Continuous Control Tasks](https://mlsanity.com/paper/1903.08792/) (2019)
- [Safe Exploration in Continuous Action Spaces](https://mlsanity.com/paper/1801.08757/) (2018)
- [Projection-Based Constrained Policy Optimization](https://mlsanity.com/paper/2010.03152/) (2020)
- [Distributed Distributional Deterministic Policy Gradients](https://mlsanity.com/paper/1804.08617/) (2018)
- [Risk-Sensitive and Robust Decision-Making: a CVaR Optimization Approach](https://mlsanity.com/paper/1506.02188/) (2015)
- [IPO: Interior-point Policy Optimization under Constraints](https://mlsanity.com/paper/1910.09615/) (2019)
- [Algorithms for CVaR Optimization in MDPs](https://mlsanity.com/paper/1406.3339/) (2014)
- [Fully Parameterized Quantile Function for Distributional Reinforcement Learning](https://mlsanity.com/paper/1911.02140/) (2019)
- [Safe Exploration in Finite Markov Decision Processes with Gaussian Processes](https://mlsanity.com/paper/1606.04753/) (2016)
- [Reinforcement Learning with Convex Constraints](https://mlsanity.com/paper/1906.09323/) (2019)
- [Convergent Policy Optimization for Safe Reinforcement Learning](https://mlsanity.com/paper/1910.12156/) (2019)
- [Variance-Constrained Actor-Critic Algorithms for Discounted and Average Reward MDPs](https://mlsanity.com/paper/1403.6530/) (2014)
- [Reinforcement Learning of Risk-Constrained Policies in Markov Decision Processes](https://mlsanity.com/paper/2002.12086/) (2020)

## Built on by (most cited first, 10 of 10)

- [Trust Region-Based Safe Distributional Reinforcement Learning for Multiple Constraints](https://mlsanity.com/paper/2301.10923/) (2023)
- [A Distributional Analogue to the Successor Representation](https://mlsanity.com/paper/2402.08530/) (2024)
- [Robust Reinforcement Learning with Distributional Risk-averse formulation](https://mlsanity.com/paper/2206.06841/) (2022)
- [Spectral-Risk Safe Reinforcement Learning with Convergence Guarantees](https://mlsanity.com/paper/2405.18698/) (2024)
- [Mind the Uncertainty: Risk-Aware and Actively Exploring Model-Based Reinforcement Learning](https://mlsanity.com/paper/2309.05582/) (2023)
- [ACReL: Adversarial Conditional value-at-risk Reinforcement Learning](https://mlsanity.com/paper/2109.09470/) (2021)
- [Learning Rewards to Optimize Global Performance Metrics in Deep Reinforcement Learning](https://mlsanity.com/paper/2303.09027/) (2023)
- [Policy Evaluation in Distributional LQR](https://mlsanity.com/paper/2303.13657/) (2023)
- [Modeling Risk in Reinforcement Learning: A Literature Mapping](https://mlsanity.com/paper/2312.05231/) (2023)
- [Safe on Average, Unsafe in the Tail: When Is the Episodic-Cost Tail Controllable?](https://mlsanity.com/paper/2610.09508/) (2026)

## Abstract (arXiv)

Safety in reinforcement learning (RL) is a key property in both training and execution in many domains such as autonomous driving or finance. In this paper, we formalize it with a constrained RL formulation in the distributional RL setting. Our general model accepts various definitions of safety(e.g., bounds on expected performance, CVaR, variance, or probability of reaching bad states). To ensure safety during learning, we extend a safe policy optimization method to solve our problem. The distributional RL perspective leads to a more efficient algorithm while additionally catering for natural safe constraints. We empirically validate our propositions on artificial and real domains against appropriate state-of-the-art safe RL algorithms.