# Conservative Offline Distributional Reinforcement Learning

arXiv: https://arxiv.org/abs/2107.06106 · HTML: https://mlsanity.com/paper/2107.06106/

## Key facts

- Cited by 79 papers in the map (data through 14 Oct 2026).
- Placed in Offline RL algorithms, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 30 of its 52 references that are in the map.
- First posted on arXiv 12 Jul 2021.

## Placed in

- Offline RL and imitation learning from data / [Offline RL algorithms](https://mlsanity.com/offlinerl/offline-rl-algorithms/)

## Builds on (most cited first, 30 of 30)

- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [Asynchronous Methods for Deep Reinforcement Learning](https://mlsanity.com/paper/1602.01783/) (2016)
- [Offline Reinforcement Learning: Tutorial, Review, and Perspectives on Open Problems](https://mlsanity.com/paper/2005.01643/) (2020)
- [Conservative Q-Learning for Offline Reinforcement Learning](https://mlsanity.com/paper/2006.04779/) (2020)
- [Deep Reinforcement Learning with Double Q-learning](https://mlsanity.com/paper/1509.06461/) (2015)
- [D4RL: Datasets for Deep Data-Driven Reinforcement Learning](https://mlsanity.com/paper/2004.07219/) (2020)
- [Off-Policy Deep Reinforcement Learning without Exploration](https://mlsanity.com/paper/1812.02900/) (2018)
- [Stabilizing Off-Policy Q-Learning via Bootstrapping Error Reduction](https://mlsanity.com/paper/1906.00949/) (2019)
- [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)
- [Behavior Regularized Offline Reinforcement Learning](https://mlsanity.com/paper/1911.11361/) (2019)
- [MOPO: Model-based Offline Policy Optimization](https://mlsanity.com/paper/2005.13239/) (2020)
- [MOReL : Model-Based Offline Reinforcement Learning](https://mlsanity.com/paper/2005.05951/) (2020)
- [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)
- [Doubly Robust Off-policy Value Evaluation for Reinforcement Learning](https://mlsanity.com/paper/1511.03722/) (2015)
- [Risk-Constrained Reinforcement Learning with Percentile Risk Criteria](https://mlsanity.com/paper/1512.01629/) (2015)
- [Data-Efficient Off-Policy Policy Evaluation for Reinforcement Learning](https://mlsanity.com/paper/1604.00923/) (2016)
- [Breaking the Curse of Horizon: Infinite-Horizon Off-Policy Estimation](https://mlsanity.com/paper/1810.12429/) (2018)
- [Distributed Distributional Deterministic Policy Gradients](https://mlsanity.com/paper/1804.08617/) (2018)
- [Fully Parameterized Quantile Function for Distributional Reinforcement Learning](https://mlsanity.com/paper/1911.02140/) (2019)
- [Risk-Averse Offline Reinforcement Learning](https://mlsanity.com/paper/2102.05371/) (2021)
- [Statistics and Samples in Distributional Reinforcement Learning](https://mlsanity.com/paper/1902.08102/) (2019)
- [Being Optimistic to Be Conservative: Quickly Learning a CVaR Policy](https://mlsanity.com/paper/1911.01546/) (2019)
- [Worst Cases Policy Gradients](https://mlsanity.com/paper/1911.03618/) (2019)
- [A Comparative Analysis of Expected and Distributional Reinforcement Learning](https://mlsanity.com/paper/1901.11084/) (2019)

## Built on by (most cited first, 30 of 79)

- [Mildly Conservative Q-Learning for Offline Reinforcement Learning](https://mlsanity.com/paper/2206.04745/) (2022)
- [Uncertainty-aware Reward Model: Teaching Reward Models to Know What is Unknown](https://mlsanity.com/paper/2410.00847/) (2024)
- [How Far I'll Go: Offline Goal-Conditioned Reinforcement Learning via f-Advantage Regression](https://mlsanity.com/paper/2206.03023/) (2022)
- [Versatile Offline Imitation from Observations and Examples via Regularized State-Occupancy Matching](https://mlsanity.com/paper/2202.02433/) (2022)
- [Multi-agent Reinforcement Learning: A Comprehensive Survey](https://mlsanity.com/paper/2312.10256/) (2023)
- [Near-Minimax-Optimal Risk-Sensitive Reinforcement Learning with CVaR](https://mlsanity.com/paper/2302.03201/) (2023)
- [The Benefits of Being Distributional: Small-Loss Bounds for Reinforcement Learning](https://mlsanity.com/paper/2305.15703/) (2023)
- [Beyond OOD State Actions: Supported Cross-Domain Offline Reinforcement Learning](https://mlsanity.com/paper/2306.12755/) (2023)
- [Regret Bounds for Risk-Sensitive Reinforcement Learning](https://mlsanity.com/paper/2210.05650/) (2022)
- [LobsDICE: Offline Learning from Observation via Stationary Distribution Correction Estimation](https://mlsanity.com/paper/2202.13536/) (2022)
- [One Risk to Rule Them All: A Risk-Sensitive Perspective on Model-Based Offline Reinforcement Learning](https://mlsanity.com/paper/2212.00124/) (2022)
- [More Benefits of Being Distributional: Second-Order Bounds for Reinforcement Learning](https://mlsanity.com/paper/2402.07198/) (2024)
- [Addressing Optimism Bias in Sequence Modeling for Reinforcement Learning](https://mlsanity.com/paper/2207.10295/) (2022)
- [Double Check Your State Before Trusting It: Confidence-Aware Bidirectional Offline Model-Based Imagination](https://mlsanity.com/paper/2206.07989/) (2022)
- [Zero-Shot Reinforcement Learning from Low Quality Data](https://mlsanity.com/paper/2309.15178/) (2023)
- [Doubly Mild Generalization for Offline Reinforcement Learning](https://mlsanity.com/paper/2411.07934/) (2024)
- [Distributional Offline Policy Evaluation with Predictive Error Guarantees](https://mlsanity.com/paper/2302.09456/) (2023)
- [Conservative and Adaptive Penalty for Model-Based Safe Reinforcement Learning](https://mlsanity.com/paper/2112.07701/) (2021)
- [Bridging Distributional and Risk-sensitive Reinforcement Learning with Provable Regret Bounds](https://mlsanity.com/paper/2210.14051/) (2022)
- [A Reductions Approach to Risk-Sensitive Reinforcement Learning with Optimized Certainty Equivalents](https://mlsanity.com/paper/2403.06323/) (2024)
- [Value Flows](https://mlsanity.com/paper/2510.07650/) (2025)
- [Uncertainty-driven Trajectory Truncation for Data Augmentation in Offline Reinforcement Learning](https://mlsanity.com/paper/2304.04660/) (2023)
- [Flow to Control: Offline Reinforcement Learning with Lossless Primitive Discovery](https://mlsanity.com/paper/2212.01105/) (2022)
- [Robust Reinforcement Learning with Distributional Risk-averse formulation](https://mlsanity.com/paper/2206.06841/) (2022)
- [Conservative and Risk-Aware Offline Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2402.08421/) (2024)
- [Quantile Constrained Reinforcement Learning: A Reinforcement Learning Framework Constraining Outage Probability](https://mlsanity.com/paper/2211.15034/) (2022)
- [Distributional Reinforcement Learning with Regularized Wasserstein Loss](https://mlsanity.com/paper/2202.00769/) (2022)
- [Design from Policies: Conservative Test-Time Adaptation for Offline Policy Optimization](https://mlsanity.com/paper/2306.14479/) (2023)
- [Risk-Aware Reinforcement Learning through Optimal Transport Theory](https://mlsanity.com/paper/2309.06239/) (2023)
- [The Central Role of the Loss Function in Reinforcement Learning](https://mlsanity.com/paper/2409.12799/) (2024)

## Abstract (arXiv)

Many reinforcement learning (RL) problems in practice are offline, learning purely from observational data. A key challenge is how to ensure the learned policy is safe, which requires quantifying the risk associated with different actions. In the online setting, distributional RL algorithms do so by learning the distribution over returns (i.e., cumulative rewards) instead of the expected return; beyond quantifying risk, they have also been shown to learn better representations for planning. We propose Conservative Offline Distributional Actor Critic (CODAC), an offline RL algorithm suitable for both risk-neutral and risk-averse domains. CODAC adapts distributional RL to the offline setting by penalizing the predicted quantiles of the return for out-of-distribution actions. We prove that CODAC learns a conservative return distribution -- in particular, for finite MDPs, CODAC converges to an uniform lower bound on the quantiles of the return distribution; our proof relies on a novel analysis of the distributional Bellman operator. In our experiments, on two challenging robot navigation tasks, CODAC successfully learns risk-averse policies using offline data collected purely from risk-neutral agents. Furthermore, CODAC is state-of-the-art on the D4RL MuJoCo benchmark in terms of both expected and risk-sensitive performance.