# Constrained Policy Optimization with Explicit Behavior Density for Offline Reinforcement Learning

arXiv: https://arxiv.org/abs/2301.12130 · HTML: https://mlsanity.com/paper/2301.12130/

## Key facts

- Cited by 16 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 53 of its 85 references that are in the map.
- First posted on arXiv 28 Jan 2023.

## 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 53)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [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)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (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)
- [Generative Adversarial Imitation Learning](https://mlsanity.com/paper/1606.03476/) (2016)
- [Decision Transformer: Reinforcement Learning via Sequence Modeling](https://mlsanity.com/paper/2106.01345/) (2021)
- [D4RL: Datasets for Deep Data-Driven Reinforcement Learning](https://mlsanity.com/paper/2004.07219/) (2020)
- [Offline Reinforcement Learning with Implicit Q-Learning](https://mlsanity.com/paper/2110.06169/) (2021)
- [Off-Policy Deep Reinforcement Learning without Exploration](https://mlsanity.com/paper/1812.02900/) (2018)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [A Minimalist Approach to Offline Reinforcement Learning](https://mlsanity.com/paper/2106.06860/) (2021)
- [End-to-End Training of Deep Visuomotor Policies](https://mlsanity.com/paper/1504.00702/) (2015)
- [Stabilizing Off-Policy Q-Learning via Bootstrapping Error Reduction](https://mlsanity.com/paper/1906.00949/) (2019)
- [Dueling Network Architectures for Deep Reinforcement Learning](https://mlsanity.com/paper/1511.06581/) (2015)
- [QT-Opt: Scalable Deep Reinforcement Learning for Vision-Based Robotic Manipulation](https://mlsanity.com/paper/1806.10293/) (2018)
- [AWAC: Accelerating Online Reinforcement Learning with Offline Datasets](https://mlsanity.com/paper/2006.09359/) (2020)
- [Behavior Regularized Offline Reinforcement Learning](https://mlsanity.com/paper/1911.11361/) (2019)
- [Diffusion Policies as an Expressive Policy Class for Offline Reinforcement Learning](https://mlsanity.com/paper/2208.06193/) (2022)
- [Guided Cost Learning: Deep Inverse Optimal Control via Policy Optimization](https://mlsanity.com/paper/1603.00448/) (2016)
- [Uncertainty-Based Offline Reinforcement Learning with Diversified Q-Ensemble](https://mlsanity.com/paper/2110.01548/) (2021)
- [Way Off-Policy Batch Deep Reinforcement Learning of Implicit Human Preferences in Dialog](https://mlsanity.com/paper/1907.00456/) (2019)

## Built on by (most cited first, 16 of 16)

- [Deep Generative Models for Offline Policy Learning: Tutorial, Survey, and Perspectives on Future Directions](https://mlsanity.com/paper/2402.13777/) (2024)
- [GenPO: Generative Diffusion Models Meet On-Policy Reinforcement Learning](https://mlsanity.com/paper/2505.18763/) (2025)
- [FlowPG: Action-constrained Policy Gradient with Normalizing Flows](https://mlsanity.com/paper/2402.05149/) (2024)
- [A Survey of Safe Reinforcement Learning and Constrained MDPs: A Technical Survey on Single-Agent and Multi-Agent Safety](https://mlsanity.com/paper/2505.17342/) (2025)
- [Iteratively Refined Behavior Regularization for Offline Reinforcement Learning](https://mlsanity.com/paper/2306.05726/) (2023)
- [Q-Distribution guided Q-learning for offline reinforcement learning: Uncertainty penalized Q-value via consistency model](https://mlsanity.com/paper/2410.20312/) (2024)
- [ReFORM: Reflected Flows for On-support Offline RL via Noise Manipulation](https://mlsanity.com/paper/2602.05051/) (2026)
- [Augmenting Offline Reinforcement Learning with State-only Interactions](https://mlsanity.com/paper/2402.00807/) (2024)
- [Adaptive Neighborhood-Constrained Q Learning for Offline Reinforcement Learning](https://mlsanity.com/paper/2511.02567/) (2025)
- [Guardian-regularized Safe Offline Reinforcement Learning for Smart Weaning of Mechanical Circulatory Devices](https://mlsanity.com/paper/2511.06111/) (2025)
- [DiffPoGAN: Diffusion Policies with Generative Adversarial Networks for Offline Reinforcement Learning](https://mlsanity.com/paper/2406.09089/) (2024)
- [Policy Constraint by Only Support Constraint for Offline Reinforcement Learning](https://mlsanity.com/paper/2503.05207/) (2025)
- [Quantile Q-Learning: Revisiting Offline Extreme Q-Learning with Quantile Regression](https://mlsanity.com/paper/2511.11973/) (2025)
- [LexiSafe: Offline Safe Reinforcement Learning with Lexicographic Safety-Reward Hierarchy](https://mlsanity.com/paper/2602.17312/) (2026)
- [Generative OOD-regularized Model-based Policy Optimization](https://mlsanity.com/paper/2605.24405/) (2026)
- [Improving Offline Goal-Conditioned Reinforcement Learning via Selective Reward Stimulation](https://mlsanity.com/paper/2609.19414/) (2026)

## Abstract (arXiv)

Due to the inability to interact with the environment, offline reinforcement learning (RL) methods face the challenge of estimating the Out-of-Distribution (OOD) points. Existing methods for addressing this issue either control policy to exclude the OOD action or make the Q function pessimistic. However, these methods can be overly conservative or fail to identify OOD areas accurately. To overcome this problem, we propose a Constrained Policy optimization with Explicit Behavior density (CPED) method that utilizes a flow-GAN model to explicitly estimate the density of behavior policy. By estimating the explicit density, CPED can accurately identify the safe region and enable optimization within the region, resulting in less conservative learning policies. We further provide theoretical results for both the flow-GAN estimator and performance guarantee for CPED by showing that CPED can find the optimal Q-function value. Empirically, CPED outperforms existing alternatives on various standard offline reinforcement learning tasks, yielding higher expected returns.