# Offline Reinforcement Learning with Soft Behavior Regularization

arXiv: https://arxiv.org/abs/2110.07395 · HTML: https://mlsanity.com/paper/2110.07395/

## Key facts

- Cited by 28 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 44 of its 57 references that are in the map.
- First posted on arXiv 14 Oct 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 44)

- [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)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [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)
- [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)
- [Constrained Policy Optimization](https://mlsanity.com/paper/1705.10528/) (2017)
- [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)
- [Advantage-Weighted Regression: Simple and Scalable Off-Policy Reinforcement Learning](https://mlsanity.com/paper/1910.00177/) (2019)
- [Learning Complex Dexterous Manipulation with Deep Reinforcement Learning and Demonstrations](https://mlsanity.com/paper/1709.10087/) (2017)
- [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)
- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [Critic Regularized Regression](https://mlsanity.com/paper/2006.15134/) (2020)
- [DualDICE: Behavior-Agnostic Estimation of Discounted Stationary Distribution Corrections](https://mlsanity.com/paper/1906.04733/) (2019)
- [Batch Policy Learning under Constraints](https://mlsanity.com/paper/1903.08738/) (2019)
- [Offline Reinforcement Learning with Fisher Divergence Critic Regularization](https://mlsanity.com/paper/2103.08050/) (2021)
- [Breaking the Curse of Horizon: Infinite-Horizon Off-Policy Estimation](https://mlsanity.com/paper/1810.12429/) (2018)
- [Keep Doing What Worked: Behavioral Modelling Priors for Offline Reinforcement Learning](https://mlsanity.com/paper/2002.08396/) (2020)
- [AlgaeDICE: Policy Gradient from Arbitrary Experience](https://mlsanity.com/paper/1912.02074/) (2019)
- [Offline RL Without Off-Policy Evaluation](https://mlsanity.com/paper/2106.08909/) (2021)
- [Safe Policy Improvement with Baseline Bootstrapping](https://mlsanity.com/paper/1712.06924/) (2017)
- [Uncertainty Weighted Actor-Critic for Offline Reinforcement Learning](https://mlsanity.com/paper/2105.08140/) (2021)
- [OptiDICE: Offline Policy Optimization via Stationary Distribution Correction Estimation](https://mlsanity.com/paper/2106.10783/) (2021)

## Built on by (most cited first, 28 of 28)

- [Offline RL with No OOD Actions: In-Sample Learning via Implicit Value Regularization](https://mlsanity.com/paper/2303.15810/) (2023)
- [Supported Policy Optimization for Offline Reinforcement Learning](https://mlsanity.com/paper/2202.06239/) (2022)
- [Score Regularized Policy Optimization through Diffusion Behavior](https://mlsanity.com/paper/2310.07297/) (2023)
- [When to Trust Your Simulator: Dynamics-Aware Hybrid Offline-and-Online Reinforcement Learning](https://mlsanity.com/paper/2206.13464/) (2022)
- [A Policy-Guided Imitation Approach for Offline Reinforcement Learning](https://mlsanity.com/paper/2210.08323/) (2022)
- [Behavior Proximal Policy Optimization](https://mlsanity.com/paper/2302.11312/) (2023)
- [Offline Multi-Agent Reinforcement Learning with Implicit Global-to-Local Value Regularization](https://mlsanity.com/paper/2307.11620/) (2023)
- [Diffusion-DICE: In-Sample Diffusion Guidance for Offline Reinforcement Learning](https://mlsanity.com/paper/2407.20109/) (2024)
- [When Data Geometry Meets Deep Function: Generalizing Offline Reinforcement Learning](https://mlsanity.com/paper/2205.11027/) (2022)
- [PROTO: Iterative Policy Regularized Offline-to-Online Reinforcement Learning](https://mlsanity.com/paper/2305.15669/) (2023)
- [Benchmarking Offline Reinforcement Learning on Real-Robot Hardware](https://mlsanity.com/paper/2307.15690/) (2023)
- [ODICE: Revealing the Mystery of Distribution Correction Estimation via Orthogonal-gradient Update](https://mlsanity.com/paper/2402.00348/) (2024)
- [Look Beneath the Surface: Exploiting Fundamental Symmetry for Sample-Efficient Offline RL](https://mlsanity.com/paper/2306.04220/) (2023)
- [Discriminator-Guided Model-Based Offline Imitation Learning](https://mlsanity.com/paper/2207.00244/) (2022)
- [Mind the Gap: Offline Policy Optimization for Imperfect Rewards](https://mlsanity.com/paper/2302.01667/) (2023)
- [Aligning Diffusion Behaviors with Q-functions for Efficient Continuous Control](https://mlsanity.com/paper/2407.09024/) (2024)
- [Guided Data Augmentation for Offline Reinforcement Learning and Imitation Learning](https://mlsanity.com/paper/2310.18247/) (2023)
- [How to Spend Your Robot Time: Bridging Kickstarting and Offline Reinforcement Learning for Vision-based Robotic Manipulation](https://mlsanity.com/paper/2205.03353/) (2022)
- [ComaDICE: Offline Cooperative Multi-Agent Reinforcement Learning with Stationary Distribution Shift Regularization](https://mlsanity.com/paper/2410.01954/) (2024)
- [Offline Reinforcement Learning with Imbalanced Datasets](https://mlsanity.com/paper/2307.02752/) (2023)
- [Environment Transformer and Policy Optimization for Model-Based Offline Reinforcement Learning](https://mlsanity.com/paper/2303.03811/) (2023)
- [Offline Diversity Maximization Under Imitation Constraints](https://mlsanity.com/paper/2307.11373/) (2023)
- [An Optimal Discriminator Weighted Imitation Perspective for Reinforcement Learning](https://mlsanity.com/paper/2504.13368/) (2025)
- [A Fully Data-Driven Approach for Realistic Traffic Signal Control Using Offline Reinforcement Learning](https://mlsanity.com/paper/2311.15920/) (2023)
- [Localized Dynamics-Aware Domain Adaption for Off-Dynamics Offline Reinforcement Learning](https://mlsanity.com/paper/2602.21072/) (2026)
- [State-Aware Proximal Pessimistic Algorithms for Offline Reinforcement Learning](https://mlsanity.com/paper/2211.15065/) (2022)
- [A Model-Based Approach for Improving Reinforcement Learning Efficiency Leveraging Expert Observations](https://mlsanity.com/paper/2402.18836/) (2024)
- [UDQL: Bridging The Gap between MSE Loss and The Optimal Value Function in Offline Reinforcement Learning](https://mlsanity.com/paper/2406.03324/) (2024)

## Abstract (arXiv)

Most prior approaches to offline reinforcement learning (RL) utilize textitbehavior regularization, typically augmenting existing off-policy actor critic algorithms with a penalty measuring divergence between the policy and the offline data. However, these approaches lack guaranteed performance improvement over the behavior policy. In this work, we start from the performance difference between the learned policy and the behavior policy, we derive a new policy learning objective that can be used in the offline setting, which corresponds to the advantage function value of the behavior policy, multiplying by a state-marginal density ratio. We propose a practical way to compute the density ratio and demonstrate its equivalence to a state-dependent behavior regularization. Unlike state-independent regularization used in prior approaches, this textitsoft regularization allows more freedom of policy deviation at high confidence states, leading to better performance and stability. We thus term our resulting algorithm Soft Behavior-regularized Actor Critic (SBAC). Our experimental results show that SBAC matches or outperforms the state-of-the-art on a set of continuous control locomotion and manipulation tasks.