# Offline Reinforcement Learning with Fisher Divergence Critic Regularization

arXiv: https://arxiv.org/abs/2103.08050 · HTML: https://mlsanity.com/paper/2103.08050/

## Key facts

- Cited by 238 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 24 of its 34 references that are in the map.
- First posted on arXiv 14 Mar 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, 24 of 24)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [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)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [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)
- [Soft Actor-Critic Algorithms and Applications](https://mlsanity.com/paper/1812.05905/) (2018)
- [Stabilizing Off-Policy Q-Learning via Bootstrapping Error Reduction](https://mlsanity.com/paper/1906.00949/) (2019)
- [Reinforcement Learning with Deep Energy-Based Policies](https://mlsanity.com/paper/1702.08165/) (2017)
- [Behavior Regularized Offline Reinforcement Learning](https://mlsanity.com/paper/1911.11361/) (2019)
- [Way Off-Policy Batch Deep Reinforcement Learning of Implicit Human Preferences in Dialog](https://mlsanity.com/paper/1907.00456/) (2019)
- [Why Normalizing Flows Fail to Detect Out-of-Distribution Data](https://mlsanity.com/paper/2006.08545/) (2020)
- [Discriminator-Actor-Critic: Addressing Sample Inefficiency and Reward Bias in Adversarial Imitation Learning](https://mlsanity.com/paper/1809.02925/) (2018)
- [AlgaeDICE: Policy Gradient from Arbitrary Experience](https://mlsanity.com/paper/1912.02074/) (2019)
- [Bridging the Gap Between Value and Policy Based Reinforcement Learning](https://mlsanity.com/paper/1702.08892/) (2017)
- [A Connection between Generative Adversarial Networks, Inverse Reinforcement Learning, and Energy-Based Models](https://mlsanity.com/paper/1611.03852/) (2016)
- [Model-Based Offline Planning](https://mlsanity.com/paper/2008.05556/) (2020)
- [Taming the Noise in Reinforcement Learning via Soft Updates](https://mlsanity.com/paper/1512.08562/) (2015)
- [Deployment-Efficient Reinforcement Learning via Model-Based Offline Optimization](https://mlsanity.com/paper/2006.03647/) (2020)
- [EMaQ: Expected-Max Q-Learning Operator for Simple Yet Effective Offline and Online RL](https://mlsanity.com/paper/2007.11091/) (2020)
- [Sequence Tutor: Conservative Fine-Tuning of Sequence Generation Models with KL-control](https://mlsanity.com/paper/1611.02796/) (2016)
- [Image-to-image translation for cross-domain disentanglement](https://mlsanity.com/paper/1805.09730/) (2018)
- [Variational (Gradient) Estimate of the Score Function in Energy-based Latent Variable Models](https://mlsanity.com/paper/2010.08258/) (2020)

## Built on by (most cited first, 30 of 238)

- [Offline Reinforcement Learning with Implicit Q-Learning](https://mlsanity.com/paper/2110.06169/) (2021)
- [A Minimalist Approach to Offline Reinforcement Learning](https://mlsanity.com/paper/2106.06860/) (2021)
- [Diffusion Policies as an Expressive Policy Class for Offline Reinforcement Learning](https://mlsanity.com/paper/2208.06193/) (2022)
- [Is Conditional Generative Modeling all you need for Decision-Making?](https://mlsanity.com/paper/2211.15657/) (2022)
- [Implicit Behavioral Cloning](https://mlsanity.com/paper/2109.00137/) (2021)
- [IDQL: Implicit Q-Learning as an Actor-Critic Method with Diffusion Policies](https://mlsanity.com/paper/2304.10573/) (2023)
- [Behavior Transformers: Cloning k modes with one stone](https://mlsanity.com/paper/2206.11251/) (2022)
- [Cal-QL: Calibrated Offline RL Pre-Training for Efficient Online Fine-Tuning](https://mlsanity.com/paper/2303.05479/) (2023)
- [A Survey on Offline Reinforcement Learning: Taxonomy, Review, and Open Problems](https://mlsanity.com/paper/2203.01387/) (2022)
- [Online Decision Transformer](https://mlsanity.com/paper/2202.05607/) (2022)
- [Offline Reinforcement Learning via High-Fidelity Generative Behavior Modeling](https://mlsanity.com/paper/2209.14548/) (2022)
- [Offline RL Without Off-Policy Evaluation](https://mlsanity.com/paper/2106.08909/) (2021)
- [Q-Transformer: Scalable Offline Reinforcement Learning via Autoregressive Q-Functions](https://mlsanity.com/paper/2309.10150/) (2023)
- [Pessimistic Bootstrapping for Uncertainty-Driven Offline Reinforcement Learning](https://mlsanity.com/paper/2202.11566/) (2022)
- [Offline RL with No OOD Actions: In-Sample Learning via Implicit Value Regularization](https://mlsanity.com/paper/2303.15810/) (2023)
- [RAMBO-RL: Robust Adversarial Model-Based Offline Reinforcement Learning](https://mlsanity.com/paper/2204.12581/) (2022)
- [Mildly Conservative Q-Learning for Offline Reinforcement Learning](https://mlsanity.com/paper/2206.04745/) (2022)
- [From Play to Policy: Conditional Behavior Generation from Uncurated Robot Data](https://mlsanity.com/paper/2210.10047/) (2022)
- [Diffusion Models for Reinforcement Learning: A Survey](https://mlsanity.com/paper/2311.01223/) (2023)
- [When Should We Prefer Offline Reinforcement Learning Over Behavioral Cloning?](https://mlsanity.com/paper/2204.05618/) (2022)
- [Latent Plans for Task-Agnostic Offline Reinforcement Learning](https://mlsanity.com/paper/2209.08959/) (2022)
- [Pre-Training for Robots: Offline RL Enables Learning New Tasks from a Handful of Trials](https://mlsanity.com/paper/2210.05178/) (2022)
- [Why So Pessimistic? Estimating Uncertainties for Offline RL through Ensembles, and Why Their Independence Matters](https://mlsanity.com/paper/2205.13703/) (2022)
- [Supported Policy Optimization for Offline Reinforcement Learning](https://mlsanity.com/paper/2202.06239/) (2022)
- [Offline Q-Learning on Diverse Multi-Task Data Both Scales And Generalizes](https://mlsanity.com/paper/2211.15144/) (2022)
- [COptiDICE: Offline Constrained Reinforcement Learning via Stationary Distribution Correction Estimation](https://mlsanity.com/paper/2204.08957/) (2022)
- [Score Regularized Policy Optimization through Diffusion Behavior](https://mlsanity.com/paper/2310.07297/) (2023)
- [A Workflow for Offline Model-Free Robotic Reinforcement Learning](https://mlsanity.com/paper/2109.10813/) (2021)
- [Constrained Decision Transformer for Offline Safe Reinforcement Learning](https://mlsanity.com/paper/2302.07351/) (2023)
- [Conservative Data Sharing for Multi-Task Offline Reinforcement Learning](https://mlsanity.com/paper/2109.08128/) (2021)

## Abstract (arXiv)

Many modern approaches to offline Reinforcement Learning (RL) utilize behavior regularization, typically augmenting a model-free actor critic algorithm with a penalty measuring divergence of the policy from the offline data. In this work, we propose an alternative approach to encouraging the learned policy to stay close to the data, namely parameterizing the critic as the log-behavior-policy, which generated the offline data, plus a state-action value offset term, which can be learned using a neural network. Behavior regularization then corresponds to an appropriate regularizer on the offset term. We propose using a gradient penalty regularizer for the offset term and demonstrate its equivalence to Fisher divergence regularization, suggesting connections to the score matching and generative energy-based model literature. We thus term our resulting algorithm Fisher-BRC (Behavior Regularized Critic). On standard offline RL benchmarks, Fisher-BRC achieves both improved performance and faster convergence over existing state-of-the-art methods.