# Pessimistic Bootstrapping for Uncertainty-Driven Offline Reinforcement Learning

arXiv: https://arxiv.org/abs/2202.11566 · HTML: https://mlsanity.com/paper/2202.11566/

## Key facts

- Cited by 125 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 56 of its 65 references that are in the map.
- First posted on arXiv 23 Feb 2022.

## 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 56)

- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (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)
- [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)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Off-Policy Deep Reinforcement Learning without Exploration](https://mlsanity.com/paper/1812.02900/) (2018)
- [A Minimalist Approach to Offline Reinforcement Learning](https://mlsanity.com/paper/2106.06860/) (2021)
- [Stabilizing Off-Policy Q-Learning via Bootstrapping Error Reduction](https://mlsanity.com/paper/1906.00949/) (2019)
- [Deep Reinforcement Learning at the Edge of the Statistical Precipice](https://mlsanity.com/paper/2108.13264/) (2021)
- [Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Models](https://mlsanity.com/paper/1805.12114/) (2018)
- [When to Trust Your Model: Model-Based Policy Optimization](https://mlsanity.com/paper/1906.08253/) (2019)
- [What Matters in Learning from Offline Human Demonstrations for Robot Manipulation](https://mlsanity.com/paper/2108.03298/) (2021)
- [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)
- [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)
- [Deep Exploration via Bootstrapped DQN](https://mlsanity.com/paper/1602.04621/) (2016)
- [Provably Efficient Reinforcement Learning with Linear Function Approximation](https://mlsanity.com/paper/1907.05388/) (2019)
- [Minimax Regret Bounds for Reinforcement Learning](https://mlsanity.com/paper/1703.05449/) (2017)
- [COMBO: Conservative Offline Model-Based Policy Optimization](https://mlsanity.com/paper/2102.08363/) (2021)
- [Planning to Explore via Self-Supervised World Models](https://mlsanity.com/paper/2005.05960/) (2020)
- [Is Pessimism Provably Efficient for Offline RL?](https://mlsanity.com/paper/2012.15085/) (2020)
- [Reinforcement Learning in Healthcare: A Survey](https://mlsanity.com/paper/1908.08796/) (2019)
- [Uncertainty-Based Offline Reinforcement Learning with Diversified Q-Ensemble](https://mlsanity.com/paper/2110.01548/) (2021)
- [Critic Regularized Regression](https://mlsanity.com/paper/2006.15134/) (2020)
- [Bellman-consistent Pessimism for Offline Reinforcement Learning](https://mlsanity.com/paper/2106.06926/) (2021)
- [Offline Reinforcement Learning with Fisher Divergence Critic Regularization](https://mlsanity.com/paper/2103.08050/) (2021)

## Built on by (most cited first, 30 of 125)

- [Offline RL with No OOD Actions: In-Sample Learning via Implicit Value Regularization](https://mlsanity.com/paper/2303.15810/) (2023)
- [Mildly Conservative Q-Learning for Offline Reinforcement Learning](https://mlsanity.com/paper/2206.04745/) (2022)
- [RORL: Robust Offline Reinforcement Learning via Conservative Smoothing](https://mlsanity.com/paper/2206.02829/) (2022)
- [Reinforcement Learning with Human Feedback: Learning Dynamic Choices via Pessimism](https://mlsanity.com/paper/2305.18438/) (2023)
- [A Policy-Guided Imitation Approach for Offline Reinforcement Learning](https://mlsanity.com/paper/2210.08323/) (2022)
- [Uncertainty-Penalized Reinforcement Learning from Human Feedback with Diverse Reward LoRA Ensembles](https://mlsanity.com/paper/2401.00243/) (2023)
- [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)
- [A Review of Uncertainty for Deep Reinforcement Learning](https://mlsanity.com/paper/2208.09052/) (2022)
- [What is Essential for Unseen Goal Generalization of Offline Goal-conditioned RL?](https://mlsanity.com/paper/2305.18882/) (2023)
- [The In-Sample Softmax for Offline Reinforcement Learning](https://mlsanity.com/paper/2302.14372/) (2023)
- [Uncertainty-aware Latent Safety Filters for Avoiding Out-of-Distribution Failures](https://mlsanity.com/paper/2505.00779/) (2025)
- [When Data Geometry Meets Deep Function: Generalizing Offline Reinforcement Learning](https://mlsanity.com/paper/2205.11027/) (2022)
- [Entropy-regularized Diffusion Policy with Q-Ensembles for Offline Reinforcement Learning](https://mlsanity.com/paper/2402.04080/) (2024)
- [PROTO: Iterative Policy Regularized Offline-to-Online Reinforcement Learning](https://mlsanity.com/paper/2305.15669/) (2023)
- [Beyond OOD State Actions: Supported Cross-Domain Offline Reinforcement Learning](https://mlsanity.com/paper/2306.12755/) (2023)
- [Improving Generalization of Alignment with Human Preferences through Group Invariant Learning](https://mlsanity.com/paper/2310.11971/) (2023)
- [Reinformer: Max-Return Sequence Modeling for Offline RL](https://mlsanity.com/paper/2405.08740/) (2024)
- [Towards Robust Offline Reinforcement Learning under Diverse Data Corruption](https://mlsanity.com/paper/2310.12955/) (2023)
- [Model-Based Offline Reinforcement Learning with Pessimism-Modulated Dynamics Belief](https://mlsanity.com/paper/2210.06692/) (2022)
- [Q-Ensemble for Offline RL: Don't Scale the Ensemble, Scale the Batch Size](https://mlsanity.com/paper/2211.11092/) (2022)
- [Zero-Shot Reinforcement Learning from Low Quality Data](https://mlsanity.com/paper/2309.15178/) (2023)
- [ODICE: Revealing the Mystery of Distribution Correction Estimation via Orthogonal-gradient Update](https://mlsanity.com/paper/2402.00348/) (2024)
- [Doubly Mild Generalization for Offline Reinforcement Learning](https://mlsanity.com/paper/2411.07934/) (2024)
- [ENOTO: Improving Offline-to-Online Reinforcement Learning with Q-Ensembles](https://mlsanity.com/paper/2306.06871/) (2023)
- [GOPlan: Goal-conditioned Offline Reinforcement Learning by Planning with Learned Models](https://mlsanity.com/paper/2310.20025/) (2023)
- [Behavior-Regularized Diffusion Policy Optimization for Offline Reinforcement Learning](https://mlsanity.com/paper/2502.04778/) (2025)
- [Look Beneath the Surface: Exploiting Fundamental Symmetry for Sample-Efficient Offline RL](https://mlsanity.com/paper/2306.04220/) (2023)
- [Contrastive Representation for Data Filtering in Cross-Domain Offline Reinforcement Learning](https://mlsanity.com/paper/2405.06192/) (2024)
- [Offline Reinforcement Learning with OOD State Correction and OOD Action Suppression](https://mlsanity.com/paper/2410.19400/) (2024)

## Abstract (arXiv)

Offline Reinforcement Learning (RL) aims to learn policies from previously collected datasets without exploring the environment. Directly applying off-policy algorithms to offline RL usually fails due to the extrapolation error caused by the out-of-distribution (OOD) actions. Previous methods tackle such problem by penalizing the Q-values of OOD actions or constraining the trained policy to be close to the behavior policy. Nevertheless, such methods typically prevent the generalization of value functions beyond the offline data and also lack precise characterization of OOD data. In this paper, we propose Pessimistic Bootstrapping for offline RL (PBRL), a purely uncertainty-driven offline algorithm without explicit policy constraints. Specifically, PBRL conducts uncertainty quantification via the disagreement of bootstrapped Q-functions, and performs pessimistic updates by penalizing the value function based on the estimated uncertainty. To tackle the extrapolating error, we further propose a novel OOD sampling method. We show that such OOD sampling and pessimistic bootstrapping yields provable uncertainty quantifier in linear MDPs, thus providing the theoretical underpinning for PBRL. Extensive experiments on D4RL benchmark show that PBRL has better performance compared to the state-of-the-art algorithms.