# MICRO: Model-Based Offline Reinforcement Learning with a Conservative Bellman Operator

arXiv: https://arxiv.org/abs/2312.03991 · HTML: https://mlsanity.com/paper/2312.03991/

## Key facts

- Cited by 9 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 36 of its 43 references that are in the map.
- First posted on arXiv 7 Dec 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 36)

- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (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)
- [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)
- [When to Trust Your Model: Model-Based Policy Optimization](https://mlsanity.com/paper/1906.08253/) (2019)
- [MOPO: Model-based Offline Policy Optimization](https://mlsanity.com/paper/2005.13239/) (2020)
- [Robust Adversarial Reinforcement Learning](https://mlsanity.com/paper/1703.02702/) (2017)
- [COMBO: Conservative Offline Model-Based Policy Optimization](https://mlsanity.com/paper/2102.08363/) (2021)
- [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)
- [Information-Theoretic Considerations in Batch Reinforcement Learning](https://mlsanity.com/paper/1905.00360/) (2019)
- [Bellman-consistent Pessimism for Offline Reinforcement Learning](https://mlsanity.com/paper/2106.06926/) (2021)
- [Robust Deep Reinforcement Learning against Adversarial Perturbations on State Observations](https://mlsanity.com/paper/2003.08938/) (2020)
- [Offline Reinforcement Learning with Fisher Divergence Critic Regularization](https://mlsanity.com/paper/2103.08050/) (2021)
- [FLAMBE: Structural Complexity and Representation Learning of Low Rank MDPs](https://mlsanity.com/paper/2006.10814/) (2020)
- [Action Robust Reinforcement Learning and Applications in Continuous Control](https://mlsanity.com/paper/1901.09184/) (2019)
- [Pessimistic Model-based Offline Reinforcement Learning under Partial Coverage](https://mlsanity.com/paper/2107.06226/) (2021)
- [Robust Deep Reinforcement Learning with Adversarial Attacks](https://mlsanity.com/paper/1712.03632/) (2017)
- [What are the Statistical Limits of Offline RL with Linear Function Approximation?](https://mlsanity.com/paper/2010.11895/) (2020)
- [Pessimistic Bootstrapping for Uncertainty-Driven Offline Reinforcement Learning](https://mlsanity.com/paper/2202.11566/) (2022)
- [RAMBO-RL: Robust Adversarial Model-Based Offline Reinforcement Learning](https://mlsanity.com/paper/2204.12581/) (2022)
- [Adversarially Trained Actor Critic for Offline Reinforcement Learning](https://mlsanity.com/paper/2202.02446/) (2022)
- [Online Robust Reinforcement Learning with Model Uncertainty](https://mlsanity.com/paper/2109.14523/) (2021)
- [Robust Reinforcement Learning using Offline Data](https://mlsanity.com/paper/2208.05129/) (2022)
- [RORL: Robust Offline Reinforcement Learning via Conservative Smoothing](https://mlsanity.com/paper/2206.02829/) (2022)
- [When to Trust Your Simulator: Dynamics-Aware Hybrid Offline-and-Online Reinforcement Learning](https://mlsanity.com/paper/2206.13464/) (2022)
- [Robust Reinforcement Learning via Adversarial training with Langevin Dynamics](https://mlsanity.com/paper/2002.06063/) (2020)

## Built on by (most cited first, 9 of 9)

- [Dual-Robust Cross-Domain Offline Reinforcement Learning Against Dynamics Shifts](https://mlsanity.com/paper/2512.02486/) (2025)
- [FOVA: Offline Federated Reinforcement Learning with Mixed-Quality Data](https://mlsanity.com/paper/2512.02350/) (2025)
- [DARLR: Dual-Agent Offline Reinforcement Learning for Recommender Systems with Dynamic Reward](https://mlsanity.com/paper/2505.07257/) (2025)
- [Pessimism Principle Can Be Effective: Towards a Framework for Zero-Shot Transfer Reinforcement Learning](https://mlsanity.com/paper/2505.18447/) (2025)
- [Robustness Evaluation of Offline Reinforcement Learning for Robot Control Against Action Perturbations](https://mlsanity.com/paper/2412.18781/) (2024)
- [LEASE: Offline Preference-based Reinforcement Learning with High Sample Efficiency](https://mlsanity.com/paper/2412.21001/) (2024)
- [Feasibility-Aware Pessimistic Estimation: Toward Long-Horizon Safety in Offline RL](https://mlsanity.com/paper/2505.08179/) (2025)
- [Adversarial Fine-tuning in Offline-to-Online Reinforcement Learning for Robust Robot Control](https://mlsanity.com/paper/2510.13358/) (2025)
- [Improving Generalization and Robustness in Offline Reinforcement Learning via Boundary-Aware Data Augmentation](https://mlsanity.com/paper/2609.20300/) (2026)

## Abstract (arXiv)

Offline reinforcement learning (RL) faces a significant challenge of distribution shift. Model-free offline RL penalizes the Q value for out-of-distribution (OOD) data or constrains the policy closed to the behavior policy to tackle this problem, but this inhibits the exploration of the OOD region. Model-based offline RL, which uses the trained environment model to generate more OOD data and performs conservative policy optimization within that model, has become an effective method for this problem. However, the current model-based algorithms rarely consider agent robustness when incorporating conservatism into policy. Therefore, the new model-based offline algorithm with a conservative Bellman operator (MICRO) is proposed. This method trades off performance and robustness via introducing the robust Bellman operator into the algorithm. Compared with previous model-based algorithms with robust adversarial models, MICRO can significantly reduce the computation cost by only choosing the minimal Q value in the state uncertainty set. Extensive experiments demonstrate that MICRO outperforms prior RL algorithms in offline RL benchmark and is considerably robust to adversarial perturbations.