# UDQL: Bridging The Gap between MSE Loss and The Optimal Value Function in Offline Reinforcement Learning

arXiv: https://arxiv.org/abs/2406.03324 · HTML: https://mlsanity.com/paper/2406.03324/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Offline RL algorithms, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 34 of its 46 references that are in the map.
- First posted on arXiv 5 Jun 2024.

## 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 34)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [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)
- [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)
- [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)
- [Diffusion Policies as an Expressive Policy Class for Offline Reinforcement Learning](https://mlsanity.com/paper/2208.06193/) (2022)
- [IDQL: Implicit Q-Learning as an Actor-Critic Method with Diffusion Policies](https://mlsanity.com/paper/2304.10573/) (2023)
- [Critic Regularized Regression](https://mlsanity.com/paper/2006.15134/) (2020)
- [Offline Reinforcement Learning with Fisher Divergence Critic Regularization](https://mlsanity.com/paper/2103.08050/) (2021)
- [Keep Doing What Worked: Behavioral Modelling Priors for Offline Reinforcement Learning](https://mlsanity.com/paper/2002.08396/) (2020)
- [Distributed Distributional Deterministic Policy Gradients](https://mlsanity.com/paper/1804.08617/) (2018)
- [AlgaeDICE: Policy Gradient from Arbitrary Experience](https://mlsanity.com/paper/1912.02074/) (2019)
- [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)
- [Contrastive Energy Prediction for Exact Energy-Guided Diffusion Sampling in Offline Reinforcement Learning](https://mlsanity.com/paper/2304.12824/) (2023)
- [Mish: A Self Regularized Non-Monotonic Activation Function](https://mlsanity.com/paper/1908.08681/) (2019)
- [Uncertainty Weighted Actor-Critic for Offline Reinforcement Learning](https://mlsanity.com/paper/2105.08140/) (2021)
- [Pessimistic Bootstrapping for Uncertainty-Driven Offline Reinforcement Learning](https://mlsanity.com/paper/2202.11566/) (2022)
- [Extreme Q-Learning: MaxEnt RL without Entropy](https://mlsanity.com/paper/2301.02328/) (2023)
- [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)
- [BAIL: Best-Action Imitation Learning for Batch Deep Reinforcement Learning](https://mlsanity.com/paper/1910.12179/) (2019)
- [Constraints Penalized Q-learning for Safe Offline Reinforcement Learning](https://mlsanity.com/paper/2107.09003/) (2021)
- [Discriminator-Weighted Offline Imitation Learning from Suboptimal Demonstrations](https://mlsanity.com/paper/2207.10050/) (2022)
- [Score Regularized Policy Optimization through Diffusion Behavior](https://mlsanity.com/paper/2310.07297/) (2023)

## Abstract (arXiv)

The Mean Square Error (MSE) is commonly utilized to estimate the solution of the optimal value function in the vast majority of offline reinforcement learning (RL) models and has achieved outstanding performance. However, we find that its principle can lead to overestimation phenomenon for the value function. In this paper, we first theoretically analyze overestimation phenomenon led by MSE and provide the theoretical upper bound of the overestimated error. Furthermore, to address it, we propose a novel Bellman underestimated operator to counteract overestimation phenomenon and then prove its contraction characteristics. At last, we propose the offline RL algorithm based on underestimated operator and diffusion policy model. Extensive experimental results on D4RL tasks show that our method can outperform state-of-the-art offline RL algorithms, which demonstrates that our theoretical analysis and underestimation way are effective for offline RL tasks.