# Offline Reinforcement Learning with Closed-Form Policy Improvement Operators

arXiv: https://arxiv.org/abs/2211.15956 · HTML: https://mlsanity.com/paper/2211.15956/

## Key facts

- Cited by 14 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 52 of its 82 references that are in the map.
- First posted on arXiv 29 Nov 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 52)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [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)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [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)
- [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)
- [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)
- [Advantage-Weighted Regression: Simple and Scalable Off-Policy Reinforcement Learning](https://mlsanity.com/paper/1910.00177/) (2019)
- [Deep Reinforcement Learning that Matters](https://mlsanity.com/paper/1709.06560/) (2017)
- [Behavior Regularized Offline Reinforcement Learning](https://mlsanity.com/paper/1911.11361/) (2019)
- [Offline Reinforcement Learning as One Big Sequence Modeling Problem](https://mlsanity.com/paper/2106.02039/) (2021)
- [MOPO: Model-based Offline Policy Optimization](https://mlsanity.com/paper/2005.13239/) (2020)
- [Distributional Reinforcement Learning with Quantile Regression](https://mlsanity.com/paper/1710.10044/) (2017)
- [COMBO: Conservative Offline Model-Based Policy Optimization](https://mlsanity.com/paper/2102.08363/) (2021)
- [Implicit Quantile Networks for Distributional Reinforcement Learning](https://mlsanity.com/paper/1806.06923/) (2018)
- [Is Pessimism Provably Efficient for Offline RL?](https://mlsanity.com/paper/2012.15085/) (2020)
- [Information-Theoretic Considerations in Batch Reinforcement Learning](https://mlsanity.com/paper/1905.00360/) (2019)
- [Way Off-Policy Batch Deep Reinforcement Learning of Implicit Human Preferences in Dialog](https://mlsanity.com/paper/1907.00456/) (2019)
- [Batch Policy Learning under Constraints](https://mlsanity.com/paper/1903.08738/) (2019)

## Built on by (most cited first, 14 of 14)

- [T2V-Turbo: Breaking the Quality Bottleneck of Video Consistency Model with Mixed Reward Feedback](https://mlsanity.com/paper/2405.18750/) (2024)
- [Linear Alignment: A Closed-form Solution for Aligning Human Preferences without Tuning and Feedback](https://mlsanity.com/paper/2401.11458/) (2024)
- [Transcendence: Generative Models Can Outperform The Experts That Train Them](https://mlsanity.com/paper/2406.11741/) (2024)
- [Mastering Robot Manipulation with Multimodal Prompts through Pretraining and Multi-task Fine-tuning](https://mlsanity.com/paper/2310.09676/) (2023)
- [BPO: Staying Close to the Behavior LLM Creates Better Online LLM Alignment](https://mlsanity.com/paper/2406.12168/) (2024)
- [Value Improved Actor Critic Algorithms](https://mlsanity.com/paper/2406.01423/) (2024)
- [Offline Reinforcement Learning with Behavioral Supervisor Tuning](https://mlsanity.com/paper/2404.16399/) (2024)
- [NetworkGym: Reinforcement Learning Environments for Multi-Access Traffic Management in Network Simulation](https://mlsanity.com/paper/2411.04138/) (2024)
- [Policy-Based Trajectory Clustering in Offline Reinforcement Learning](https://mlsanity.com/paper/2506.09202/) (2025)
- [Mildly Constrained Evaluation Policy for Offline Reinforcement Learning](https://mlsanity.com/paper/2306.03680/) (2023)
- [Behavior Preference Regression for Offline Reinforcement Learning](https://mlsanity.com/paper/2503.00930/) (2025)
- [Less is More: Clustered Cross-Covariance Control for Offline RL](https://mlsanity.com/paper/2601.20765/) (2026)
- [Non-Parametric Rehearsal Learning via Conditional Mean Embeddings](https://mlsanity.com/paper/2605.08999/) (2026)
- [Multi-step Proximal Policy Improvement in Offline Reinforcement Learning](https://mlsanity.com/paper/2609.03842/) (2026)

## Abstract (arXiv)

Behavior constrained policy optimization has been demonstrated to be a successful paradigm for tackling Offline Reinforcement Learning. By exploiting historical transitions, a policy is trained to maximize a learned value function while constrained by the behavior policy to avoid a significant distributional shift. In this paper, we propose our closed-form policy improvement operators. We make a novel observation that the behavior constraint naturally motivates the use of first-order Taylor approximation, leading to a linear approximation of the policy objective. Additionally, as practical datasets are usually collected by heterogeneous policies, we model the behavior policies as a Gaussian Mixture and overcome the induced optimization difficulties by leveraging the LogSumExp's lower bound and Jensen's Inequality, giving rise to a closed-form policy improvement operator. We instantiate offline RL algorithms with our novel policy improvement operators and empirically demonstrate their effectiveness over state-of-the-art algorithms on the standard D4RL benchmark. Our code is available at https://cfpi-icml23.github.io/.