# Optimal Conservative Offline RL with General Function Approximation via Augmented Lagrangian

arXiv: https://arxiv.org/abs/2211.00716 · HTML: https://mlsanity.com/paper/2211.00716/

## Key facts

- Cited by 29 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 67 of its 101 references that are in the map.
- First posted on arXiv 1 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 67)

- [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)
- [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)
- [Advantage-Weighted Regression: Simple and Scalable Off-Policy Reinforcement Learning](https://mlsanity.com/paper/1910.00177/) (2019)
- [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)
- [COMBO: Conservative Offline Model-Based Policy Optimization](https://mlsanity.com/paper/2102.08363/) (2021)
- [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)
- [Bridging Offline Reinforcement Learning and Imitation Learning: A Tale of Pessimism](https://mlsanity.com/paper/2103.12021/) (2021)
- [StarCraft II: A New Challenge for Reinforcement Learning](https://mlsanity.com/paper/1708.04782/) (2017)
- [Bellman-consistent Pessimism for Offline Reinforcement Learning](https://mlsanity.com/paper/2106.06926/) (2021)
- [DualDICE: Behavior-Agnostic Estimation of Discounted Stationary Distribution Corrections](https://mlsanity.com/paper/1906.04733/) (2019)
- [Offline Reinforcement Learning with Fisher Divergence Critic Regularization](https://mlsanity.com/paper/2103.08050/) (2021)
- [DeepStack: Expert-Level Artificial Intelligence in No-Limit Poker](https://mlsanity.com/paper/1701.01724/) (2017)
- [Breaking the Curse of Horizon: Infinite-Horizon Off-Policy Estimation](https://mlsanity.com/paper/1810.12429/) (2018)
- [Keep Doing What Worked: Behavioral Modelling Priors for Offline Reinforcement Learning](https://mlsanity.com/paper/2002.08396/) (2020)
- [AlgaeDICE: Policy Gradient from Arbitrary Experience](https://mlsanity.com/paper/1912.02074/) (2019)
- [Pessimistic Model-based Offline Reinforcement Learning under Partial Coverage](https://mlsanity.com/paper/2107.06226/) (2021)
- [Hybrid RL: Using Both Offline and Online Data Can Make RL Efficient](https://mlsanity.com/paper/2210.06718/) (2022)
- [Neural Policy Gradient Methods: Global Optimality and Rates of Convergence](https://mlsanity.com/paper/1909.01150/) (2019)
- [Minimax Weight and Q-Function Learning for Off-Policy Evaluation](https://mlsanity.com/paper/1910.12809/) (2019)
- [Is a Good Representation Sufficient for Sample Efficient Reinforcement Learning?](https://mlsanity.com/paper/1910.03016/) (2019)
- [What are the Statistical Limits of Offline RL with Linear Function Approximation?](https://mlsanity.com/paper/2010.11895/) (2020)
- [Representation Learning for Online and Offline RL in Low-rank MDPs](https://mlsanity.com/paper/2110.04652/) (2021)

## Built on by (most cited first, 29 of 29)

- [Provably Mitigating Overoptimization in RLHF: Your SFT Loss is Implicitly an Adversarial Regularizer](https://mlsanity.com/paper/2405.16436/) (2024)
- [Double Pessimism is Provably Efficient for Distributionally Robust Offline Reinforcement Learning: Generic Algorithm and Robust Partial Coverage](https://mlsanity.com/paper/2305.09659/) (2023)
- [Policy learning "without" overlap: Pessimism and generalized empirical Bernstein's inequality](https://mlsanity.com/paper/2212.09900/) (2022)
- [Beyond Uniform Sampling: Offline Reinforcement Learning with Imbalanced Datasets](https://mlsanity.com/paper/2310.04413/) (2023)
- [When is Realizability Sufficient for Off-Policy Reinforcement Learning?](https://mlsanity.com/paper/2211.05311/) (2022)
- [Offline Primal-Dual Reinforcement Learning for Linear MDPs](https://mlsanity.com/paper/2305.12944/) (2023)
- [Oracle-Efficient Pessimism: Offline Policy Optimization in Contextual Bandits](https://mlsanity.com/paper/2306.07923/) (2023)
- [Importance Weighted Actor-Critic for Optimal Conservative Offline Reinforcement Learning](https://mlsanity.com/paper/2301.12714/) (2023)
- [Policy Finetuning in Reinforcement Learning via Design of Experiments using Offline Data](https://mlsanity.com/paper/2307.04354/) (2023)
- [Offline Reinforcement Learning: Role of State Aggregation and Trajectory Data](https://mlsanity.com/paper/2403.17091/) (2024)
- [Offline Minimax Soft-Q-learning Under Realizability and Partial Coverage](https://mlsanity.com/paper/2302.02392/) (2023)
- [Pessimistic Nonlinear Least-Squares Value Iteration for Offline Reinforcement Learning](https://mlsanity.com/paper/2310.01380/) (2023)
- [On Representation Complexity of Model-based and Model-free Reinforcement Learning](https://mlsanity.com/paper/2310.01706/) (2023)
- [On Sample-Efficient Offline Reinforcement Learning: Data Diversity, Posterior Sampling, and Beyond](https://mlsanity.com/paper/2401.03301/) (2024)
- [Provably Efficient Offline Goal-Conditioned Reinforcement Learning with General Function Approximation and Single-Policy Concentrability](https://mlsanity.com/paper/2302.03770/) (2023)
- [Offline Learning for Combinatorial Multi-armed Bandits](https://mlsanity.com/paper/2501.19300/) (2025)
- [Adversarially Trained Weighted Actor-Critic for Safe Offline Reinforcement Learning](https://mlsanity.com/paper/2401.00629/) (2024)
- [A Unified Linear Programming Framework for Offline Reward Learning from Human Demonstrations and Feedback](https://mlsanity.com/paper/2405.12421/) (2024)
- [Q-Distribution guided Q-learning for offline reinforcement learning: Uncertainty penalized Q-value via consistency model](https://mlsanity.com/paper/2410.20312/) (2024)
- [Learning an Optimal Assortment Policy under Observational Data](https://mlsanity.com/paper/2502.06777/) (2025)
- [On the Optimal Sample Complexity of Offline Multi-Armed Bandits with KL Regularization](https://mlsanity.com/paper/2605.02141/) (2026)
- [Achieving the Asymptotically Optimal Sample Complexity of Offline Reinforcement Learning: A DRO-Based Approach](https://mlsanity.com/paper/2305.13289/) (2023)
- [Offline RL via Feature-Occupancy Gradient Ascent](https://mlsanity.com/paper/2405.13755/) (2024)
- [Offline Reinforcement Learning with Additional Covering Distributions](https://mlsanity.com/paper/2305.12679/) (2023)
- [Neural Network Approximation for Pessimistic Offline Reinforcement Learning](https://mlsanity.com/paper/2312.11863/) (2023)
- [Offline Constrained Reinforcement Learning under Partial Data Coverage](https://mlsanity.com/paper/2505.17506/) (2025)
- [MoMA: Model-based Mirror Ascent for Offline Reinforcement Learning](https://mlsanity.com/paper/2401.11380/) (2024)
- [Reachability Weighted Offline Goal-conditioned Resampling](https://mlsanity.com/paper/2506.02577/) (2025)
- [On the Complexity of Offline Reinforcement Learning with Q^star-Approximation and Partial Coverage](https://mlsanity.com/paper/2602.12107/) (2026)

## Abstract (arXiv)

Offline reinforcement learning (RL), which refers to decision-making from a previously-collected dataset of interactions, has received significant attention over the past years. Much effort has focused on improving offline RL practicality by addressing the prevalent issue of partial data coverage through various forms of conservative policy learning. While the majority of algorithms do not have finite-sample guarantees, several provable conservative offline RL algorithms are designed and analyzed within the single-policy concentrability framework that handles partial coverage. Yet, in the nonlinear function approximation setting where confidence intervals are difficult to obtain, existing provable algorithms suffer from computational intractability, prohibitively strong assumptions, and suboptimal statistical rates. In this paper, we leverage the marginalized importance sampling (MIS) formulation of RL and present the first set of offline RL algorithms that are statistically optimal and practical under general function approximation and single-policy concentrability, bypassing the need for uncertainty quantification. We identify that the key to successfully solving the sample-based approximation of the MIS problem is ensuring that certain occupancy validity constraints are nearly satisfied. We enforce these constraints by a novel application of the augmented Lagrangian method and prove the following result: with the MIS formulation, augmented Lagrangian is enough for statistically optimal offline RL. In stark contrast to prior algorithms that induce additional conservatism through methods such as behavior regularization, our approach provably eliminates this need and reinterprets regularizers as "enforcers of occupancy validity" than "promoters of conservatism."