# Adversarially Trained Weighted Actor-Critic for Safe Offline Reinforcement Learning

arXiv: https://arxiv.org/abs/2401.00629 · HTML: https://mlsanity.com/paper/2401.00629/

## Key facts

- Cited by 4 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 41 of its 59 references that are in the map.
- First posted on arXiv 1 Jan 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 41)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [Decision Transformer: Reinforcement Learning via Sequence Modeling](https://mlsanity.com/paper/2106.01345/) (2021)
- [Off-Policy Deep Reinforcement Learning without Exploration](https://mlsanity.com/paper/1812.02900/) (2018)
- [Constrained Policy Optimization](https://mlsanity.com/paper/1705.10528/) (2017)
- [Stabilizing Off-Policy Q-Learning via Bootstrapping Error Reduction](https://mlsanity.com/paper/1906.00949/) (2019)
- [Risk-Constrained Reinforcement Learning with Percentile Risk Criteria](https://mlsanity.com/paper/1512.01629/) (2015)
- [Responsive Safety in Reinforcement Learning by PID Lagrangian Methods](https://mlsanity.com/paper/2007.03964/) (2020)
- [Information-Theoretic Considerations in Batch Reinforcement Learning](https://mlsanity.com/paper/1905.00360/) (2019)
- [A Theory of Regularized Markov Decision Processes](https://mlsanity.com/paper/1901.11275/) (2019)
- [Bridging Offline Reinforcement Learning and Imitation Learning: A Tale of Pessimism](https://mlsanity.com/paper/2103.12021/) (2021)
- [Bellman-consistent Pessimism for Offline Reinforcement Learning](https://mlsanity.com/paper/2106.06926/) (2021)
- [Batch Policy Learning under Constraints](https://mlsanity.com/paper/1903.08738/) (2019)
- [Keep Doing What Worked: Behavioral Modelling Priors for Offline Reinforcement Learning](https://mlsanity.com/paper/2002.08396/) (2020)
- [Pessimistic Model-based Offline Reinforcement Learning under Partial Coverage](https://mlsanity.com/paper/2107.06226/) (2021)
- [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)
- [Exploration-Exploitation in Constrained MDPs](https://mlsanity.com/paper/2003.02189/) (2020)
- [Safe Policy Improvement with Baseline Bootstrapping](https://mlsanity.com/paper/1712.06924/) (2017)
- [Offline Reinforcement Learning with Realizability and Single-policy Concentrability](https://mlsanity.com/paper/2202.04634/) (2022)
- [OptiDICE: Offline Policy Optimization via Stationary Distribution Correction Estimation](https://mlsanity.com/paper/2106.10783/) (2021)
- [Variational Policy Gradient Method for Reinforcement Learning with General Utilities](https://mlsanity.com/paper/2007.02151/) (2020)
- [Adversarially Trained Actor Critic for Offline Reinforcement Learning](https://mlsanity.com/paper/2202.02446/) (2022)
- [Batch Value-function Approximation with Only Realizability](https://mlsanity.com/paper/2008.04990/) (2020)
- [Toward the Fundamental Limits of Imitation Learning](https://mlsanity.com/paper/2009.05990/) (2020)
- [Constraints Penalized Q-learning for Safe Offline Reinforcement Learning](https://mlsanity.com/paper/2107.09003/) (2021)
- [Towards Instance-Optimal Offline Reinforcement Learning with Pessimism](https://mlsanity.com/paper/2110.08695/) (2021)
- [COptiDICE: Offline Constrained Reinforcement Learning via Stationary Distribution Correction Estimation](https://mlsanity.com/paper/2204.08957/) (2022)
- [Batch Policy Learning in Average Reward Markov Decision Processes](https://mlsanity.com/paper/2007.11771/) (2020)

## Built on by (most cited first, 4 of 4)

- [V-OCBF: Learning Safety Filters from Offline Data via Value-Guided Offline Control Barrier Functions](https://mlsanity.com/paper/2512.10822/) (2025)
- [Offline Constrained Reinforcement Learning under Partial Data Coverage](https://mlsanity.com/paper/2505.17506/) (2025)
- [Online Optimization for Offline Safe Reinforcement Learning](https://mlsanity.com/paper/2510.22027/) (2025)
- [GAS: Enhancing Reward-Cost Balance of Generative Model-assisted Offline Safe RL](https://mlsanity.com/paper/2602.05323/) (2026)

## Abstract (arXiv)

We propose WSAC (Weighted Safe Actor-Critic), a novel algorithm for Safe Offline Reinforcement Learning (RL) under functional approximation, which can robustly optimize policies to improve upon an arbitrary reference policy with limited data coverage. WSAC is designed as a two-player Stackelberg game to optimize a refined objective function. The actor optimizes the policy against two adversarially trained value critics with small importance-weighted Bellman errors, which focus on scenarios where the actor's performance is inferior to the reference policy. In theory, we demonstrate that when the actor employs a no-regret optimization oracle, WSAC achieves a number of guarantees: (i) For the first time in the safe offline RL setting, we establish that WSAC can produce a policy that outperforms any reference policy while maintaining the same level of safety, which is critical to designing a safe algorithm for offline RL. (ii) WSAC achieves the optimal statistical convergence rate of 1/√N to the reference policy, where N is the size of the offline dataset. (iii) We theoretically show that WSAC guarantees a safe policy improvement across a broad range of hyperparameters that control the degree of pessimism, indicating its practical robustness. Additionally, we offer a practical version of WSAC and compare it with existing state-of-the-art safe offline RL algorithms in several continuous control environments. WSAC outperforms all baselines across a range of tasks, supporting the theoretical results.