# Off-Policy Primal-Dual Safe Reinforcement Learning

arXiv: https://arxiv.org/abs/2401.14758 · HTML: https://mlsanity.com/paper/2401.14758/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Placed in Safe and constrained RL, one of 15 directions in Deep reinforcement learning methods.
- Builds on 27 of its 43 references that are in the map.
- First posted on arXiv 26 Jan 2024.

## Placed in

- Deep reinforcement learning methods / [Safe and constrained RL](https://mlsanity.com/deeprl/safe-and-constrained-rl/)

## Builds on (most cited first, 27 of 27)

- [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)
- [Offline Reinforcement Learning: Tutorial, Review, and Perspectives on Open Problems](https://mlsanity.com/paper/2005.01643/) (2020)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Models](https://mlsanity.com/paper/1805.12114/) (2018)
- [Deep Exploration via Bootstrapped DQN](https://mlsanity.com/paper/1602.04621/) (2016)
- [Reward Constrained Policy Optimization](https://mlsanity.com/paper/1805.11074/) (2018)
- [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)
- [Randomized Ensembled Double Q-Learning: Learning Fast Without a Model](https://mlsanity.com/paper/2101.05982/) (2021)
- [Batch Policy Learning under Constraints](https://mlsanity.com/paper/1903.08738/) (2019)
- [Reinforcement learning based recommender systems: A survey](https://mlsanity.com/paper/2101.06286/) (2021)
- [A Review of Safe Reinforcement Learning: Methods, Theory and Applications](https://mlsanity.com/paper/2205.10330/) (2022)
- [Constrained Reinforcement Learning Has Zero Duality Gap](https://mlsanity.com/paper/1910.13393/) (2019)
- [CRPO: A New Approach for Safe Reinforcement Learning with Convergence Guarantee](https://mlsanity.com/paper/2011.05869/) (2020)
- [IPO: Interior-point Policy Optimization under Constraints](https://mlsanity.com/paper/1910.09615/) (2019)
- [Pessimistic Bootstrapping for Uncertainty-Driven Offline Reinforcement Learning](https://mlsanity.com/paper/2202.11566/) (2022)
- [Deployment-Efficient Reinforcement Learning via Model-Based Offline Optimization](https://mlsanity.com/paper/2006.03647/) (2020)
- [Constraints Penalized Q-learning for Safe Offline Reinforcement Learning](https://mlsanity.com/paper/2107.09003/) (2021)
- [OmniSafe: An Infrastructure for Accelerating Safe Reinforcement Learning Research](https://mlsanity.com/paper/2305.09304/) (2023)
- [Why So Pessimistic? Estimating Uncertainties for Offline RL through Ensembles, and Why Their Independence Matters](https://mlsanity.com/paper/2205.13703/) (2022)
- [Constrained Variational Policy Optimization for Safe Reinforcement Learning](https://mlsanity.com/paper/2201.11927/) (2022)
- [COptiDICE: Offline Constrained Reinforcement Learning via Stationary Distribution Correction Estimation](https://mlsanity.com/paper/2204.08957/) (2022)
- [Constrained Decision Transformer for Offline Safe Reinforcement Learning](https://mlsanity.com/paper/2302.07351/) (2023)
- [Constrained Update Projection Approach to Safe Policy Optimization](https://mlsanity.com/paper/2209.07089/) (2022)
- [Trustworthy Reinforcement Learning Against Intrinsic Vulnerabilities: Robustness, Safety, and Generalizability](https://mlsanity.com/paper/2209.08025/) (2022)
- [Safe Offline Reinforcement Learning with Real-Time Budget Constraints](https://mlsanity.com/paper/2306.00603/) (2023)

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

- [OASIS: Conditional Distribution Shaping for Offline Safe Reinforcement Learning](https://mlsanity.com/paper/2407.14653/) (2024)
- [Return Capping: Sample-Efficient CVaR Policy Gradient Optimisation](https://mlsanity.com/paper/2504.20887/) (2025)
- [How Does the Lagrangian Guide Safe Reinforcement Learning through Diffusion Models?](https://mlsanity.com/paper/2602.02924/) (2026)
- [Optimistic Exploration for Risk-Averse Constrained Reinforcement Learning](https://mlsanity.com/paper/2507.08793/) (2025)
- [Off-Policy Safe Reinforcement Learning with Constrained Optimistic Exploration](https://mlsanity.com/paper/2603.23889/) (2026)
- [Don't Trade Off Safety: Diffusion Regularization for Constrained Offline RL](https://mlsanity.com/paper/2502.12391/) (2025)
- [Situational-Constrained Sequential Resources Allocation via Reinforcement Learning](https://mlsanity.com/paper/2506.14125/) (2025)
- [COP-Q: Safety-First Reinforcement Learning for Robot Control via Cholesky-Ordered Projection](https://mlsanity.com/paper/2606.04749/) (2026)
- [Utility-Constrained Policy Optimization](https://mlsanity.com/paper/2606.14029/) (2026)
- [Boundary-Seeking Policy Gradient for Safe Reinforcement Learning](https://mlsanity.com/paper/2608.10204/) (2026)
- [Constrained Flow Policy Updates: A Generalized Schr"odinger Bridge View](https://mlsanity.com/paper/2609.32952/) (2026)
- [Safe Score Matching: Diffusion Policies with Hamilton-Jacobi Reachability for Online Safe Reinforcement Learning](https://mlsanity.com/paper/2609.33337/) (2026)
- [VERA: Verifiable Feasibility Representations with Counterfactual Credit for Constrained Multi-Agent Control](https://mlsanity.com/paper/2609.38889/) (2026)
- [Reachability-Aware Diffusion Policy Optimization](https://mlsanity.com/paper/2610.05969/) (2026)

## Abstract (arXiv)

Primal-dual safe RL methods commonly perform iterations between the primal update of the policy and the dual update of the Lagrange Multiplier. Such a training paradigm is highly susceptible to the error in cumulative cost estimation since this estimation serves as the key bond connecting the primal and dual update processes. We show that this problem causes significant underestimation of cost when using off-policy methods, leading to the failure to satisfy the safety constraint. To address this issue, we propose conservative policy optimization, which learns a policy in a constraint-satisfying area by considering the uncertainty in cost estimation. This improves constraint satisfaction but also potentially hinders reward maximization. We then introduce local policy convexification to help eliminate such suboptimality by gradually reducing the estimation uncertainty. We provide theoretical interpretations of the joint coupling effect of these two ingredients and further verify them by extensive experiments. Results on benchmark tasks show that our method not only achieves an asymptotic performance comparable to state-of-the-art on-policy methods while using much fewer samples, but also significantly reduces constraint violation during training. Our code is available at https://github.com/ZifanWu/CAL.