# Safe Flow Q-Learning: Offline Safe Reinforcement Learning with Reachability-Based Flow Policies

arXiv: https://arxiv.org/abs/2603.15136 · HTML: https://mlsanity.com/paper/2603.15136/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Safe offline RL, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 36 of its 48 references that are in the map.
- First posted on arXiv 16 Mar 2026.

## Placed in

- Offline RL and imitation learning from data / [Safe offline RL](https://mlsanity.com/offlinerl/safe-offline-rl/)

## Builds on (most cited first, 30 of 36)

- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [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)
- [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)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [Constrained Policy Optimization](https://mlsanity.com/paper/1705.10528/) (2017)
- [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)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Diffusion Policies as an Expressive Policy Class for Offline Reinforcement Learning](https://mlsanity.com/paper/2208.06193/) (2022)
- [Safe Reinforcement Learning via Shielding](https://mlsanity.com/paper/1708.08611/) (2017)
- [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)
- [Control Barrier Function Based Quadratic Programs for Safety Critical Systems](https://mlsanity.com/paper/1609.06408/) (2016)
- [Hamilton-Jacobi Reachability: A Brief Overview and Recent Advances](https://mlsanity.com/paper/1709.07523/) (2017)
- [Flow Q-Learning](https://mlsanity.com/paper/2502.02538/) (2025)
- [Consistency Policy: Accelerated Visuomotor Policies via Consistency Distillation](https://mlsanity.com/paper/2405.07503/) (2024)
- [Safety-Gymnasium: A Unified Safe Reinforcement Learning Benchmark](https://mlsanity.com/paper/2310.12567/) (2023)
- [Constraints Penalized Q-learning for Safe Offline Reinforcement Learning](https://mlsanity.com/paper/2107.09003/) (2021)
- [Is Value Learning Really the Main Bottleneck in Offline RL?](https://mlsanity.com/paper/2406.09329/) (2024)
- [Energy-Weighted Flow Matching for Offline Reinforcement Learning](https://mlsanity.com/paper/2503.04975/) (2025)
- [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)
- [Safe Offline Reinforcement Learning with Feasibility-Guided Diffusion Model](https://mlsanity.com/paper/2401.10700/) (2024)
- [Enforcing Hard Constraints with Soft Barriers: Safe Reinforcement Learning in Unknown Stochastic Environments](https://mlsanity.com/paper/2209.15090/) (2022)
- [Datasets and Benchmarks for Offline Safe Reinforcement Learning](https://mlsanity.com/paper/2306.09303/) (2023)

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

- [CrossSafe: Towards Cross-Embodiment Latent Safety Filters](https://mlsanity.com/paper/2609.28984/) (2026)
- [Constrained Flow Policy Updates: A Generalized Schr"odinger Bridge View](https://mlsanity.com/paper/2609.32952/) (2026)
- [ORACLE: Optimizer-Relative Alignment for Constrained LEarning](https://mlsanity.com/paper/2610.09040/) (2026)
- [A Unified Bellman Operator for Safety-Critical Reinforcement Learning](https://mlsanity.com/paper/2610.12420/) (2026)

## Abstract (arXiv)

Offline safe reinforcement learning (RL) seeks reward-maximizing policies from static datasets under strict safety constraints. Existing methods often rely on soft expected-cost objectives or iterative generative inference, which can be insufficient for safety-critical real-time control. We propose Safe Flow Q-Learning (SafeFQL), which extends FQL to safe offline RL by combining a Hamilton--Jacobi reachability-inspired safety value function with an efficient one-step flow policy. SafeFQL learns the safety value via a self-consistency Bellman recursion, trains a flow policy by behavioral cloning, and distills it into a one-step actor for reward-maximizing safe action selection without rejection sampling at deployment. Empirically, SafeFQL trades modestly higher offline training cost for substantially lower inference latency than diffusion-style safe generative baselines, which is advantageous for real-time safety-critical deployment. Across boat navigation, and Safety Gymnasium MuJoCo tasks, SafeFQL matches or exceeds prior offline safe RL performance while substantially reducing constraint violations.