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

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.