Beyond Hard Constraints: Budget-Conditioned Reachability For Safe Offline Reinforcement Learning

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.

When safety is formulated as a limit of cumulative cost, safe reinforcement learning (RL) aims to learn policies that maximize return subject to the cost constraint in data collection and deployment. Off-policy safe RL methods, although offering high sample efficiency, suffer from constraint violations due to cost-agnostic exploration and estimation bias in cumulative cost. To address this issue, we propose Constrained Optimistic eXploration Q-learning (COX-Q), an off-policy safe RL algorithm that integrates cost-bounded online exploration and conservative offline distributional value learning. First, we introduce a novel cost-constrained optimistic exploration strategy that resolves gradient conflicts between reward and cost in the action space and adaptively adjusts the trust region to control the training cost. Second, we adopt truncated quantile critics to stabilize the cost value learning. Quantile critics also quantify epistemic uncertainty to guide exploration. Experiments on safe velocity, safe navigation, and autonomous driving tasks demonstrate that COX-Q achieves high sample efficiency, competitive test safety performance, and controlled data collection cost. The results highlight COX-Q as a promising RL method for safety-critical applications.

This paper addresses the problem of safe offline reinforcement learning, which involves training a policy to satisfy safety constraints using an offline dataset. This problem is inherently challenging as it requires balancing three highly interconnected and competing objectives: satisfying safety constraints, maximizing rewards, and adhering to the behavior regularization imposed by the offline dataset. To tackle this trilogy challenge, we propose Q-learning Penalized Transformer policy (QPT), a training--inference consistent framework that bridges conditional sequence modeling with constraint-aware value estimation. QPT trains a Transformer policy that generates actions conditioned on trajectory context and target return/cost, retaining strong behavior regularization. To inject explicit safety semantics during learning, we augment sequence-model training with a Q-shaped penalty using learned reward and cost Q-functions to favor high return under low constraint violation. At inference, the same Q-functions enforce the cost threshold and choose the highest-reward feasible action, closing the loop between training and deployment. We provide a principled analysis under stylized near-deterministic CMDPs, characterizing how Q-penalized conditional generation improve safety and performance. Empirically, QPT consistently outperforms strong safe offline RL baselines across 38 tasks on the DSRL benchmark, and exhibits robust zero-shot adaptation to different constraint thresholds.