Donggeon David Oh

Donggeon David Oh, Duy P. Nguyen, Haimin Hu et al.

Robust control barrier functions (CBFs) provide a principled mechanism for smooth safety enforcement under worst-case disturbances. However, existing approaches typically rely on explicit, closed-form structure in the dynamics (e.g., control-affine) and uncertainty models. This has led to limited scalability and generality, with most robust CBFs certifying only conservative subsets of the maximal robust safe set. In this paper, we introduce a new robust CBF framework for general nonlinear systems under bounded uncertainty. We first show that the safety value function solving the dynamic programming Isaacs equation is a valid robust discrete-time CBF that enforces safety on the maximal robust safe set. We then adopt the key reinforcement learning (RL) notion of quality function (or Q-function), which removes the need for explicit dynamics by lifting the barrier certificate into state-action space and yields a novel robust Q-CBF constraint for safety filtering. Combined with adversarial RL, this enables the synthesis and deployment of robust Q-CBFs on general nonlinear systems with black-box dynamics and unknown uncertainty structure. We validate the framework on a canonical inverted pendulum benchmark and a 36-D quadruped simulator, achieving substantially less conservative safe sets than barrier-based baselines on the pendulum and reliable safety enforcement even under adversarial uncertainty realizations on the quadruped.

Donggeon David Oh, Duy P. Nguyen, Haimin Hu et al.

Recent advances in reinforcement learning (RL) enable its use on increasingly complex tasks, but the lack of formal safety guarantees still limits its application in safety-critical settings. A common practical approach is to augment the RL policy with a safety filter that overrides unsafe actions to prevent failures during both training and deployment. However, safety filtering is often perceived as sacrificing performance and hindering the learning process. We show that this perceived safety-performance tradeoff is not inherent and prove, for the first time, that enforcing safety with a sufficiently permissive safety filter does not degrade asymptotic performance. We formalize RL safety with a safety-critical Markov decision process (SC-MDP), which requires categorical, rather than high-probability, avoidance of catastrophic failure states. Additionally, we define an associated filtered MDP in which all actions result in safe effects, thanks to a safety filter that is considered to be a part of the environment. Our main theorem establishes that (i) learning in the filtered MDP is safe categorically, (ii) standard RL convergence carries over to the filtered MDP, and (iii) any policy that is optimal in the filtered MDP-when executed through the same filter-achieves the same asymptotic return as the best safe policy in the SC-MDP, yielding a complete separation between safety enforcement and performance optimization. We validate the theory on Safety Gymnasium with representative tasks and constraints, observing zero violations during training and final performance matching or exceeding unfiltered baselines. Together, these results shed light on a long-standing question in safety-filtered learning and provide a simple, principled recipe for safe RL: train and deploy RL policies with the most permissive safety filter that is available.