Utility-Constrained Policy Optimization

Safe reinforcement learning (Safe RL) aims to maximize expected return while satisfying safety constraints, typically modeled as Constrained Markov Decision Processes (CMDPs). While primal-dual methods scale well to deep RL, they often suffer from delayed constraint correction, leading to oscillatory behavior and prolonged safety violations. In this paper, we propose Constraint-Sensitive Policy Optimization (CSPO), a first-order primal-dual method that incorporates local constraint sensitivity into policy updates. CSPO augments the primal objective with a constraint-sensitive correction derived from the shortest signed distance to the safety boundary, enabling smarter recovery steps back to safety, compensating for delayed Lagrange multiplier updates, reducing oscillations near the boundary, and preserving the KKT solutions of the original constrained problem. Experiments on navigation and locomotion benchmarks demonstrate that CSPO achieves faster safety recovery and high reward preservation, resulting in higher constrained returns compared to state-of-the-art primal-dual and penalty-based methods

Safe reinforcement learning (RL) is commonly formalized as a Constrained Markov Decision Process (CMDP), in which an agent maximizes expected reward while keeping its expected cumulative cost below a specified safety bound. Existing safe RL benchmarks predominantly report whether an algorithm is safe on average, following this expectation-based guarantee. We argue that this convention is insufficient to reliably characterize an algorithm's true safety: it fails to capture how often and how severely the safety bound is violated, whether this holds consistently across tasks and safety bounds, and whether training-time behavior is representative of behavior of the final converged policy. Therefore, we introduce (i) evaluation metrics for safe RL that address each of these concerns and in addition allow for aggregation across tasks and safety bounds. We furthermore define (ii) a safety tier system to systematically categorize and compare algorithms in terms of safety and reliability at both training and for a final policy. Using this framework, we provide (iii) an empirical safety evaluation across multiple safety navigation tasks. Our results show that aggregate metrics, distributional reporting, and task- and safety bound-specific results each reveal information the other metrics cannot. We therefore recommend reporting all three jointly, rather than compressing this information into a single value, as is common practice. We provide SafeRLEval, an open-source evaluation suite to support the reliable characterization of safety in future safe RL research.

We study \emph{online episodic Constrained Markov Decision Processes} (CMDPs) under both stochastic and adversarial constraints. We provide a novel algorithm whose guarantees greatly improve those of the state-of-the-art best-of-both-worlds algorithm introduced by Stradi et al. (2025). In the stochastic regime, \emph{i.e.}, when the constraints are sampled from fixed but unknown distributions, our method achieves $\widetilde{\mathcal{O}}(\sqrt{T})$ regret and constraint violation without relying on Slater's condition, thereby handling settings where no strictly feasible solution exists. Moreover, we provide guarantees on the stronger notion of \emph{positive} constraint violation, which does not allow to recover from large violation in the early episodes by playing strictly safe policies. In the adversarial regime, \emph{i.e.}, when the constraints may change arbitrarily between episodes, our algorithm ensures sublinear constraint violation without Slater's condition, and achieves sublinear $α$-regret with respect to the \emph{unconstrained} optimum, where $α$ is a suitably defined multiplicative approximation factor. We further validate our results through synthetic experiments, showing the practical effectiveness of our algorithm.