Directional Constraints for Efficient Exploration in Safe Reinforcement Learning

Safe exploration remains a fundamental challenge in reinforcement learning (RL), limiting the deployment of RL agents in the real world. We propose Sampling-Based Safe Reinforcement Learning (SBSRL), a model-based RL algorithm that maintains safety throughout the learning process by enforcing constraints jointly across a finite set of dynamics samples. This formulation approximates an intractable worst-case optimization over uncertain dynamics and enables practical safety guarantees in continuous domains. We further introduce an exploration strategy based on constraining epistemic uncertainty, eliminating the need for explicit exploration bonuses. Under regularity conditions, we derive high-probability guarantees of safety throughout learning and a finite-time sample complexity bound for recovering a near-optimal policy. Empirically, SBSRL achieves safe and efficient exploration both in simulation and in real robotic hardware, and readily extends to practical deep-ensemble implementations that scale to high-dimensional continuous control problems.

Reinforcement Learning (RL) has demonstrated remarkable capabilities for solving complex robotic control problems, but its lack of safety guarantees severely limits deployment on hardware. In particular, as legged robots and manipulators often operate near safety-critical boundaries, out-of-distribution states can lead to failure upon deployment. To address this, we introduce Acc-CBF-QP, an acceleration-based Quadratic Program (QP) safety filter using Control Barrier Functions (CBFs) that constrains any RL policy onto a safe set at runtime without modifying training. The method applies to unconstrained and Safe-RL policies, and enforces joint position, velocity, torque, and collision constraints within a unified optimization framework. A key contribution is the formulation of RL+QP tasks that regulate deviation from the RL command when constraints would otherwise be violated. We introduce a TorqueTask, minimizing torque deviation, and a Forward Dynamics Task, minimizing induced acceleration deviation, thus providing principled control over safety-performance trade-offs. Experiments on a 7-DoF Kinova Gen3 manipulator and a 19-DoF Unitree H1 humanoid, both in simulation and on hardware, highlight substantial reductions in constraint violations. On the real H1 hardware, a Safe-RL policy alone yielded 10.04 violations/s, which were reduced by 92% to 0.80 violations/s when augmented with Acc-CBF-QP. On the Kinova Gen3, Acc-CBF-QP fully eliminated violations. Nominal task performance of the RL objective is preserved in violation-free regimes. Under aggressive velocity commands on H1, Acc-CBF-QP improves execution by preventing constraint-induced shutdowns, yielding longer survival times. The full pipeline is open-source.

Safe navigation for mobile robots demands policies that remain reliable under the high-consequence perception uncertainty of cluttered environments. Yet most existing safe reinforcement learning (RL) methods assess safety through average cumulative cost. Such metrics can mask dangerous tail-risk behaviors. To address this, we propose a framework that trains risk-sensitive policies through Conditional Value-at-Risk (CVaR) constrained optimization on an off-policy TD3 backbone and evaluates their safety margins post-training through neural network reachability verification. During training, the policy is optimized under CVaR constraints on cumulative costs, promoting sensitivity to high-cost tail outcomes rather than average behavior alone. After training, we compute action reachable sets under bounded observation uncertainty using Taylor Model analysis, yielding a safety rate metric that quantifies the proportion of evaluated states at which the policy's reachable action set remains within prescribed safety margins. A key finding is that policies trained with CVaR constraints maintain larger safety margins from obstacles across evaluated states. This makes them significantly more amenable to formal reachability verification. Experiments across ten navigation scenarios and six baselines show that our method achieves a 98.3% success rate, the highest safety verification rate among all compared methods, while revealing that average cost rankings and reachability-based safety rankings can diverge. This indicates that reachability verification captures risks which are missed by empirical cost metrics alone. We further validate our approach on a physical Clearpath Jackal robot, demonstrating successful sim-to-real transfer.