CSPO: Constraint-Sensitive Policy Optimization for Safe Reinforcement Learning

Safe reinforcement learning maximizes reward subject to safety constraints. For Constrained Markov Decision Processes, the linear-programming view over occupancy measures implies that whenever the constraint is active at optimality, the optimal policy lies exactly on the constraint boundary, yet standard gradient-based methods do not exploit this structure and often settle in the feasible interior. We introduce Boundary-Seeking Policy Gradient (BSPG), a first-order method whose update combines a tangential component that improves reward while preserving cost to first order with a signed, residual-driven normal component that regulates the policy toward the active boundary from either side; the combined direction admits an algebraic Lagrangian form with an induced coefficient and no learned dual variable. Under exact gradients and stated regularity conditions, the constraint residual converges to zero from either side with a finite-horizon $O(1/\sqrt{T})$ bound, the tangential component is a reward-ascent direction on the boundary, and any convergent parameter sequence is stationary on the active constraint set, satisfying the KKT conditions when the limit is also a local maximizer over the feasible set. This complements existing analyses, which certify feasibility but do not characterize the constraint value at convergence. On a standard Safety-Gymnasium navigation task, BSPG attains higher reward while tracking the boundary more tightly than the compared baselines.

Reinforcement learning (RL) has emerged as a promising solution to accomplish complex robotic control tasks; however, most of the current work ignores the safety requirements. Safe RL seeks to maximize task performance while satisfying explicit physical constraints, but current algorithms struggle to learn the policy efficiently with precise constraint satisfaction. This work proposes PPO-EAL, a novel first-order constrained policy optimization framework that integrates exact augmented Lagrangian optimization into proximal policy optimization for safe robotic control. By combining clipped policy updates with exact quadratic penalty terms, PPO-EAL achieves theoretically grounded constraint enforcement without requiring impractically large penalty factors. A momentum-regulated multiplier update further improves dual-variable stability, reducing constraint oscillation and unsafe behavior while preserving task performance. We provide exactness and convergence analysis under standard stochastic approximation assumptions. Extensive validation across diverse GPU-accelerated robotic benchmarks-including cart-pole balancing, cart-double-pendulum stabilization, 7-DoF Franka end-effector reaching, and quadrupedal locomotion-demonstrates superior safety precision and reward performance compared with state-of-the-art first-order safe RL baselines. Finally, we demonstrate zero-shot sim-to-real deployment in a contact-rich gear assembly task, where PPO-EAL substantially improves task success, reduces peak contact force, and enhances operational robustness. These results establish PPO-EAL as a general and practically deployable safe RL framework for diverse safety-critical robotic systems.

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.