Most safe RL works rely on reward shaping to discourage violations of a safety constraint. However, such soft constraints do not guarantee safety. Previous works trying to enforce hard constraints in RL typical suffer from two limitations: either they need an accurate model of the environment, or their learned safety certificate only approximate without guarantees an actual safety certificate.
On the other hand, our POLICEd RL approach can provably enforce hard constraint satisfaction in closed-loop with a black-box environment. We build a repulsive buffer region in front of the constraint to prevent trajectories from approaching it. Since trajectories cannot cross this buffer, they also cannot violate the constraint.
Phase portrait of constrained output $y$ illustrating our High Relative Degree POLICEd RL method on a system of relative degree $2$. To prevent states from violating constraint $y \leq y_{max}$ (red dashed line), our policy guarantees that trajectories entering buffer region $\mathcal{B}$ (blue) cannot leave it through its upper bound (blue dotted line). Our policy makes $\ddot y$ sufficiently negative in buffer $\mathcal{B}$ to bring $\dot y$ to $0$ in all trajectories entering $\mathcal{B}$. Once $\dot y < 0$, trajectories cannot approach the constraint. Due to the states' inertia, it is physically impossible to prevent all constraint violations. For instance, $y = y_{max}$, $\dot y >> 1$ will yield $y > y_{max}$ at the next timestep. Hence, we only aim at guaranteeing the safety of trajectories entering buffer $\mathcal{B}$. We use the POLICE algorithm to make our policy affine inside buffer region $\mathcal{B}$.
