Feasible Policy Iteration

Safe reinforcement learning (RL) aims to solve an optimal control problem under safety constraints. Existing $\textit{direct}$ safe RL methods use the original constraint throughout the learning process. They either lack theoretical guarantees of the policy during iteration or suffer from infeasibility problems. To address this issue, we propose an $\textit{indirect}$ safe RL method called feasible policy iteration (FPI) that iteratively uses the feasible region of the last policy to constrain the current policy. The feasible region is represented by a feasibility function called constraint decay function (CDF). The core of FPI is a region-wise policy update rule called feasible policy improvement, which maximizes the return under the constraint of the CDF inside the feasible region and minimizes the CDF outside the feasible region. This update rule is always feasible and ensures that the feasible region monotonically expands and the state-value function monotonically increases inside the feasible region. Using the feasible Bellman equation, we prove that FPI converges to the maximum feasible region and the optimal state-value function. Experiments on classic control tasks and Safety Gym show that our algorithms achieve lower constraint violations and comparable or higher performance than the baselines.