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The safety constraints commonly used by existing safe reinforcement learning(RL) methods are defined only on expectation of initial states, but allow eachcertain state to be unsafe, which is unsatisfying for real-worldsafety-critical tasks. In this paper, we introduce the feasible actor-critic(FAC) algorithm, which is the first model-free constrained RL method thatconsiders statewise safety, e.g, safety for each initial state. We claim thatsome states are inherently unsafe no matter what policy we choose, while forother states there exist policies ensuring safety, where we say such states andpolicies are feasible. By constructing a statewise Lagrange function availableon RL sampling and adopting an additional neural network to approximate thestatewise Lagrange multiplier, we manage to obtain the optimal feasible policywhich ensures safety for each feasible state and the safest possible policy forinfeasible states. Furthermore, the trained multiplier net can indicate whethera given state is feasible or not through the statewise complementary slacknesscondition. We provide theoretical guarantees that FAC outperforms previousexpectation-based constrained RL methods in terms of both constraintsatisfaction and reward optimization. Experimental results on both robotlocomotive tasks and safe exploration tasks verify the safety enhancement andfeasibility interpretation of the proposed method.

Feasible Actor-Critic: Constrained Reinforcement Learning for Ensuring Statewise Safety