  The safety constraints commonly used by existing safe reinforcement learning
(RL) methods are defined only on expectation of initial states, but allow each
certain state to be unsafe, which is unsatisfying for real-world
safety-critical tasks. In this paper, we introduce the feasible actor-critic
(FAC) algorithm, which is the first model-free constrained RL method that
considers statewise safety, e.g, safety for each initial state. We claim that
some states are inherently unsafe no matter what policy we choose, while for
other states there exist policies ensuring safety, where we say such states and
policies are feasible. By constructing a statewise Lagrange function available
on RL sampling and adopting an additional neural network to approximate the
statewise Lagrange multiplier, we manage to obtain the optimal feasible policy
which ensures safety for each feasible state and the safest possible policy for
infeasible states. Furthermore, the trained multiplier net can indicate whether
a given state is feasible or not through the statewise complementary slackness
condition. We provide theoretical guarantees that FAC outperforms previous
expectation-based constrained RL methods in terms of both constraint
satisfaction and reward optimization. Experimental results on both robot
locomotive tasks and safe exploration tasks verify the safety enhancement and
feasibility interpretation of the proposed method.
