  Despite the tremendous success of Reinforcement Learning (RL) algorithms in
simulation environments, applying RL to real-world applications still faces
many challenges. A major concern is safety, in another word, constraint
satisfaction. State-wise constraints are one of the most common constraints in
real-world applications and one of the most challenging constraints in Safe RL.
Enforcing state-wise constraints is necessary and essential to many challenging
tasks such as autonomous driving, robot manipulation. This paper provides a
comprehensive review of existing approaches that address state-wise constraints
in RL. Under the framework of State-wise Constrained Markov Decision Process
(SCMDP), we will discuss the connections, differences, and trade-offs of
existing approaches in terms of (i) safety guarantee and scalability, (ii)
safety and reward performance, and (iii) safety after convergence and during
training. We also summarize limitations of current methods and discuss
potential future directions.
