Reviews: Safe Exploration in Finite Markov Decision Processes with Gaussian Processes

The paper is well-written and clear. The proposed idea is interesting. I have the following comments/questions: 1) Does the Liptschiz assumption hold here with a probability or is it assumed to always hold? 2) Figure 1: should it be \bar{s}_2 instead of s_2 in the caption? The use of bar for non-sets is confusing. I do not see the need for the last intersection in Equation 4. 4) When you repeatedly apply Equation 4, the number of states that satisfy the safety constraint shrinks because you use Liptschiz in the worst scenario sense.