Response to Reviewer # 1

"I would like to see Theorem 4 reworded. It assumes that the underlying process has a correct clustering of states?" Thm 4 assumes there is an underlying partition that attains the smallest value of distortion (eq(4)). We will reword Thm 4 to make it easier to interpret. "How to find state pairs in DQN analysis" Then we screened the top 100 closest pairs and pick those with large raw-data distances.