We appreciate the detailed, insightful, and encouraging comments from the revewiers, as well as the constructive

Subsequently, we respond to specific comments from individual reviewers. As the reveiwers noted, the main technical results (Theorems 1 and 2) are new. For MDSs (Appendix A), we worked with a quadratic form of dependent r.v.s, had to first The parameter estimation error rate depends on the minimum eigenvalue of the design matrix. We will expand on this LCB application in Sec. 3. We appreciate the detailed comments and will update the draft to address these. First, we give a concrete example above on LCB [1] where the main results can be directly used.