We thank the reviewers for their thoughtful comments and suggestions and we respond below to some concrete 1 questions/comments that were raised

The setup there is also a special case of our setup, where the reward is linear in the treatment vector, i.e. Hence, we omitted such an analysis. We will add some more elaborate discussion on these rates expanding on Remark 4. See response also to Reviewer #4 regarding efficiency. These extra moments can be used to construct more efficient estimators. However, these extra moment conditions have no bite in the case of homoskedastic noise.