Appendix A Fully interactive model

C.2 Gaussian Mean Estimation ............................ Next we discuss how our technique extends to the full interactive model. Here we can define a similar notion of "channel" for a communication protocol for the ith player We proceed to prove a bound similar to Theorem 1 in terms of the "channel" defined in Eq. (17), as Theorem 4 (Information contraction bound). We can see the bound is in identical form to Theorem 1 except that we replace each player's channel Analogously to Eq. (33), we can get Plugging the above bound into Eq. We here provide a variant of Talagrand's transportation-cost inequality which is used in deriving Eq. (5) (under Assumption 3) in the second part of Theorem 2. We note that this type of result Lemma 3 (A measure change bound). We now describe and analyze the interactive algorithms for the estimation tasks we consider.