Before revision:  We focus on the inference tasks of learning (density estimation) and identity testing ( goodness-of-fit ) for discrete distributionsunder total variation distance, and establish general lower bounds that take into account the local constraints modeled as a channel family. Our main technical contribution is an approach to handle the correlation that builds due to interactivity and quantifies how effectively one can exploit this correlation in spite of the local constraints.
After revision:  We focus on the inference tasks of learning (density estimation) and identity testing ( goodness-of-fit testing and estimation of discrete distributions. From prior work, these tasks are well understood under noninteractive protocols. Extending these approaches directly for interactive protocols is difficult due to correlations that can build due to interactivity and quantifies how effectively one can exploit this correlation in spite of the local constraints.