Before revision:  Prior to our work, this was known only for the problem of testing under local privacy constraints (Amin, Joseph, and Mao (2020); Berrett and Butucea (2020)). Our results show that interactivity does not help for learning or testing under these two constraints. Finally, we provide the first instance of a natural family of "leaky query" local constraints under which interactive protocols strictly outperform the noninteractive ones for distribution testing .
After revision:  Prior to our work, this was known only for the problem of testing under local differential privacy and communication constraints. We also provide an example of a natural family of "leaky query" local constraints under which interactive protocols strictly outperform the noninteractive ones for distribution testing .