Return ˆ α We show the following generalization of Proposition 2.1. Moreover, Alg. 4 has sample complexity The sample complexity is clear so we focus on the first statement. Theorem 4.5 in [MU17]) on these events as i varies and noting that Hence recalling (A.2) above, we conclude that The other direction is similar. Using (A.2) in the same way as above, we find First we analyze the expected sample complexity. Finally Alg. 4 has sample complexity We do this using Bayes' rule.