  Many applications, including natural language processing, sensor networks,
collaborative filtering, and federated learning, call for estimating discrete
distributions from data collected in batches, some of which may be
untrustworthy, erroneous, faulty, or even adversarial.
  Previous estimators for this setting ran in exponential time, and for some
regimes required a suboptimal number of batches. We provide the first
polynomial-time estimator that is optimal in the number of batches and achieves
essentially the best possible estimation accuracy.
