  We investigate replicable learning algorithms. Ideally, we would like to
design algorithms that output the same canonical model over multiple runs, even
when different runs observe a different set of samples from the unknown data
distribution. In general, such a strong notion of replicability is not
achievable. Thus we consider two feasible notions of replicability called list
replicability and certificate replicability. Intuitively, these notions capture
the degree of (non) replicability. We design algorithms for certain learning
problems that are optimal in list and certificate complexity. We establish
matching impossibility results.
