List and Certificate Complexities in Replicable Learning

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.