  We investigate the effects of non-Hermiticity on topological pumping, and
uncover a connection between a topological edge invariant based on topological
pumping and the winding numbers of exceptional points. In Hermitian lattices,
it is known that the topologically nontrivial regime of the topological pump
only arises in the infinite-system limit. In finite non-Hermitian lattices,
however, topologically nontrivial behavior can also appear. We show that this
can be understood in terms of the effects of encircling a pair of exceptional
points during a pumping cycle. This phenomenon is observed experimentally, in a
non-Hermitian microwave network containing variable gain amplifiers.
