General lower bounds beyond zero-respecting algorithms

Extend the lower bounds for constrained nonsmooth nonconvex stochastic optimization from randomized zero-respecting first-order algorithms to arbitrary randomized algorithms.

Background

The lower-bound results in the paper are formally established for possibly randomized zero-respecting first-order algorithms, a class that includes the algorithms considered in the work. Although the authors state that extending the result to arbitrary randomized algorithms appears feasible through known reduction techniques, that extension is not formally proved.