Abstract:In this paper, we establish lower bounds for the oracle complexity of the first-order methods minimizing regularized convex functions. We consider the composite representation of the objective. The smooth part has Hölder continuous gradient of degree ν ∈ [0, 1] and is accessible by a black-box local oracle. The composite part is a power of a norm. We prove that the best possible rate for the first-order methods in the large-scale setting for Euclidean norms is of the order O(k −p(1+3ν)/(2(p−1−ν)) ) for the fun… Show more
Set email alert for when this publication receives citations?
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.