A.1 PyTorchpseudo-codeforMIRA Algorithm1PyTorchpseudo-codeofMIRA

In this subsection, we derive the necessary and sufficient condition in proposition??. Denote B,K be some natural numbers. We introduce the proposition from [8] that proves geometrical convergence of positive concave mapping. Bycorollary 2, g(v(n);Q) is a concave mapping. Wedonotapplyweightdecayanduse cosine scheduled the learning rate.