3b91129cf07287aac3de7b8adba2196f-Supplemental-Conference.pdf

As we choosec2 = 2 and c3 = 0, all the conditions in Theorem 2.2 are satisfied. Therefore, the exponential stability of the zero solution is assured. ApplyingItˆo'sformulato log x yields: log x log x(0) = Convergence Time for ESFrom the conditions in Theorem 2.2 and the equivalent condition (10),(11), the hyperparameterb for ES can be substantially regarded as A.3.5 MoreDiscussionofAS/ES Understanding ASLoss We utilize the formula x 2(2 x,F(x) + G(x) 2F) (2 α) x G(x) 2 q(x) in (3) to construct the AS loss. Here we explain this term in more detail. Particularly, we sample5,000pointsfrom ( ρ1,, ρ20) ( θ1,, θ19) U([0,5]20) U([ 5,5]19), and get the information of the dynamics based on system(18) with (19) and (20).