a376033f78e144f494bfc743c0be3330-Supplemental.pdf

Inthis section, we provide theoretical analysis ofHSPG. Moreover, we further point out that: (1) theSub-gradient Descent Stepwe used to achieve a "close enough" solution canbereplaced byothermethods, and(2)theAssumption 4isonlyasufficientcondition thatwecouldusetoshowthe"closeenough"condition. B.1 RelatedWork Problem (12)has been well studied indeterministic optimization with various algorithms that are capable ofreturning solutions with both lowobjectivevalueandhigh group sparsity under proper λ(95;73;42;64). For example, proximal stochastic variance-reduced gradient method (Prox-SVRG)(88)and proximal spider (Prox-Spider) (97) are developed to adopt multi-stage schemes based on the well-known variance reduction technique SVRG proposed in (46) and Spider developed in (22) respectively. Under Assumption 1, the search directiondk is a descent direction forψBk(xk), i.e., d>k ψBk(xk)<0.