MM ▁methods ▁suffer ▁from ▁cur se ▁of ▁dimensional ity . ▁Their ▁convergence ▁rate ▁is ▁proportional ▁to ▁square ▁of ▁the ▁dimension ▁and ▁in ▁practice ▁they ▁scale ▁poor ly . ▁See ▁figure ▁RE A SON ▁vs ▁Sto ch astic ▁AD MM ▁ ▁Rec ently , ▁a ▁general ▁framework ▁has ▁been ▁proposed ▁for ▁st ochastic ▁optimization ▁in ▁high - dim ensions ▁that ▁solves ▁this ▁bott l ene ck ▁by ▁adding ▁simple ▁and ▁cheap ▁modifications ▁to ▁AD MM . ▁The ▁method ▁is ▁called ▁RE A SON ▁( Reg ular ized ▁E po ch - based ▁Ad mm ▁for ▁Sto ch astic ▁Opt im ization ▁in ▁high - dim ens io N ). ▁The ▁modifications ▁are ▁in ▁terms ▁of ▁added ▁projection ▁which ▁goes ▁a ▁long ▁way ▁and ▁results ▁in ▁log arith mic ▁dimension ▁dependency . ▁RE A SON ▁can ▁be ▁performed ▁on ▁any ▁regular ized ▁optimization ▁with ▁any ▁number ▁of ▁regular izers . ▁The ▁specific ▁cases ▁of ▁sparse ▁optimization ▁framework ▁and ▁no isy ▁decomposition ▁framework ▁are ▁discussed ▁further . ▁In ▁both ▁cases , ▁RE A SON ▁obtain s ▁minim ax ▁optimal ▁convergence ▁rate . ▁RE A SON ▁provides ▁the ▁first ▁online ▁guarante es ▁for ▁no isy ▁matrix ▁decomposition . ▁Ex periment ▁results ▁show ▁that ▁in ▁a for ement ioned ▁cases , ▁RE A SON ▁out per forms ▁state - of - the - art . ▁ ▁Altern ative ▁approaches ▁ ▁Se qu ential ▁quadratic ▁programming ▁ ▁Se qu ential ▁linear ▁programming ▁ ▁Se qu ential ▁linear - quad r atic ▁programming ▁ ▁Software ▁ ▁Open ▁source ▁and ▁non