In[]:=
CompoundExpression[
]
​​deploy
Mon 13 Nov 2023 17:19:12
In[]:=
Clear["Global`*"];​​d=2000;​​h=1./Range[d];​​h=h/Total[h];​​​​outer2[h_]:=Transpose[{h}].{h};​​​​stepL1SGD[h_]:=
2
Tr[h]+2Max[h]
;​​​​stepL2SGDfast[h_]:=Module[{d=Length[h],normalize,step,evec},​​normalize[v_]:=v/Sqrt@Total[v*v];​​step[v_]:=2h*v+h*Total[v];​​evec=FixedPoint[normalize[step[#]]&,ConstantArray[1.,d],1000];​​2/Norm[step@evec]​​];​​l2critical=stepL2SGDfast[h];​​l1critical=stepL1SGD[h];​​l1optimal=l1critical/2;​​​​ii=IdentityMatrix[d]//N;​​H=DiagonalMatrix[h];​​Hm=outer2[h];​​getMat[α_?NumericQ]:=ii-2αH+2
2
α
H.H+
2
α
Hm;​​​​l2optimal=α/.Last@FindMinimum[Norm[getMat[α]],{α,l1optimal,0,l2critical}]
Out[]=
1.48074