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newton_QADMM.m
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function [obj_GD, loss_GD,transmitted_bits]=newton_QADMM...
(XX,YY, no_workers, num_feature, noSamples, num_iter, obj0, lambda_logistic, bitsToSend, rho, alpha)
s1=num_feature;
s2=noSamples;
%rho=500;
%alpha = 0;
grads=ones(num_feature,no_workers);
hessian = zeros(num_feature,num_feature, no_workers);
prev_w=zeros(s1,no_workers);
q_w=zeros(s1,no_workers);
w_central = zeros(num_feature,1);
w=zeros(num_feature,no_workers);
lambda=zeros(num_feature,no_workers);
out_central=zeros(s1,1);
max_iter = num_iter;
R=1;
for i = 1:max_iter
% if i==1
% transmitted_bits(i)=num_feature*bitsToSend+32;
% else
% transmitted_bits(i)=transmitted_bits(i-1)+num_feature*bitsToSend+32;
% end
transmitted_bits(i) = i*R*(num_feature*bitsToSend + 32);
for ii =1:no_workers
first = (ii-1)*s2+1;
last = first+s2-1;
%grads(:,ii)=XX(first:last,1:num_feature)'*XX(first:last,1:num_feature)*out_central-XX(first:last,1:num_feature)'*YY(first:last);
grads(:,ii)=-(XX(first:last,1:num_feature)'*(YY(first:last)./(1+exp(YY(first:last).*(XX(first:last,1:num_feature)*out_central)))))+lambda_logistic*out_central;
%hessian(:,:,ii)= XX(first:last,1:num_feature)'*XX(first:last,1:num_feature);
if (i==1)
temp = (lambda_logistic + alpha)*eye(num_feature,num_feature);
for jj=first:last
temp=temp+YY(jj)^2*XX(jj,:)'*XX(jj,:)*(exp(YY(jj)*XX(jj,:)*out_central)/(1+exp(YY(jj)*XX(jj,:)*out_central))^2);
end
hessian(:,:,ii)=temp;
end
end
for r=1:R
for ii=1:no_workers
%temp2= (hessian(:,:,ii)+(rho)*eye(num_feature,num_feature))\(grads(:,ii)-lambda(:,ii)+rho*w_central);
temp2= pinv(hessian(:,:,ii)+(rho)*eye(num_feature,num_feature))*(grads(:,ii)-lambda(:,ii)+rho*w_central);
w(:,ii) =temp2;
[q_w(:,ii)]=stochastic_quantization(q_w(:,ii),w(:,ii),prev_w(:,ii),bitsToSend);
w(:,ii) = q_w(:,ii);
prev_w(:,ii) = q_w(:,ii);
end
w_central = (rho * sum(w,2)+sum(lambda,2))/(no_workers*rho);
for ii=1:no_workers
lambda(:,ii)=lambda(:,ii)+rho*(w(:,ii)-w_central);
end
end
out_central=out_central-w_central;
%final_obj = 0;
final_obj =lambda_logistic*0.5*norm(out_central)^2;
for ii =1:no_workers
first = (ii-1)*s2+1;
last = first+s2-1;
%final_obj = final_obj + 0.5*norm(XX(first:last,1:s1)*out_central - YY(first:last))^2;
final_obj = final_obj+sum(log(1+exp(-YY(first:last).*(XX(first:last,1:s1)*out_central))));
end
obj_GD(i)=final_obj;
final_obj
loss_GD(i)=abs(final_obj-obj0);
abs(final_obj-obj0)
end
end