FedNS.m

function [obj_FedNS, loss_FedNS, transmitted_bits]=FedNS...
    (XX,YY, no_workers, num_feature, noSamples, num_iter, obj0, lambda_logistic, m, method, mu)


s1=num_feature;
s2=noSamples;
grads=ones(num_feature,no_workers);
alpha = 0.0001;
out_central=zeros(s1,1);

max_iter = num_iter;

 for i = 1:max_iter
     
     transmitted_bits(i) = i*num_feature*32;
    
    for ii =1:no_workers
        first = (ii-1)*s2+1;
        last = first+s2-1;
        
        S(:, :, ii) = gen_sketch_mat(m, num_feature, method);
        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;
  
        temp = lambda_logistic*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
        sketchHessian(:,:,ii) = S(:, :, ii) * sqrtm(temp);
        hessian(:, :, ii) = sketchHessian(:,:,ii)' * sketchHessian(:,:,ii);
        %  hessian(:, :, ii) = temp;
    end
    
    out_central=out_central-mu*sum(hessian,3)\sum(grads,2);
        %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
        %i
        obj_FedNS(i)=final_obj;
        loss_FedNS(i)=abs(final_obj-obj0);
    end   
    
end