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nips2018synlogit.m
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nips2018synlogit.m
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%% LAG - logistic regression real data
clear all
close all
%% data allocation
[Xdata_28] = load('data2/data.txt');
[ydata_28] = load('data2/y.txt');
[Xdata_29] = load('data9/data.txt');
[ydata_29] = load('data9/y.txt');
[Xdata_30] = load('data11/data.txt');
[ydata_30] = load('data11/y.txt');
accuracy=1e-7;
num_iter=30000;
num_split=3;
num_workers=num_split*3;
X=cell(num_workers);
y=cell(num_workers);
num_feature=size(Xdata_29(1:50,:),2);
total_sample=size(Xdata_29(1:50,:),1);
Xdata=randn(total_sample,num_feature);
ydata=[ydata_29(1:50)];
[Q R]=qr(Xdata);
diagmatrix=diag(ones(total_sample,1));
% [lambda]=eig(Xdata'*Xdata);
Hmax=zeros(num_workers,1);
for i=1:num_workers
X{i}=1^(i-1)*Q(:,i)*Q(:,i)'+diag(ones(total_sample,1));
Hmax(i)=max(eig(X{i}'*X{i}));
y{i}=ydata;
end
num_feature=size(X{1},2);
Hmax_sum=sum(Hmax);
%% data pre-analysis
lambda=0.001;
Hmax=zeros(num_workers,1);
for i=1:num_workers
Hmax(i)=0.25*max(abs(eig(X{i}'*X{i})))+lambda;
end
Hmax_sum=sum(Hmax);
hfun=Hmax_sum./Hmax;
nonprob=Hmax/Hmax_sum;
Hmin=zeros(num_workers,1);
Hcond=zeros(num_workers,1);
for i=1:num_workers
Hmin(i)=lambda;
Hcond(i)=Hmax(i)/Hmin(i);
end
X_fede=[];
y_fede=[];
for i=1:num_workers
X_fede=[X_fede;X{i}];
y_fede=[y_fede;y{i}];
end
triggerslot=10;
Hmaxall=0.25*max(eig(X_fede'*X_fede))+lambda;
[cdff,cdfx] = ecdf(Hmax*num_workers/Hmaxall);
comm_save=0;
for i=1:triggerslot
comm_save=comm_save+(1/i-1/(i+1))*cdff(find(cdfx>=min(max(cdfx),sqrt(1/(triggerslot*i))),1));
end
heterconst=mean(exp(Hmax/Hmaxall));
heterconst2=mean(Hmax/Hmaxall);
rate=1/(1+sum(Hmin)/(4*sum(Hmax)));
%% parameter initialization
%triggerslot=100;
theta=zeros(num_feature,num_iter);
grads=ones(num_feature,num_workers);
%stepsize=1/(num_workers*max(Hmax));
stepsize=1/Hmaxall;
thrd=10/(stepsize^2*num_workers^2)/triggerslot;
comm_count=ones(num_workers,1);
theta2=zeros(num_feature,num_iter);
grads2=ones(num_feature,1);
stepsize2=stepsize;
theta3=zeros(num_feature,num_iter);
grads3=ones(num_feature,num_workers);
stepsize3=stepsize2/num_workers; % cyclic access learning
theta4=zeros(num_feature,num_iter);
grads4=ones(num_feature,num_workers);
stepsize4=stepsize/num_workers; % nonuniform-random access learning
thrd5=1/(stepsize^2*num_workers^2)/triggerslot;
theta5=zeros(num_feature,1);
grads5=ones(num_feature,num_workers);
stepsize5=stepsize;
comm_count5=ones(num_workers,1);
%thrd6=2/(stepsize*num_workers);
theta6=zeros(num_feature,1);
grads6=ones(num_feature,1);
stepsize6=0.5*stepsize;
comm_count6=ones(num_workers,1);
theta7=zeros(num_feature,1);
grads7=ones(num_feature,num_workers);
stepsize7=stepsize;
comm_count7=ones(num_workers,1);
% lambda=0.000;
%% GD
comm_error2=[];
comm_grad2=[];
for iter=1:num_iter*10
if mod(iter,1000)==0
iter
end
% central server computation
if iter>1
grads2=-(X_fede'*(y_fede./(1+exp(y_fede.*(X_fede*theta2(:,iter))))))+num_workers*lambda*theta2(:,iter);
end
grad_error2(iter)=norm(sum(grads2,2),2);
loss2(iter)=num_workers*lambda*0.5*norm(theta2(:,iter))^2+sum(log(1+exp(-y_fede.*(X_fede*theta2(:,iter)))));
theta2(:,iter+1)=theta2(:,iter)-stepsize2*grads2;
comm_error2=[comm_error2;iter*num_workers,loss2(iter)];
comm_grad2=[comm_grad2;iter*num_workers,grad_error2(iter)];
end
for iter=i:num_iter
if abs(loss2(iter)-loss2(end))<accuracy
fprintf('Communication rounds of GD\n');
iter*num_workers
break
end
end
%% LAG-PS
comm_iter=1;
comm_index=zeros(num_workers,num_iter);
comm_error=[];
comm_grad=[];
theta_temp=zeros(num_feature,num_workers);
for iter=1:num_iter*5
comm_flag=0;
% local worker computation
for i=1:num_workers
if iter>triggerslot
trigger=0;
for n=1:triggerslot
trigger=trigger+norm(theta(:,iter-(n-1))-theta(:,iter-n),2)^2;
end
if Hmax(i)^2*norm(theta_temp(:,i)-theta(:,iter),2)^2>thrd*trigger
grads(:,i)=-(X{i}'*(y{i}./(1+exp(y{i}.*(X{i}*theta(:,iter))))))+lambda*theta(:,iter);
theta_temp(:,i)=theta(:,iter);
comm_index(i,iter)=1;
comm_count(i)=comm_count(i)+1;
comm_iter=comm_iter+1;
comm_flag=1;
end
end
end
% central server computation
grad_error(iter)=norm(sum(grads,2),2);
loss(iter)=num_workers*lambda*0.5*norm(theta(:,iter))^2+sum(log(1+exp(-y_fede.*(X_fede*theta(:,iter)))));
theta(:,iter+1)=theta(:,iter)-stepsize*sum(grads,2);
if comm_flag==1
comm_error=[comm_error;comm_iter,loss(iter)];
comm_grad=[comm_grad;comm_iter,grad_error(iter)];
elseif mod(iter,1000)==0
iter
comm_iter=comm_iter+1;
comm_error=[comm_error;comm_iter,loss(iter)];
comm_grad=[comm_grad;comm_iter,grad_error(iter)];
end
if abs(loss(iter)-loss2(end))<accuracy
fprintf('Communication rounds of LAG-PS\n');
comm_iter
break
end
end
%% LAG-WK
comm_iter5=1;
comm_index5=zeros(num_workers,num_iter);
comm_error5=[];
comm_grad5=[];
for iter=1:num_iter*5
comm_flag=0;
% local worker computation
for i=1:num_workers
grad_temp=-(X{i}'*(y{i}./(1+exp(y{i}.*(X{i}*theta5(:,iter))))))+lambda*theta5(:,iter);
if iter>triggerslot
trigger=0;
for n=1:triggerslot
trigger=trigger+norm(theta5(:,iter-(n-1))-theta5(:,iter-n),2)^2;
end
if norm(grad_temp-grads5(:,i),2)^2>thrd5*trigger
grads5(:,i)=grad_temp;
comm_count5(i)=comm_count5(i)+1;
comm_index5(i,iter)=1;
comm_iter5=comm_iter5+1;
comm_flag=1;
end
end
end
grad_error5(iter)=norm(sum(grads5,2),2);
loss5(iter)=num_workers*lambda*0.5*norm(theta5(:,iter))^2+sum(log(1+exp(-y_fede.*(X_fede*theta5(:,iter)))));
if comm_flag==1
comm_error5=[comm_error5;comm_iter5,loss5(iter)];
comm_grad5=[comm_grad5;comm_iter5,grad_error5(iter)];
elseif mod(iter,1000)==0
iter
comm_iter5=comm_iter5+1;
comm_error5=[comm_error5;comm_iter5,loss5(iter)];
comm_grad5=[comm_grad5;comm_iter5,grad_error5(iter)];
end
theta5(:,iter+1)=theta5(:,iter)-stepsize5*sum(grads5,2);
if abs(loss5(iter)-loss2(end))<accuracy
fprintf('Communication rounds of LAG-WK\n');
comm_iter5
break
end
end
%% cyclic IAG
for iter=1:num_iter*floor(num_workers)
if mod(iter,100)==0
iter
end
if iter>1
% local worker computation
i=mod(iter,num_workers)+1;
grads3(:,i)=-(X{i}'*(y{i}./(1+exp(y{i}.*(X{i}*theta3(:,iter))))))+lambda*theta3(:,iter);
end
% central server computation
grad_error3(iter)=norm(sum(grads3,2),2);
loss3(iter)=num_workers*lambda*0.5*norm(theta3(:,iter))^2+sum(log(1+exp(-y_fede.*(X_fede*theta3(:,iter)))));
theta3(:,iter+1)=theta3(:,iter)-stepsize3*sum(grads3,2);
if abs(loss3(iter)-loss2(end))<accuracy
fprintf('Communication rounds of Cyc-IAG\n');
iter
break
end
end
%% non-uniform RANDOMIZED IAG
for iter=1:num_iter*floor(num_workers)
if mod(iter,100)==0
iter
end
% local worker computation
workprob=rand;
for i=1:num_workers
if workprob<=sum(nonprob(1:i));
break;
end
end
%i=randi(num_workers);
if iter>1
grads4(:,i)=-(X{i}'*(y{i}./(1+exp(y{i}.*(X{i}*theta4(:,iter))))))+lambda*theta4(:,iter);
end
% central server computation
grad_error4(iter)=norm(sum(grads4,2),2);
loss4(iter)=num_workers*lambda*0.5*norm(theta4(:,iter))^2+sum(log(1+exp(-y_fede.*(X_fede*theta4(:,iter)))));
theta4(:,iter+1)=theta4(:,iter)-stepsize4*sum(grads4,2);
if abs(loss4(iter)-loss2(end))<accuracy
fprintf('Communication rounds of Num-IAG\n');
iter
break
end
end
figure
semilogy(abs(loss3-loss2(end)),'k-','LineWidth',2);
hold on
semilogy(abs(loss4-loss2(end)),'g--','LineWidth',4);
hold on
semilogy(abs(loss-loss2(end)),'r-','LineWidth',2);
hold on
semilogy(abs(loss5-loss2(end)),'r--','LineWidth',2);
hold on
semilogy(abs(loss2-loss2(end)),'b-','LineWidth',2);
xlabel('Number of iteration','fontsize',16,'fontname','Times New Roman')
ylabel('Objective error','fontsize',16,'fontname','Times New Roman')
legend('Cyc-IAG','Num-IAG','LAG-PS','LAG-WK','Batch-GD')
figure
semilogy(abs(loss3-loss2(end)),'k-','LineWidth',2);
hold on
semilogy(abs(loss4-loss2(end)),'g--','LineWidth',4);
hold on
semilogy(comm_grad(:,1),abs(comm_error(:,2)-loss2(end)),'r-','LineWidth',2);
hold on
semilogy(comm_grad5(:,1),abs(comm_error5(:,2)-loss2(end)),'r--','LineWidth',2);
hold on
semilogy(comm_grad2(:,1),abs(comm_error2(:,2)-loss2(end)),'b-','LineWidth',2);
xlabel('Number of communications (uploads)','fontsize',16,'fontname','Times New Roman')
ylabel('Objective error','fontsize',16,'fontname','Times New Roman')
legend('Cyc-IAG','Num-IAG','LAG-PS','LAG-WK','Batch-GD')