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linbcfwopt.m
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linbcfwopt.m
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function res = linbcfwopt(X,lambda,nConst,k,kapa,blocks,block_square,slack_block,prob,n_iter)
X = full(X);
X = double(X);
X = cat(2,X,100*ones(size(X,1),1));
n = size(X,1);
n_iter
T = zeros(n*k+nConst,1);
params.MSK_IPAR_LOG = 0;
n_blocks = length(blocks);
for i=1:n_blocks
prob(i).c = rand(length(blocks{i}),1);
[~,res] = mosekopt('minimize echo(0)',prob(i),params);
Ti = res.sol.itr.xx;
T(blocks{i}) = Ti;
end
fprintf('building P ...\n');
P = build_PQ(X,lambda);
fprintf('done ! ...\n');
% Init a Z in the convex hull
fprintf('Begin LINBCFW iterations ...\n');
gap = 10*ones(length(blocks),1);
samples = rand(n_iter+1,1);
Z = reshape(T(1:n*k),n,k);
fprintf('init W ...\n');
W = P*Z;
total = size(X,1);
display_loss_value = 0;
gap_values = [];
e_time = [];
epoch_update = 10;
gap_update = epoch_update*total;
tic;
fprintf('building blocks ...\n');
for i=1:n_blocks
fprintf('preparing block: %d \n',i);
X_block{i} = X(block_square{i},:);
end
fprintf('done ! \n');
c = 0;
%clear X;
for i=1:n_blocks
i
P_block{i} = P(:,block_square{i});
end
clear P;
display = 10;
n_blocks
tic;
for i=1:n_iter
if mod(i,1000) == 0
fprintf('updating gap block ...\n');
Z = reshape(T(1:n*k),n,k);
for j=1:n_blocks
fprintf('block : %d\n',j);
current_block = blocks{j};
current_block_square = block_square{j};
current_slack_block = slack_block{j};
% computing gradient with the trick
grad = Z(current_block_square,:) - X_block{j}*W;
grad = reshape(grad,[],1);
%add slacks to the gradient
if length(current_slack_block) > 0
slacks = T(n*k+1:end);
grad = cat(1,grad,n*kapa*slacks(current_slack_block));
end
prob(j).c = grad;
[~,Tmin] = mosekopt('minimize echo(0)',prob(j));
Tmin = Tmin.sol.itr.xx;
diff = T(current_block)-Tmin;
gap(j) = diff'*grad;
gap(j) = 1/n*gap(j);
end
total_gap = sum(gap);
gap_values = [gap_values; total_gap];
tt = toc;
e_time = [e_time;tt];
fprintf('Gap: %.4e ------------------------------------\n',total_gap);
%{
Z = reshape(T(1:n*k),n,k);
aux2 = Z.*(Z-X*(P*Z));
d_slacks = T(n*k+1:end);
loss = sum(aux2(:))/n + kapa*norm(d_slacks)^2;
toc;
%}
end
%adaptatively sampling a block
r = samples(i+1);
prob_distribution = [0;cumsum(gap(:))/sum(gap)];
[~,j] = histc(r,prob_distribution);
current_block = blocks{j};
current_block_square = block_square{j};
current_slack_block = slack_block{j};
if mod(i,display) == 0
fprintf(sprintf('iteration: %02d \t',i));
end
Z = reshape(T(current_block(1:end-length(current_slack_block))),[],k);
% computing gradient with the trick
grad = Z - X_block{j}*W;
c = c + size(X_block{j},1);
grad = reshape(grad,[],1);
%add slacks to the gradient
if length(current_slack_block) > 0
slacks = T(n*k+1:end);
grad = cat(1,grad,n*kapa*slacks(current_slack_block));
end
prob(j).c = grad;
[~,Tmin] = mosekopt('minimize echo(0)',prob(j));
Tmin = Tmin.sol.itr.xx;
diff = T(current_block)-Tmin;
gap(j) = diff'*grad;
gap(j) = 1/n*gap(j);
diff_square = reshape(diff(1:end-length(current_slack_block)),[],k);
if length(current_slack_block) > 0
d_slacks = diff(end+1-length(current_slack_block):end);
n_slacks = kapa*norm(d_slacks)^2;
else
n_slacks = 0;
end
precomp = (P_block{j}*diff_square);
aux = diff_square.*(diff_square-X_block{j}*precomp);
aux = 1/n*sum(aux(:)) + n_slacks;
%aux = compute_loss(diff);
gamma_rate = min(1,gap(j)/aux);
%gamma_rate = 2*66/(n_iter+2*66);
W = W - gamma_rate*precomp;
T(current_block) = T(current_block) - gamma_rate*diff;
if mod(i,display) == 0
if display_loss_value
T_current = T(current_block);
T_square = reshape(T_current(1:end-length(current_slack_block)),[],k);
if length(current_slack_block) > 0
d_slacks = T_current(end+1-length(current_slack_block):end);
n_slacks = kapa*norm(d_slacks)^2;
else
n_slacks = 0;
end
block_loss = T_square.*(T_square-X(current_block_square,:)*(P(:,current_block_square)*T_square));
block_loss = 1/n*sum(block_loss(:)) + n_slacks;
fprintf('Block gap %d value: %.3e - gamma: %.3e - block loss: %.3e\n',j,gap(j),gamma_rate,block_loss);
else
fprintf('Block gap %d value: %.3e - gamma: %.3e\n',j,gap(j),gamma_rate);
end
end
end
res = reshape(T(1:n*k),n,k);
end