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LassoRun.m
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LassoRun.m
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function eval_list = LassoRun()
K = 10;
m_per_round = 10;
R = 2000; % round number
bs = 10; % batch size
plot_path = 'lasso_results.eps';
results_path = 'lasso_results.mat';
% data generation process
rng('default');
d = 1024;
m = 64; % numeber of clients
nm = 128; % pairs of observations
w_real=zeros(d,1);
%b_real = mvnrnd(0,1);
b_real = 0;
for i=1:512
w_real(i)=1;
end
mu = mvnrnd(zeros(d,1),eye(d), m);
Sigma = zeros(d);
for i = 1:d
for j = 1:d
Sigma(i, j) = 0.5^(abs(i - j));
end
end
delta = mvnrnd(zeros(d,1), Sigma, m*nm);
epsilon = mvnrnd(0, 1, nm*m);
mu = mu';
delta=delta';
X = zeros(d, nm*m);
for i=1:m
X(:,nm*(i-1)+1:nm*i) = repmat(mu(:,i),1,nm)+delta(:,nm*(i-1)+1:nm*i);
end
Y = zeros(1, nm*m);
Y = X'*w_real + epsilon;
eval_list = cell(5, 1);
lambda = 0.5^5; % regularization parameter
% same initial point for 5 methods
ini_x0 = randn(d,1);
% learning rate for FedDA, FedMid
etac = 0.001; % client learning rate
etas = 1; % server learning rate
%% FedAvg
% wr = zeros(d,1);
% W = zeros(d, m);
% Delta = zeros(d, 1);
% wtemp = zeros(d, 1);
% res_fedavg = zeros(R, 5);
% for r=1:R
% W = repmat(wr, 1, m);
% wtemp = wr; % record the snapshot
% for i = 1:m
% for k=1:K
% idx = datasample(nm*(i-1)+1:nm*i, bs, 'Replace', false); % sample minibatch size 1
% g = loss_grad(W(:, l), X(:,idx), Y(idx));
% g = g + lambda * sign(wtemp);
% W(:, l) = W(:, l) - etac*g; % client dual update
% end
% end
% Delta = mean(W - wtemp, 2); % correspond to delta_r
% wr = wr + etas*Delta; % server dual update;
% res_fedavg(r, :) = eval_metric_lasso(wr, w_real, X, Y);
% if mod(r, 100) == 0
% disp(norm(wr - w_real))
% end
% end
%% FedMirror
wr = ini_x0;
Delta = zeros(d, 1);
wtemp = zeros(d, 1);
res_FedMid = zeros(R, 4);
for r=1:R
wtemp = wr; % record the snapshot
id_client = datasample(1:m, m_per_round, 'Replace', false);
W = repmat(wr, 1, m_per_round);
l = 0;
for i = id_client
l = l + 1;
for k=1:K
idx = datasample(nm*(i-1)+1:nm*i, bs, 'Replace', false); % sample minibatch
g = loss_grad(W(:, l), X(:,idx), Y(idx));
W(:, l) = l1_soft(W(:, l) - etac*g, etac*lambda); % client dual update
end
end
Delta = mean(W - wtemp, 2); % correspond to delta_r
wr = l1_soft(wr + etas*Delta, etas*etac*lambda); % server dual update;
res_FedMid(r, :) = eval_metric_lasso(wr, w_real, X, Y);
if mod(r, 100) == 0
disp(norm(wr - w_real))
end
end
eval_list{1} = res_FedMid;
%% FedDualAvg
z = ini_x0;
Delta = zeros(d, 1);
Ztemp = zeros(d,m);
wrk=zeros(d,1);
res_FedDA = zeros(R, 4);
for r=1:R
id_client = datasample(1:m, m_per_round, 'Replace', false);
Z=repmat(z, 1, m_per_round);
Ztemp = Z; % record the snapshot
l = 0;
for i = id_client
l = l+1;
for k=1:K
etark = etas * etac*r*K+etac*k;
wtemp = l1_soft(Z(:, l),etark*lambda); % proximal mapping, retrieve primal
idx = datasample(nm*(i-1)+1:nm*i,bs, 'Replace',false); % sample minibatch size 1
g = loss_grad(wtemp,X(:,idx), Y(idx));
Z(:, l) = Z(:, l)-etac*g; % client dual update
end
end
Delta = mean(Z-Ztemp, 2); % correspond to delta_r
z = z+etas*Delta; % server dual update;
wr = l1_soft(z, etas*etac*(r+1)*K*lambda);
res_FedDA(r, :) = eval_metric_lasso(wr, w_real, X, Y);
if mod(r, 100) == 0
disp(norm(wr-w_real))
end
end
eval_list{2} = res_FedDA;
% Fast FedDualAvg with strong convexity (Our proposal)
mu = 0.1;
gamma = 550;
x0 = ini_x0;
xr = x0; % cumulative primal variable
wr = x0; % primal
gr = zeros(d, 1); % cumulative gradient of server
res_FastFedDA = zeros(R, 4);
for r = 1:R
cr = lambda;
id_client = datasample(1:m, m_per_round, 'Replace', false);
gr_client = repmat(gr, 1, m_per_round);
xr_client = repmat(xr, 1, m_per_round);
l = 0;
for i = id_client
wr_i = wr; %same starting point
l = l+1;
for k = 1:K
idx = datasample(nm*(i-1)+1:nm*i, bs, 'Replace', false); % sample minbatch
G_i = loss_grad(wr_i, X(:,idx), Y(idx)); % compute gradients
gr_client(:, l) = gr_client(:, l) + G_i; % cumulative gradient of cilent
eta_k = (r-1)*K + k;
ar_i = gr_client(:, l)/eta_k - 0.5*mu * xr_client(:, l)/eta_k - gamma * x0/eta_k; %parameter in client's optimization
br_i = 0.5*mu + gamma/eta_k;
wr_i = l1_soft(-ar_i/br_i, cr/br_i); % primal update of client
xr_client(:, l) = xr_client(:, l) + wr_i;
end
end
eta_r = r*K;
gr = mean(gr_client, 2); % aggregate gradients
xr = mean(xr_client, 2);
ar = gr/eta_r - 0.5*mu * xr/eta_r - gamma * x0/eta_r; % parameter in server's optimization
br = 0.5*mu + gamma/eta_r;
wr = l1_soft(-ar/br, cr/br); % primal update of client
res_FastFedDA(r, :) = eval_metric_lasso(wr, w_real, X, Y);
if mod(r, 100) == 0
disp(norm(wr-w_real))
end
xr = xr + wr;
end
eval_list{3} = res_FastFedDA;
% FedDualAvg with strong convexity
mu = 0.1;
gamma = 600;
xr = ini_x0; % cumulative primal
wr = xr; % primal
gr = zeros(d, 1); % gradient
res_AFedDA = zeros(R, 4);
for r = 1:R
br = 0.5*mu + gamma/(r*K);
cr = lambda;
id_client = datasample(1:m, m_per_round, 'Replace', false);
gr_client = repmat(gr, 1, m_per_round);
l = 0;
for i = id_client
l = l+1;
wr_i = wr; %same starting point
for k = 1:K
idx = datasample(nm*(i-1)+1:nm*i, bs, 'Replace', false); % sample minbatch
G_i = loss_grad(wr_i, X(:,idx), Y(idx)); % compute gradients
gr_client(:, l) = gr_client(:, l) + G_i; % cumulative gradient of cilent
ar_i = gr_client(:, l)/(r*K) - 0.5*mu * xr/r - gamma * x0/(r*K); %parameter in client's optimization
wr_i = l1_soft(-ar_i/br, cr/br); % primal update of client
end
end
gr = mean(gr_client, 2); % aggregate gradients
ar = gr/(r*K) - 0.5*mu * xr/r - gamma * x0/(r*K); % parameter in server's optimization
wr = l1_soft(-ar/br, cr/br); % primal update of client
res_AFedDA(r, :) = eval_metric_lasso(wr, w_real, X, Y);
if mod(r, 100) == 0
disp(norm(wr-w_real))
end
xr = xr + wr;
end
eval_list{4} = res_AFedDA;
% Multi-stage FedDualAvg with strong convexity
mu = 0.1;
gamma = 600;
x0 = ini_x0;
xr = x0; % cumulative primal
wr = x0; % primal
gr = zeros(d, 1); % gradient
S = 3;
res_MFedDA = zeros(R, 4);
lambda_set = [0.5^3 0.5^4 0.5^5];
rho_set = [1e4*(0.5) 1e4*(0.5)^2 1e4*(0.5)^3];
R_set = [250 250 1500];
r_now = 0;
for s = 1:S
x0 = wr; % re-start
xr = wr;
gr = zeros(d, 1);
rho = rho_set(s); % update radius of L1 ball
lambda_s = lambda_set(s); % update lambda value
for r = 1:R_set(s)
br = 0.5*mu + gamma/(r*K);
cr = lambda_s;
id_client = datasample(1:m, m_per_round, 'Replace', false);
gr_client = repmat(gr, 1, m_per_round);
l = 0;
for i = id_client
l = l + 1;
wr_i = wr; %same starting point
for k = 1:K
idx = datasample(nm*(i-1)+1:nm*i, bs, 'Replace', false); % sample minbatch
G_i = loss_grad(wr_i, X(:,idx), Y(idx)); % compute gradients
gr_client(:, l) = gr_client(:, l) + G_i; % cumulative gradient of cilent
ar_i = gr_client(:, l)/(r*K) - 0.5*mu * xr/r - gamma * x0/(r*K); %parameter in client's optimization
wr_i = l1_soft_cs(-ar_i/br, cr/br, x0, rho); % primal update of client
end
end
gr = mean(gr_client, 2); % aggregate gradients
ar = gr/(r*K) - 0.5*mu * xr/r - gamma * x0/(r*K); % parameter in server's optimization
wr = l1_soft_cs(-ar/br, cr/br, x0, rho); % primal update of client
r_now = r_now + 1;
res_MFedDA(r_now, :) = eval_metric_lasso(wr, w_real, X, Y);
if mod(r, 100) == 0
disp(norm(wr-w_real))
end
xr = xr + wr;
end
end
eval_list{5} = res_MFedDA;
% save and plot results
plot_lasso(eval_list, plot_path);
results = struct('eval_list', eval_list);
save(results_path, 'results');