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show_centroid_plots.m
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function show_centroid_plots()
clc; close all; clear
%% Define parameters
tolgradnorm = 1e-8;
inner_repeat = 1;
if 1
% Large instance
maxepoch = 30;
N = 5000;
d = 10;
cn = 5;
srg_varpi = 0.05;
else
% Small instance
maxepoch = 60;
N = 1500;
d = 3;
cn = 5;
srg_varpi = 0.05;
end
input_filename = sprintf('./dataset/psd/psd_mean_%d_%d_%d.mat', d, N, cn);
fprintf('Reading file %s with (d:%d N:%d cn:%d) .... ', input_filename, d, N, cn);
input_data = load(input_filename);
A = zeros(d, d, N);
A = input_data.x_sample{1};
fprintf('done\n');
f_sol = input_data.f_sol{1};
fprintf('f_sol: %.16e\n', f_sol);
%% Set manifold
problem.M = sympositivedefinitefactory_mod(d);
problem.ncostterms = N;
% Cost function
problem.cost = @cost;
function f = cost(X)
f=0;
sqrtX = sqrtm(X);
for i=1:N
arg = sqrtX\A(:, :, i)/sqrtX;
if (norm(imag(eig(arg)),'fro')>1e-15)
f = Inf;
break;
elseif (any(real(eig(arg))<0))
f = Inf;
break;
end
f = f + norm(logm(arg),'fro')^2;
end
f = f/(N);
end
% Riemannian gradient of the cost function
problem.rgrad = @rgrad;
function g = rgrad(X)
logsum = zeros(size(X,1));
invX = pinv(X);
for i = 1 : N
logsum = logsum + logm(A(:, :, i) * invX);
end
g = 2*X*logsum;
g = (g+g')/2;
g = g/N;
end
% Riemannian stochastic gradient of the cost function
problem.partialgrad = @partialgrad;
function g = partialgrad(X, idx_batchsize)
m_batchsize = length(idx_batchsize);
logsum = zeros(size(X,1));
for k = 1 : m_batchsize
curr_index = idx_batchsize(k);
logsum = logsum + logm(A(:, :, curr_index)\X);
end
g = 2*X*logsum;
g = (g+g')/2;
g = g/m_batchsize;
end
% % Consistency checks
% checkgradient(problem)
% pause;
%% Run algorithms
% Initialize
Uinit = problem.M.rand();
% Run R-SD
clear options;
options.maxiter = maxepoch;
options.tolgradnorm = tolgradnorm;
[~, ~, infos_sd, options_sd] = steepestdescent(problem, Uinit, options);
% Run R-CG
clear options;
options.maxiter = maxepoch;
options.tolgradnorm = tolgradnorm;
[~, ~, infos_cg, options_cg] = conjugategradient(problem, Uinit, options);
% Run SGD with decay step-size
clear options;
options.verbosity = 1;
options.batchsize = 10;
options.update_type='sgd';
options.maxepoch = maxepoch;
options.tolgradnorm = tolgradnorm;
options.stepsize_type = 'decay';
options.stepsize = 1e-3;
options.stepsize_lambda = 0.01;
options.transport = 'ret_vector_locking';
options.maxinneriter = inner_repeat*N;
[~, ~, infos_sgd, options_sgd] = Riemannian_svrg(problem, Uinit, options);
% Run SVRG
clear options;
options.verbosity = 1;
options.batchsize = 10;
options.update_type='svrg';
options.maxepoch = maxepoch / (1 + 2 * inner_repeat);
options.tolgradnorm = tolgradnorm;
options.svrg_type = 2;
options.stepsize_type = 'fix';
options.stepsize = 0.01;
options.boost = 0;
options.transport = 'ret_vector_locking';
options.store_innerinfo = false;
options.maxinneriter = inner_repeat*N;
[~, ~, infos_svrg, options_svrg] = Riemannian_svrg(problem, Uinit, options);
% Run SRG
clear options;
options.verbosity = 1;
options.batchsize = 10;
options.maxepoch = maxepoch / (1 + 2 * inner_repeat);
options.tolgradnorm = tolgradnorm;
options.stepsize_type = 'fix';
options.stepsize = 0.01;
options.transport = 'ret_vector_locking';
options.store_innerinfo = false;
options.maxinneriter = inner_repeat*N;
[~, ~, infos_srg, options_srg] = Riemannian_srg(problem, Uinit, options);
% Run SRG+
clear options;
options.verbosity = 1;
options.batchsize = 10;
options.maxepoch = maxepoch / (1 + 2 * inner_repeat);
options.tolgradnorm = tolgradnorm;
options.stepsize_type = 'fix';
options.stepsize = 0.01;
options.gamma = srg_varpi;
options.transport = 'ret_vector_locking';
options.store_innerinfo = false;
options.maxinneriter = inner_repeat*N;
[~, ~, infos_srg_plus, options_srg_plus] = Riemannian_srg(problem, Uinit, options);
% Calculate # of gradient evaluations
num_grads_sd = (1:length([infos_sd.cost])) - 1; % N*options_sd.maxiter;
num_grads_cg = (1:length([infos_cg.cost])) - 1; % N*options_sd.maxiter;
num_grads_sgd = ceil(options_sgd.maxinneriter/N)*((1:length([infos_sgd.cost])) - 1); % options.maxepoch*(options_sgd.maxinneriter);
num_grads_svrg = ceil((N + 2*options_svrg.maxinneriter)/N)*((1:length([infos_svrg.cost])) - 1); %options.maxepoch*(N + options_svrg.maxinneriter); % Per epoch we compute equivalent of 2 batch grads.
for kk = 1 : size(infos_srg,2)
num_grads_srg(kk) = infos_srg(kk).grad_cnt;
end
num_grads_srg = num_grads_srg/N;
for kk = 1 : size(infos_srg_plus,2)
num_grads_srg_plus(kk) = infos_srg_plus(kk).grad_cnt;
end
num_grads_srg_plus = num_grads_srg_plus/N;
%% Plots
fs = 20;
% Optimality gap (Train loss - optimum) versus #grads/N
optgap_sd = abs([infos_sd.cost] - f_sol);
optgap_cg = abs([infos_cg.cost] - f_sol);
optgap_sgd = abs([infos_sgd.cost] - f_sol);
optgap_svrg = abs([infos_svrg.cost] - f_sol);
optgap_srg = abs([infos_srg.cost] - f_sol);
optgap_srg_plus = abs([infos_srg_plus.cost] - f_sol);
% Optimality gap versus #grads/N
figure;
semilogy(num_grads_sd, optgap_sd,'-','LineWidth',2,'Color', [255, 128, 0]/255); hold on;
semilogy(num_grads_cg, optgap_cg,'-','LineWidth',2,'Color', [76, 153, 0]/255); hold on;
semilogy(num_grads_sgd, optgap_sgd,'-','LineWidth',2,'Color', [255,0,255]/255); hold on;
semilogy(num_grads_svrg, optgap_svrg, '-', 'LineWidth',2,'Color', [255, 0, 0]/255); hold on;
semilogy(num_grads_srg, optgap_srg, '-', 'LineWidth',2,'Color', [0, 0, 255]/255); hold on;
semilogy(num_grads_srg_plus, optgap_srg_plus, '-.', 'LineWidth',2,'Color', [0, 0, 255]/255); hold on;
hold off;
ax1 = gca;
set(ax1,'FontSize',fs);
xlabel(ax1,'#grad/N','FontName','Arial','FontSize',fs,'FontWeight','bold');
ylabel(ax1,'Traning loss - optimum','FontName','Arial','FontSize',fs,'FontWeight','bold');
legend('R-SD', 'R-CG', 'R-SGD', 'R-SVRG', 'R-SRG', 'R-SRG+');
% Optimality gap versus #grads/N
figure;
semilogy(abs([infos_sd.time]), optgap_sd,'-','LineWidth',2,'Color', [255, 128, 0]/255); hold on;
semilogy(abs([infos_cg.time]), optgap_cg,'-','LineWidth',2,'Color', [76, 153, 0]/255); hold on;
semilogy(abs([infos_sgd.time]), optgap_sgd,'-','LineWidth',2,'Color', [255,0,255]/255); hold on;
semilogy(abs([infos_svrg.time]), optgap_svrg, '-', 'LineWidth',2,'Color', [255, 0, 0]/255); hold on;
semilogy(abs([infos_srg.time]), optgap_srg, '-', 'LineWidth',2,'Color', [0, 0, 255]/255); hold on;
semilogy(abs([infos_srg_plus.time]), optgap_srg_plus, '-.', 'LineWidth',2,'Color', [0, 0, 255]/255); hold on;
hold off;
ax1 = gca;
set(ax1,'FontSize',fs);
xlabel(ax1,'Time [sec]','FontName','Arial','FontSize',fs,'FontWeight','bold');
ylabel(ax1,'Traning loss - optimum','FontName','Arial','FontSize',fs,'FontWeight','bold');
legend('R-SD', 'R-CG', 'R-SGD', 'R-SVRG', 'R-SRG', 'R-SRG+');
% Gradient norm versus #grads/N
figure;
semilogy(num_grads_sd, [infos_sd.gradnorm],'-','LineWidth',2,'Color', [255, 128, 0]/255); hold on;
semilogy(num_grads_cg, [infos_cg.gradnorm],'-','LineWidth',2,'Color', [76, 153, 0]/255); hold on;
semilogy(num_grads_sgd, [infos_sgd.gradnorm],'-','LineWidth',2,'Color', [255,0,255]/255); hold on;
semilogy(num_grads_svrg, [infos_svrg.gradnorm], '-', 'LineWidth',2, 'Color',[255, 0, 0]/255); hold on;
semilogy(num_grads_srg, [infos_srg.gradnorm], '-', 'LineWidth',2,'Color', [0, 0, 255]/255); hold on;
semilogy(num_grads_srg_plus, [infos_srg_plus.gradnorm], '-.', 'LineWidth',2, 'Color', [0, 0, 255]/255); hold on;
hold off;
ax1 = gca;
set(ax1,'FontSize',fs);
xlabel(ax1,'#grad/N','FontName','Arial','FontSize',fs,'FontWeight','bold');
ylabel(ax1,'Norm of gradient','FontName','Arial','FontSize',fs,'FontWeight','bold');
legend('R-SD', 'R-CG', 'R-SGD', 'R-SVRG', 'R-SRG', 'R-SRG+');
end