def binary_search_x(x_minus, x_plus, y_minus, y_plus):
#users must make sure there exits a feasible solution in the rectangular area
#the search range is x_minus <= x <= x_plus, 0 <= y <= y_plus
with torch.no_grad():
a,b,c = plane(x_minus,y_plus)
q_loss, valid = qualification_loss(x_minus, x_plus, y_minus, y_plus,
a, b ,c, confidence=-0)
if valid.min()<1:
idx = valid<1
print(x_minus[idx], x_plus[idx], y_minus[idx], y_plus[idx],
a[idx], b[idx] ,c[idx])
raise Exception('(x_minus, y_plus) is not always feasible')
alpha_u = torch.ones(x_minus.shape, device=x_minus.device)
#alpha_u is always feasible
alpha_l = alpha_u * 0
for i in range(10):
alpha = (alpha_u + alpha_l)/2
x = x_minus * alpha
y = y_plus * alpha + (1-alpha)*y_minus
a,b,c = plane(x,y)
q_loss, valid = qualification_loss(x_minus, x_plus, y_minus, y_plus,
a, b ,c, confidence=-0)
valid = valid.float()
alpha_l = (1-valid)*alpha + valid*alpha_l
alpha_u = valid*alpha + (1-valid)*alpha_u
return x_minus * alpha_u, alpha_u*y_plus + (1-alpha)*y_minus
def binary_search_k(x_minus, x_plus, y_minus, y_plus):
with torch.no_grad():
# ka = a #a = a - ka, ka from 0 to a
# kb = b #b = b - kb, kb from 0 to b
a0,b0,c0 = plane(x_minus,y_plus)
alpha_u = torch.ones(x_minus.shape, device=x_minus.device)
#alpha_u is always feasible
alpha_l = alpha_u * 0
#ka = alpha * a, a = a - ka = (1-alpha) * a
#kb = alpha * b, b = b - kb = (1-alpha) * b
for i in range(10):
alpha = (alpha_u + alpha_l)/2
ka = a0 * alpha
kb = -b0 * alpha
a = a0 - ka
# c = c0 - ka * x_minus
b = b0 + kb
c = c0 - kb * y_plus + ka * x_minus
q_loss, valid = qualification_loss(x_minus, x_plus, y_minus, y_plus,
a, b ,c, confidence=-0)
valid = valid.float()
alpha_l = (1-valid)*alpha + valid*alpha_l
alpha_u = valid*alpha + (1-valid)*alpha_u
return a0*alpha_u, -b0*alpha_u
def find_initial_feasible_solution(x_minus, x_plus, y_minus, y_plus):
with torch.no_grad():
device = x_minus.device
x_best = torch.zeros(x_minus.shape).to(device)
y_best = torch.zeros(x_minus.shape).to(device)
# c_best = torch.zeros(x_minus.shape)
ka_best = torch.zeros(x_minus.shape).to(device)
kb_best = torch.zeros(x_minus.shape).to(device)
x = x_minus
y = y_plus
a,b,c = plane(x,y)
q_loss, valid = qualification_loss(x_minus, x_plus, y_minus, y_plus,
a, b ,c, confidence=-0)
if valid.sum()>0:
x_temp, y_temp = binary_search_x(x_minus[valid], x_plus[valid],
y_minus[valid], y_plus[valid])
x_best[valid] = x_temp
y_best[valid] = y_temp
ka_best[valid] = 0
kb_best[valid] = 0
valid = ~valid
if valid.sum()>0:
ka_temp, kb_temp = binary_search_k(x_minus[valid], x_plus[valid],
y_minus[valid], y_plus[valid])
x_best[valid] = x_minus[valid]
y_best[valid] = y_plus[valid]
ka_best[valid] = ka_temp
kb_best[valid] = kb_temp
return x_best, y_best, ka_best, kb_best
def train_lower(x0,
y0,
x_minus,
x_plus,
y_minus,
y_plus,
lr=1e-3,
max_iter=100,
print_info=True):
# search over (x,y) \in (x_minus, x_plus) * (y_minus, y_plus)
# the plane z = ax + by + c is the tangent plane of the surface tanh(x) sigmoid(y) at point (x,y)
x = x0.data.clone()
x.requires_grad = True
y = y0.data.clone()
y.requires_grad = True
a_best = torch.zeros(x_minus.shape, device=x_minus.device)
b_best = torch.zeros(x_minus.shape, device=x_minus.device)
c_best = torch.zeros(x_minus.shape, device=x_minus.device)
x_best = torch.zeros(x_minus.shape, device=x_minus.device)
y_best = torch.zeros(x_minus.shape, device=x_minus.device)
optimizer = optim.Adam([x, y], lr=lr)
cubic = torch.abs((x_plus - x_minus) * (y_plus - y_minus) *
torch.tanh(x_minus) * torch.sigmoid(y_plus))
cubic = torch.clamp(cubic, min=1e-3)
v_best = -torch.ones(x_minus.shape, device=x_minus.device) * 1000
#we want to maximize the volume
for i in range(max_iter):
q_loss, valid = qualification_loss_lower(x, y, x_minus, x_plus,
y_minus, y_plus)
a, b, c = plane(x, y)
v_loss = get_volume(a, b, c, x_minus, x_plus, y_minus, y_plus) / cubic
best = (v_loss > v_best) * valid
a_best[best] = a[best]
b_best[best] = b[best]
c_best[best] = c[best]
x_best[best] = x[best]
y_best[best] = y[best]
v_best[best] = v_loss[best]
# print('volume', v_loss)
if print_info:
print('2l q loss: %.4f volume: %.4f' %
(q_loss.mean().item(), v_loss.mean().item()))
loss = q_loss - (valid.float() + 0.1) * v_loss
loss = loss.mean()
optimizer.zero_grad()
loss.backward()
optimizer.step()
# print('x,y',x,y)
return a_best, b_best, c_best, x_best, y_best
def binary_search_x(x_minus, x_plus, y_minus, y_plus):
#users must make sure it is feasible
with torch.no_grad():
a, b, c = plane(x_minus, y_plus)
q_loss, valid = qualification_loss_lower(a,
b,
c,
x_minus,
x_plus,
y_minus,
y_plus,
confidence=-0)
if valid.min() < 1:
raise Exception('(x_minus, y_plus) is not always feasible')
alpha_u = torch.ones(x_minus.shape, device=x_minus.device)
#alpha_u is always feasible
alpha_l = alpha_u * 0
for i in range(10):
alpha = (alpha_u + alpha_l) / 2
x = x_minus * alpha
y = y_plus * alpha
a, b, c = plane(x, y)
q_loss, valid = qualification_loss_lower(a,
b,
c,
x_minus,
x_plus,
y_minus,
y_plus,
confidence=-0)
valid = valid.float()
alpha_l = (1 - valid) * alpha + valid * alpha_l
alpha_u = valid * alpha + (1 - valid) * alpha_u
return alpha_u * x_minus, alpha_u * y_plus
def adjust_upper_plane(x0,
y0,
x_minus,
x_plus,
y_minus,
y_plus,
lr=1e-2,
max_iter=100,
print_info=True):
# this function finds the minimum value of a*x + b*y + c - torch.tanh(x)*torch.sigmoid(y)
# if it is less than zero, we will need to raise the plane z = ax + by + c a little bit
x0 = x0.detach()
y0 = y0.detach()
x1 = ((x0 + x_minus) / 2).data.clone()
y1 = ((y0 + y_minus) / 2).data.clone()
x2 = ((x0 + x_minus) / 2).data.clone()
y2 = ((y0 + y_plus) / 2).data.clone()
x3 = ((x0 + x_plus) / 2).data.clone()
y3 = ((y0 + y_plus) / 2).data.clone()
x4 = ((x0 + x_plus) / 2).data.clone()
y4 = ((y0 + y_minus) / 2).data.clone()
x1.requires_grad = True
y1.requires_grad = True
x2.requires_grad = True
y2.requires_grad = True
x3.requires_grad = True
y3.requires_grad = True
x4.requires_grad = True
y4.requires_grad = True
a, b, c = plane(x0, y0)
optimizer = optim.Adam([x1, y1, x2, y2, x3, y3, x4, y4], lr=lr)
x1_best = torch.zeros(x_minus.shape, device=x_minus.device)
y1_best = torch.zeros(x_minus.shape, device=x_minus.device)
loss1_best = torch.ones(x_minus.shape, device=x_minus.device) * 1000
x2_best = torch.zeros(x_minus.shape, device=x_minus.device)
y2_best = torch.zeros(x_minus.shape, device=x_minus.device)
loss2_best = torch.ones(x_minus.shape, device=x_minus.device) * 1000
x3_best = torch.zeros(x_minus.shape, device=x_minus.device)
y3_best = torch.zeros(x_minus.shape, device=x_minus.device)
loss3_best = torch.ones(x_minus.shape, device=x_minus.device) * 1000
x4_best = torch.zeros(x_minus.shape, device=x_minus.device)
y4_best = torch.zeros(x_minus.shape, device=x_minus.device)
loss4_best = torch.ones(x_minus.shape, device=x_minus.device) * 1000
for i in range(max_iter):
loss1 = a * x1 + b * y1 + c - torch.tanh(x1) * torch.sigmoid(y1)
loss2 = a * x2 + b * y2 + c - torch.tanh(x2) * torch.sigmoid(y2)
loss3 = a * x3 + b * y3 + c - torch.tanh(x3) * torch.sigmoid(y3)
loss4 = a * x4 + b * y4 + c - torch.tanh(x4) * torch.sigmoid(y4)
qloss1, valid1 = qualification_loss_upper(x1, y1, x_minus, x_plus,
y_minus, y_plus)
best1 = (loss1 < loss1_best) * valid1
x1_best[best1] = x1[best1]
y1_best[best1] = y1[best1]
loss1_best[best1] = loss1[best1]
qloss2, valid2 = qualification_loss_upper(x2, y2, x_minus, x_plus,
y_minus, y_plus)
best2 = (loss2 < loss2_best) * valid2
x2_best[best2] = x2[best2]
y2_best[best2] = y2[best2]
loss2_best[best2] = loss2[best2]
qloss3, valid3 = qualification_loss_upper(x3, y3, x_minus, x_plus,
y_minus, y_plus)
best3 = (loss3 < loss3_best) * valid3
x3_best[best3] = x3[best3]
y3_best[best3] = y3[best3]
loss3_best[best3] = loss3[best3]
qloss4, valid4 = qualification_loss_upper(x4, y4, x_minus, x_plus,
y_minus, y_plus)
best4 = (loss4 < loss4_best) * valid4
x4_best[best4] = x4[best4]
y4_best[best4] = y4[best4]
loss4_best[best4] = loss4[best4]
loss = loss1 * (valid1.float() + 0.1) + qloss1
loss = loss + loss2 * (valid2.float() + 0.1) + qloss2
loss = loss + loss3 * (valid3.float() + 0.1) + qloss3
loss = loss + loss4 * (valid4.float() + 0.1) + qloss4
loss = loss.mean()
optimizer.zero_grad()
loss.backward()
optimizer.step()
if print_info:
print('1 adjust upper plane loss: %.4f' % loss.item())
return x1_best, y1_best, x2_best, y2_best, x3_best, y3_best, x4_best, y4_best, loss1_best, loss2_best, loss3_best, loss4_best
def train_lower(u0, v0, ka0, kb0, x_minus, x_plus, y_minus, y_plus,
lr_x = 1e-3, lr_k=1e-2, max_iter = 100, print_info = True):
device = x_minus.device
x_best = torch.zeros(x_minus.shape).to(device)
y_best = torch.zeros(x_minus.shape).to(device)
a_best = torch.zeros(x_minus.shape).to(device)
b_best = torch.zeros(x_minus.shape).to(device)
c_best = torch.zeros(x_minus.shape).to(device)
ka_best = torch.zeros(x_minus.shape).to(device)
kb_best = torch.zeros(x_minus.shape).to(device)
cubic = -(x_plus-x_minus) * (y_plus-y_minus) * torch.tanh(x_minus) * torch.sigmoid(y_plus)
cubic = torch.clamp(cubic, min=1e-3)
v_best = -cubic/cubic * 10000
# eps = 0.1
u = u0.data.clone()#torch.clamp(x_plus.data.clone(), max=3)#torch.rand(x_plus.shape)#torch.Tensor([3])
v = v0.data.clone()#torch.clamp(y_plus.data.clone(), max=3)#torch.rand(y_plus.shape)#torch.Tensor([3])
ka = ka0.data.clone()#torch.Tensor([1])
kb = kb0.data.clone()#torch.Tensor([1])
u.requires_grad = True
v.requires_grad = True
ka.requires_grad = True
kb.requires_grad = True
# optimizer = optim.SGD([u,v,ka,kb], lr=lr, momentum=momentum)
optimizer_x = optim.Adam([u,v], lr=lr_x)
optimizer_k = optim.Adam([ka,kb], lr=lr_k)
max_iter = max_iter
# tanh_l_min = tanh_lmin(x_minus, y_minus)
# sigmoid_l_min = sigmoid_lmin(x_plus, y_minus)
for i in range(max_iter):
#x: 0 to x_minus <=0
#y: 0 to y_plus
slop = 0.01
u_minus = -F.leaky_relu(-u, negative_slope=slop)
#this makes u_minus grows much slower when u>=0
idx_v = (v>=y_minus).float()
v_plus = v * idx_v + (1-idx_v)*(slop*(v-y_minus)+y_minus)
#this makes v_plus decrease slower when v< y_minus
idx_x = (u>=x_minus).float()
x = u_minus * idx_x + (1-idx_x)*(slop*(u_minus-x_minus)+x_minus)
#make x decrease slower when u<x_minus
idx_y = (v<=y_plus).float()
y = v_plus * idx_y + (1-idx_y)*(slop*(v_plus-y_plus)+y_plus)
#make y grows slower when v>y_plus
a,b,c = plane(x,y)
idx = (x<=x_minus).float()
a = a - F.leaky_relu(ka, negative_slope=slop) * idx
c = c + F.leaky_relu(ka, negative_slope=slop) * x * idx
#ka = ka * idx
#if x<=x_minus, we keep its original value
#if x>x_minus, we reset it to 0
idx = (y>=y_plus).float()
b = b + F.leaky_relu(kb, negative_slope=slop) * idx
c = c - F.leaky_relu(kb, negative_slope=slop) * y * idx
# q_loss, valid = qualification_loss_lower(a,b,c,x_minus, x_plus, y_minus, y_plus,
# tanh_l_min,
# sigmoid_l_min, confidence=-0)
q_loss, valid = qualification_loss(x_minus, x_plus, y_minus, y_plus,
a, b ,c, confidence=-1e-3)
# print('q_loss:',q_loss)
v_loss = get_volume(a,b,c,x_minus, x_plus, y_minus, y_plus)
v_loss = v_loss/cubic
# print('volume', v_loss)
if print_info:
print('12l q loss: %.4f volume: %.4f' % (q_loss.mean().item(), v_loss.mean().item()))
loss = (q_loss - v_loss*(valid.float()+0.01)).mean() #we want to maximize the volume
best = (v_loss > v_best) * (valid)
v_best[best] = v_loss[best]
x_best[best] = x[best]
y_best[best] = y[best]
ka_best[best] = ka[best]
kb_best[best] = kb[best]
a_best[best] = a[best]
b_best[best] = b[best]
c_best[best] = c[best]
optimizer_x.zero_grad()
optimizer_k.zero_grad()
loss.backward()
idx = (y>y_plus) * (kb>0)
#if y>y_plus and kb>0, we don't move v
v.grad = v.grad * (1-idx.float())
idx = (x<x_minus) * (ka>0)
#if x<x_minus and ka>0, we don't move u
u.grad = u.grad * (1-idx.float())
# if y>=y_plus and kb >=0:
# v.grad = v.grad * 0
# if x<=x_plus and ka >=0:
# u.grad = u.grad * 0
optimizer_x.step()
optimizer_k.step()
# print('u,v:',u,v)
return x_best,y_best,ka_best,kb_best,a_best,b_best,c_best,v_best
def train_lower(u0,
v0,
ka0,
kb0,
x_minus,
x_plus,
y_minus,
y_plus,
lr_x=1e-3,
lr_k=1e-2,
max_iter=100,
print_info=True):
device = x_minus.device
x_best = torch.zeros(x_minus.shape).to(device)
y_best = torch.zeros(x_minus.shape).to(device)
a_best = torch.zeros(x_minus.shape).to(device)
b_best = torch.zeros(x_minus.shape).to(device)
c_best = torch.zeros(x_minus.shape).to(device)
ka_best = torch.zeros(x_minus.shape).to(device)
kb_best = torch.zeros(x_minus.shape).to(device)
cubic = (x_plus - x_minus) * (y_plus - y_minus)
cubic = torch.clamp(cubic, min=1e-4)
v_best = -torch.ones(x_minus.shape).to(device)
# eps = 0.1
u = u0 #torch.clamp(x_plus.data.clone(), max=3)#torch.rand(x_plus.shape)#torch.Tensor([3])
v = v0 #torch.clamp(y_plus.data.clone(), max=3)#torch.rand(y_plus.shape)#torch.Tensor([3])
ka = ka0 #torch.Tensor([1])
kb = kb0 #torch.Tensor([1])
u.requires_grad = True
v.requires_grad = True
ka.requires_grad = True
kb.requires_grad = True
# optimizer = optim.SGD([u,v,ka,kb], lr=lr, momentum=momentum)
optimizer_x = optim.Adam([u, v], lr=lr_x)
optimizer_k = optim.Adam([ka, kb], lr=lr_k)
max_iter = max_iter
for i in range(max_iter):
#x: 0 to x_minus <=0
#y: 0 to y_plus
slop = 0.01
u_minus = -F.leaky_relu(-u, negative_slope=0.01)
v_plus = F.leaky_relu(v, negative_slope=0.01)
idx_x = (u >= x_minus).float()
x = u_minus * idx_x + (1 - idx_x) * (slop *
(u_minus - x_minus) + x_minus)
idx_y = (v <= y_plus).float()
y = v_plus * idx_y + (1 - idx_y) * (slop * (v_plus - y_plus) + y_plus)
a, b, c = plane(x, y)
idx = (x <= x_minus).float()
a = a - F.leaky_relu(ka, negative_slope=0.01) * idx
c = c + F.leaky_relu(ka, negative_slope=0.01) * x * idx
#ka = ka * idx
#if x<=x_minus, we keep its original value
#if x>x_minus, we reset it to 0
idx = (y >= y_plus).float()
b = b + F.leaky_relu(kb, negative_slope=0.01) * idx
c = c - F.leaky_relu(kb, negative_slope=0.01) * y * idx
q_loss, valid = qualification_loss_lower(a,
b,
c,
x_minus,
x_plus,
y_minus,
y_plus,
confidence=-0)
# print('q_loss:',q_loss)
v_loss = get_volume(a, b, c, x_minus, x_plus, y_minus, y_plus)
v_loss = v_loss / cubic
# print('cubic', cubic.min())
# print('u,v', u.max(), u.min(), v.max(), v.min())
# print('ka,kb', ka.max(), ka.min(), ka.max(), ka.min())
# # print('volume', v_loss)
# print('a,b,c',a.max(),b.max(),c.max(), a.min,b.min,c.min)
if print_info:
print('all 4l q_loss %.4f, volume %.4f' %
(q_loss.mean().item(), v_loss.mean().item()))
loss = q_loss - (v_loss * (valid.float() + 0.1)).mean()
best = (v_loss > v_best) * (valid)
v_best[best] = v_loss[best]
x_best[best] = x[best]
y_best[best] = y[best]
ka_best[best] = ka[best]
kb_best[best] = kb[best]
a_best[best] = a[best]
b_best[best] = b[best]
c_best[best] = c[best]
optimizer_x.zero_grad()
optimizer_k.zero_grad()
loss.backward()
idx = (y > y_plus) * (kb > 0)
v.grad = v.grad * (1 - idx.float())
idx = (x < x_minus) * (ka > 0)
u.grad = u.grad * (1 - idx.float())
# print('u grad', u.grad)
# print('v grad', v.grad)
# nan = (u.grad != u.grad)
# print('not a number', u0[nan], v0[nan], ka0[nan], kb0[nan],
# x_minus[nan], x_plus[nan], y_minus[nan], y_plus[nan])
# print('u', u)
# print('v', v)
# if y>=y_plus and kb >=0:
# v.grad = v.grad * 0
# if x<=x_plus and ka >=0:
# u.grad = u.grad * 0
u.grad[u.grad != u.grad] = 0
v.grad[v.grad != v.grad] = 0
ka.grad[ka.grad != ka.grad] = 0
kb.grad[kb.grad != kb.grad] = 0
optimizer_x.step()
optimizer_k.step()
# print('u,v:',u,v)
return x_best, y_best, ka_best, kb_best, a_best, b_best, c_best, v_best