Wasserstein GAN implemtation in pytorch. How to implement the loss? - deep-learning

Question

I'm currently working on a project in pytorch on Wasserstein GAN (https://arxiv.org/pdf/1701.07875.pdf).
In Wasserstain GAN a new objective function is defined using the wasserstein distance as :
Which leads to the following algorithms for training the GAN:
My question is :
When implementing line 5 and 6 of the algorithm in pytorch should I be multiplying my loss -1 ? As in my code (I use RMSprop as my optimizer for both the generator and critic):
############################
# (1) Update D network: maximize (D(x)) + (D(G(x)))
###########################
for n in range(n_critic):
D.zero_grad()
real_cpu = data[0].to(device)
b_size = real_cpu.size(0)
output = D(real_cpu)
#errD_real = -criterion(output, label) #DCGAN
errD_real = torch.mean(output)
# Calculate gradients for D in backward pass
errD_real.backward()
D_x = output.mean().item()
## Train with all-fake batch
# Generate batch of latent vectors
noise = torch.randn(b_size, 100, device=device) #Careful here we changed shape of input (original : torch.randn(4, 100, 1, 1, device=device))
# Generate fake image batch with G
fake = G(noise)
# Classify all fake batch with D
output = D(fake.detach())
# Calculate D's loss on the all-fake batch
errD_fake = torch.mean(output)
# Calculate the gradients for this batch
errD_fake.backward()
D_G_z1 = output.mean().item()
# Add the gradients from the all-real and all-fake batches
errD = -(errD_real - errD_fake)
# Update D
optimizerD.step()
#Clipping weights
for p in D.parameters():
p.data.clamp_(-0.01, 0.01)
As you can see, I do the operation errD = -(errD_real - errD_fake), with errD_real and errD_fake being respectively the mean of the predictions of the critic on real and fake samples.
To my understanding RMSprop should optimize the weights of the critic the following way :
w <- w - alpha*gradient(w)
(alpha being the learning rate divided by the square root of the weighted moving average of the squared gradient)
Since the optimization problem requires to "go" in the same direction as the gradient it should be required to multiply gradient(w) by -1 before optimizing the weights.
Do you think that my reasoning is right ?
The program runs but my results are quiet poor.
I follow the same logic for the generator's weights but this time in order to go in the opposite direction of the gradient:
############################
# (2) Update G network: minimize -D(G(x))
###########################
G.zero_grad()
noise = torch.randn(b_size, 100, device=device)
fake = G(noise)
#label.fill_(fake_label) # fake labels are real for generator cost
# Since we just updated D, perform another forward pass of all-fake batch through D
output = D(fake).view(-1)
# Calculate G's loss based on this output
#errG = criterion(output, label) #DCGAN
errG = -torch.mean(output)
# Calculate gradients for G
errG.backward()
D_G_z2 = output.mean().item()
# Update G
optimizerG.step()
Sorry for the long question, I tried to explain my doubt as clear as possible. Thank you everyone.

Answer 1

I noticed some errors in the implementation of your discriminator training protocol. You call your backward functions twice with both the real and fake values loss being backpropagated at different time steps.
Technically an implementation using this scheme is possible but highly unreadable. There was a mistake with your errD_real in which your output is going to be positive instead of negative as an optimal D(G(z))>0 and so you penalize it for being correct. Overall your model converges simply by predicting D(x)<0 for all inputs.
To fix this do not call your errD_readl.backward() or your errD_fake.backward(). Simply using an errD.backward() after you define errD would work perfectly fine. Otherwise, your generator seems to be correct.