Loss jumps abruptly when I decay the learning rate with Adam optimizer in PyTorch

Question

I'm training an auto-encoder network with Adam optimizer (with amsgrad=True) and MSE loss for Single channel Audio Source Separation task. Whenever I decay the learning rate by a factor, the network loss jumps abruptly and then decreases until the next decay in learning rate.

I'm using Pytorch for network implementation and training.

Following are my experimental setups:

 Setup-1: NO learning rate decay, and 
          Using the same Adam optimizer for all epochs

 Setup-2: NO learning rate decay, and 
          Creating a new Adam optimizer with same initial values every epoch

 Setup-3: 0.25 decay in learning rate every 25 epochs, and
          Creating a new Adam optimizer every epoch

 Setup-4: 0.25 decay in learning rate every 25 epochs, and
          NOT creating a new Adam optimizer every time rather
          using PyTorch's "multiStepLR" and "ExponentialLR" decay scheduler 
          every 25 epochs

I am getting very surprising results for setups #2, #3, #4 and am unable to reason any explanation for it. Following are my results:

Setup-1 Results:

Here I'm NOT decaying the learning rate and 
I'm using the same Adam optimizer. So my results are as expected.
My loss decreases with more epochs.
Below is the loss plot this setup.

Plot-1:

optimizer = torch.optim.Adam(lr=m_lr,amsgrad=True, ...........)

for epoch in range(num_epochs):
    running_loss = 0.0
    for i in range(num_train):
        train_input_tensor = ..........                    
        train_label_tensor = ..........
        optimizer.zero_grad()
        pred_label_tensor = model(train_input_tensor)
        loss = criterion(pred_label_tensor, train_label_tensor)
        loss.backward()
        optimizer.step()
        running_loss += loss.item()
    loss_history[m_lr].append(running_loss/num_train)

---

Setup-2 Results:  

Here I'm NOT decaying the learning rate but every epoch I'm creating a new
Adam optimizer with the same initial parameters.
Here also results show similar behavior as Setup-1.

Because at every epoch a new Adam optimizer is created, so the calculated gradients
for each parameter should be lost, but it seems that this doesnot affect the 
network learning. Can anyone please help on this?

Plot-2:

for epoch in range(num_epochs):
    optimizer = torch.optim.Adam(lr=m_lr,amsgrad=True, ...........)

    running_loss = 0.0
    for i in range(num_train):
        train_input_tensor = ..........                    
        train_label_tensor = ..........
        optimizer.zero_grad()
        pred_label_tensor = model(train_input_tensor)
        loss = criterion(pred_label_tensor, train_label_tensor)
        loss.backward()
        optimizer.step()
        running_loss += loss.item()
    loss_history[m_lr].append(running_loss/num_train)

---

Setup-3 Results: 

As can be seen from the results in below plot, 
my loss jumps every time I decay the learning rate. This is a weird behavior.

If it was happening due to the fact that I'm creating a new Adam 
optimizer every epoch then, it should have happened in Setup #1, #2 as well.
And if it is happening due to the creation of a new Adam optimizer with a new 
learning rate (alpha) every 25 epochs, then the results of Setup #4 below also 
denies such correlation.

Plot-3:

decay_rate = 0.25
for epoch in range(num_epochs):
    optimizer = torch.optim.Adam(lr=m_lr,amsgrad=True, ...........)

    if epoch % 25 == 0  and epoch != 0:
        lr *= decay_rate   # decay the learning rate

    running_loss = 0.0
    for i in range(num_train):
        train_input_tensor = ..........                    
        train_label_tensor = ..........
        optimizer.zero_grad()
        pred_label_tensor = model(train_input_tensor)
        loss = criterion(pred_label_tensor, train_label_tensor)
        loss.backward()
        optimizer.step()
        running_loss += loss.item()
    loss_history[m_lr].append(running_loss/num_train)

---

Setup-4 Results:  

In this setup, I'm using Pytorch's learning-rate-decay scheduler (multiStepLR)
which decays the learning rate every 25 epochs by 0.25.
Here also, the loss jumps everytime the learning rate is decayed.

As suggested by @Dennis in the comments below, I tried with both ReLU and 1e-02 leakyReLU nonlinearities. But, the results seem to behave similar and loss first decreases, then increases and then saturates at a higher value than what I would achieve without learning rate decay.

Plot-4 shows the results.

Plot-4:

scheduler = torch.optim.lr_scheduler.MultiStepLR(optimizer=optimizer, milestones=[25,50,75], gamma=0.25)

scheduler = torch.optim.lr_scheduler.ExponentialLR(optimizer=optimizer, gamma=0.95)

scheduler = ......... # defined above
optimizer = torch.optim.Adam(lr=m_lr,amsgrad=True, ...........)

for epoch in range(num_epochs):

    scheduler.step()

    running_loss = 0.0
    for i in range(num_train):
        train_input_tensor = ..........                    
        train_label_tensor = ..........
        optimizer.zero_grad()
        pred_label_tensor = model(train_input_tensor)
        loss = criterion(pred_label_tensor, train_label_tensor)
        loss.backward()
        optimizer.step()
        running_loss += loss.item()
    loss_history[m_lr].append(running_loss/num_train)

---

EDITS:

• As suggested in the comments and reply below, I've made changes to my code and trained the model. I've added the code and plots for the same.
• I tried with various lr_scheduler in PyTorch (multiStepLR, ExponentialLR) and plots for the same are listed in Setup-4 as suggested by @Dennis in comments below.
• Trying with leakyReLU as suggested by @Dennis in comments.

Any help. Thanks

Answer 1

I see no reason why decaying learning rates should create the kinds of jumps in losses that you are observing. It should "slow down" how quickly you "move", which in the case of a loss that otherwise consistently shrinks really should, at worst, just lead to a plateau in your losses (rather than those jumps).

The first thing I observe in your code is that you re-create the optimizer from scratch every epoch. I have not yet worked enough with PyTorch to tell for sure, but doesn't this just destroy the internal state / memory of the optimizer every time? I think you should just create the optimizer once, before the loop through the epochs. If this is indeed a bug in your code, it should also actually still be a bug in the case where you do not use learning rate decay... but maybe you simply get lucky there and don't experience the same negative effects of the bug.

For learning rate decay, I'd recommend using the official API for that, rather than a manual solution. In your particular case, you'll want to instantiate a StepLR scheduler, with:

• optimizer = the ADAM optimizer, which you probably should only instantiate once.
• step_size = 25
• gamma = 0.25

You can then simply call scheduler.step() at the start of every epoch (or maybe at the end? the example in the API link calls it at the start of every epoch).

---

If, after the changes above, you still experience the issue, it would also be useful to run each of your experiments multiple times and plot average results (or plot lines for all experiments). Your experiments should theoretically be identical during the first 25 epochs, but we still see huge differences between the two figures even during those first 25 epochs in which no learning rate decay occurs (e.g., one figure starts at a loss of ~28K, the other starts at a loss of ~40K). This may simply be due to different random initializations, so it'd be good to average that nondeterminisim out of your plots.