PyTorch autograd accumulates gradients, which can be used to increase effective batch size, for example, one can use following algorithm

for each mini-batch from train_loader
do forward and backward passes
once every two iterations do:
optimizer.step()
optimizer.zero_grad()

This process will double the effective mini-batch size.
I have tested following two scenarios using above algorithm
Case 1:
mini_batch_size = 100
multi_batch_update = 4

for each iteration:
do forward and backward pass
if iteration_number % 4 == 0:

   scale down all parameter-gradients by factor of 4



   optimizer.step()



   optmizer.zero_grad()



ie. above algorithm will allow 4 backward passes, so gradients are accumulated and once every 4 iteration optimizer will perform weight updates. The effective batch size this way is 400!
Case 2:
mini_batch_size = 200
multi_batch_update = 2
ie. we consider the exact same scenario but with minibatch of 200 and with weight updates after every 2 iterations (after scaling down all gradients by factor of 2), thus effective batch size is still 400.
However, both algorithms seem to follow different learning curve.
For example, I use algorithm from Case 1 for few iterations and then switch to Case 2 at about 4500th iteration, following is a learning curve

On the other hand if I start with Case 2 and then switch to Case 1 at about 2500th iteration, following is a learning curve

One can notice from learning curves that effective learning rate of Case 1 is lower than that for Case 2,
Can someone please explain this particular behaviour?
PS:

I use Adam optimiser with default settings.
Batchnorm is enabled (however, same behaviour is seen even without Batchnorm)
Results are generated for fashionMnist dataset and can be reproduced with any simple CNN network.