Average Stochastic Gradient Descent, abbreviated as ASGD, averages the weights that are calculated in every iteration.

$$w_{t+1}=w_t-\eta \nabla Q(w_t)$$

where $w_t$ being the weight tensor , $\eta$ being the base learning rate and $\nabla Q(w_t)$ being the gradient of the objective function evaluated at $w_t$.

With the given update rule SGD assigns calculated weight to the model. But with ASGD assigns the following averaged weight $\overline{w}$,

$$\overline{w}=\frac{1}{N} \sum_{t=1}^Nw_t$$

where $w_t$ is the weight tensor calculated in iteration 't'.

Such averaging is used when the data is noisy.

It is the decay term for the past weights used in the average.

It is the power value that is used to update the learning rate.

It is the optimization step at which the averaging is started. If the required number of iteration is lower than the TO value, then the averaging will not happen.

      # importing the library
import torch
import torch.nn as nn

x = torch.randn(10, 3)
y = torch.randn(10, 2)

# Build a fully connected layer.
linear = nn.Linear(3, 2)

# Build MSE loss function and optimizer.
criterion = nn.MSELoss()

# Optimization method using ASGD
optimizer = torch.optim.ASGD(linear.parameters(), lr=0.01, lambd=0.0001, 
alpha=0.75, t0=1000000.0, weight_decay=0)

# Forward pass.
pred = linear(x)

# Compute loss.
loss = criterion(pred, y)
print('loss:', loss.item())


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