Adadelta

Adadelta was proposed with the aim to solve the diminishing learning rate problem that was seen in the Adagrad. Adagrad uses the knowledge of all the past gradients in its update, whereas Adadelta uses only a certain "window" of past gradients to update the parameters.

The mathematical formulation of Adadelta is similar to that of RMSprop.

Major Parameters

• Base Learning Rate
• Weight Decay
• Epsilon Coefficient
• Rho

Rho

Rho is same as the $beta$ of RMSprop. It is the smoothing constant whose value ranges from 0 to 1. Higher value of Rho suggests that more number of previously calculated squares of gradient are taken into account, making the curve relatively "smooth".

Code Implementation

      # 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 RMSprop
optimizer = torch.optim.RMSProp(linear.parameters(), lr=1.0, rho=0.9, eps=1e-06, weight_decay=0)

# Forward pass.
pred = linear(x)

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

optimizer.step()