Gradient descent

For t=1, …, number_of_batches:

Vectorized Forward prop on $X^{t}$
  $Z^{[1]} = W^{[1]} X^{t} + b^{[1]}$
  $A^{[1]} = g^{[1]}(Z^{[1]})$
  ...
  $A^{[L]} = g^{[L]}(Z^{[L]})$
Compute cost $J^{[t]}$ = 1/1000 * ...
Backprop to compute gradients for $J^{[t]}$
Update weights $W^{[l]} = W^{[l]} - \alpha d W^{[l]}; b^{[l]} = b^{[l]} - \alpha d b^{[l]}$

$V_t = \beta V_{t-1} + (1-\beta) \Theta_t$

$\beta = 0.98$ is smoother than $\beta = 0.5$ (2 days for average in latter case)

$V_\Theta = 0$

$V_\Theta = \beta V + (1-\beta) \Theta_1$

$V_\Theta = \beta V + (1-\beta) \Theta_2$

…

Easy method to compute averages for longer periods

$V_0 = 0$

$V_1 = \beta V_0 + 0,02 \Theta_1$

$V_\Theta = \beta V + 0,02 \Theta_2$

…

Corrected:

$\frac{V_t}{1-\beta^t}$

Root mean squared