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Neha Kumawat

4 years ago

In
my previous article **“Optimizers in Machine Learning and Deep Learning.”**
I gave a brief introduction about Adam optimizers. In this article, I will try
to give an in-depth explanation of the optimizer’s algorithm.

If
you didn’t read my previous articles. I recommend you to first go through my
previous articles on optimizers mentioned below and then come back to this
article for more better understanding:

So,
let’s start

Adam stands for Adaptive Moment Estimation, is another method that computes adaptive learning rates for each
parameter. In addition to storing an exponentially decaying average of past
squared gradients like Adadelta and RMSprop.

Adam also keeps an exponentially decaying average of past
gradients, similar to momentum.

Adam can be viewed as a combination of Adagrad and RMSprop,
(Adagrad) which works well on sparse gradients and (RMSProp) which works well
in online and nonstationary settings respectively.

Adam implements the exponential moving average of the gradients to scale the learning rate instead of a simple
average as in Adagrad. It keeps an exponentially decaying average of past
gradients.

Adam is computationally efficient and has very less memory
requirement.

Adam optimizer is one of the most popular and famous gradient
descent optimization algorithms.

We can simply say that, do
everything that RMSProp does to solve the denominator decay problem of AdaGrad.
In addition to that, use a cumulative history of gradients that how Adam
optimizers work.

The updating rule for Adam is shown below

If you have already gone through my previous article
on optimizers and especially RMSprop optimizer then you may notice that the
update rule for Adam optimizer is much similar to RMSProp optimizer, except
notations and help we also look at the cumulative history of gradients (**m**_t).

Note that the third step in the update rule above is used
for bias correction.

So, we can define Adam
function in python as shown below.

```
def adam():
w, b, eta, max_epochs = 1, 1, 0.01, 100,
mw, mb, vw, vb, eps, beta1, beta2 = 0, 0, 0, 0, 1e-8, 0.9, 0.99
for i in range(max_epochs):
dw, db = 0, 0
for x,y in data:
dw+= grad_w(w, b, x, y)
db+= grad_b(w, b, x, y)
mw = beta1 * mw + (1-beta1) * dw
mb = beta1 * mb + (1-beta1) * db
vw = beta2 * vw + (1-beta2) * dw**2
vb = beta2 * vb + (1-beta2) * db**2
mw = mw/(1-beta1**(i+1))
mb = mb/(1-beta1**(i+1))
vw = vw/(1-beta2**(i+1))
vb = vb/(1-beta2**(i+1))
w = w - eta * mw/np.sqrt(vw + eps)
b = b - eta * mb/np.sqrt(vb + eps)
print(error(w,b))
```

I hope after reading this article, finally, you came to know about
**what is Adam, how it works? and What’s the difference between Adam and other
optimizers algorithms and You also see how it is most important optimizer**.
In the next articles, I will come with a detailed explanation of some other
type of optimizers.** **For more blogs/courses on data science, machine
learning, artificial intelligence and new technologies do visit us at **InsideAIML**.

Thanks for reading…