Gradient Descent  Problem of Hiking Down a Mountain
Udacity
Have you ever climbed a mountain? I am sure you had to hike down at some point? Hiking
down is a great exercise and it is going to help us understand gradient descent.
Whats the goal when you are hiking down a mountain?
 To have fun and to
reach the bottom. Let’s focus on reaching the bottom for now.
What is the red dot doing when it’s hiking down?
It’s always going in the downward
direction, until it hits the bottom. Let’s call our friend calculus and see what she has to
say about this.
Derivatives
Before we hop in, let me remind you a little bit about derivatives. There are different ways
to look at derivatives, two of the most common ones are
•
Slope of the tangent line to the graph of the function
•
Rate of change of the function
1
Following are some of the common derivatives:
•
d
(
x
2
)
dx
= 2
x
•
d
(

2
y
5
)
dy
=

10
y
4
•
d
(5

θ
)
2
dθ
=

2(5

θ
) (negative sign coming from

θ
)
Sounds great! What if, we have more than one variable in our function? Well, we will talk
about partial derivatives then! Let’s look at some examples:
•
∂
∂x
(
x
2
y
2
) = 2
xy
2
•
∂
∂y
(

2
y
5
+
z
2
) =

10
y
4
•
∂
∂θ
2
(5
θ
1
+ 2
θ
2

12
θ
3
) = 2
•
∂
∂θ
2
(0
.
55

(5
θ
1
+ 2
θ
2

12
θ
3
)) =

2 (Can you convince yourself where the

is coming
from?)