All language subtitles for 02_implementing-gradient-descent.en

Let's take a look at
how you can actually

implement the gradient
descent algorithm.

Let me write down the
gradient descent algorithm.

Here it is. On each step,

w, the parameter,

is updated to the
old value of w minus

Alpha times this term d/dw

of the cos function J of wb.

What this expression
is saying is,

after your parameter w by
taking the current value of

w and adjusting it
a small amount,

which is this expression
on the right,

minus Alpha times
this term over here.

If you feel like there's a lot

going on in this equation,

it's okay, don't worry about it.

We'll unpack it together.

First, this equal notation here.

Now, since I said
we're assigning

w a value using this equal sign,

so in this context,

this equal sign is the
assignment operator.

Specifically, in this context,

if you write code
that says a equals c,

it means take the value c and
store it in your computer,

in the variable a.

Or if you write a
equals a plus 1,

it means set the value of
a to be equal to a plus 1,

or increments the
value of a by one.

The assignment
operator encoding is

different than truth
assertions in mathematics.

Where if I write a equals c,

I'm asserting, that is,

I'm claiming that the values

of a and c are equal
to each other.

Hopefully, I will never write
a truth assertion a equals

a plus 1 because that just
can't possibly be true.

In Python and in other
programming languages,

truth assertions are sometimes
written as equals equals,

so you may see oh,

that says a equals
equals c if you're

testing whether a is equal
to c. But in math notation,

as we conventionally use it,

like in these videos,

the equal sign can be used for

either assignments or
for truth assertion.

I try to make sure I was clear

when I write an equal sign,

whether we're assigning
a value to a variable,

or whether we're
asserting the truth of

the equality of two values.

Now, this dive more deeply

into what the symbols
in this equation means.

The symbol here is the
Greek alphabet Alpha.

In this equation, Alpha is
also called the learning rate.

The learning rate is usually
a small positive number

between 0 and 1 and it
might be say, 0.01.

What Alpha does is,

it basically controls how

big of a step you take downhill.

If Alpha is very large,

then that corresponds to

a very aggressive gradient
descent procedure

where you're trying to
take huge steps downhill.

If Alpha is very small,

then you'd be taking small
baby steps downhill.

We'll come back later to
dive more deeply into

how to choose a good
learning rate Alpha.

Finally, this term here,

that's the derivative term
of the cost function J.

Let's not worry
about the details

of this derivative right now.

But later on, you'll get to

see more about the
derivative term.

But for now, you can think of

this derivative term that I drew

a magenta box around
as telling you

in which direction you want
to take your baby step.

In combination with the
learning rate Alpha,

it also determines the size

of the steps you want
to take downhill.

Now, I do want to mention that

derivatives come from calculus.

Even if you aren't familiar with

calculus, don't worry about it.

Even without knowing
any calculus,

you'd be able to figure
out all you need

to know about this
derivative term

in this video and the
next. One more thing.

Remember your model
has two parameters,

not just w, but also b.

You also have an
assignment operations

update the parameter b
that looks very similar.

b is assigned the
old value of b minus

the learning rate Alpha times

this slightly different
derivative term,

d/db of J of wb.

Remember in the graph
of the surface plot

where you're taking baby steps

until you get to the
bottom of the value,

well, for the gradient
descent algorithm,

you're going to repeat

these two update steps until
the algorithm converges.

By converges, I mean that you

reach the point at a
local minimum where

the parameters w and b no longer

change much with each
additional step that you take.

Now, there's one
more subtle detail

about how to correctly in
semantic gradient descent,

you're going to update
two parameters, w and b.

This update takes place for
both parameters, w and b.

One important detail is
that for gradient descent,

you want to simultaneously
update w and b,

meaning you want to update

both parameters
at the same time.

What I mean by that, is
that in this expression,

you're going to update w
from the old w to a new w,

and you're also updating b from

its oldest value to
a new value of b.

The way to implement this is
to compute the right side,

computing this
thing for w and b,

and simultaneously
at the same time,

update w and b to
the new values.

Let's take a look
at what this means.

Here's the correct
way to implement

gradient descent which does
a simultaneous update.

This sets a variable temp_w
equal to that expression,

which is w minus that term here.

There's also a set in another
variable temp_b to that,

which is b minus that term.

You compute both for hand
sides, both updates,

and store them into
variables temp_w and temp_b.

Then you copy the value
of temp_w into w,

and you also copy the
value of temp_b into b.

Now, one thing you may
notice is that this value of

w is from the for
w gets updated.

Here, I noticed that
the pre-update w

is where it goes into the
derivative term over here.

In contrast, here is

an incorrect implementation of

gradient descent that does
not do a simultaneous update.

In this incorrect
implementation,

we compute temp_w,

same as before, so
far that's okay.

Now here's where things
start to differ.

We then update w
with the value in

temp_w before calculating
the new value

for the other parameter to be.

Next, we calculate temp_b
as b minus that term here,

and finally, we update b
with the value in temp_b.

The difference between
the right-hand side and

the left-hand side
implementations

is that if you look over here,

this w has already been
updated to this new value,

and this is updated
w that actually

goes into the cost
function j of w, b.

It means that this term here
on the right is not the

same as this term over here
that you see on the left.

That also means
this temp_b term on

the right is not quite the

same as the temp b
term on the left,

and thus this updated value for

b on the right is not the same

as this updated value for
variable b on the left.

The way that gradient descent
is implemented in code,

it actually turns out to be
more natural to implement

it the correct way with
simultaneous updates.

When you hear someone talk
about gradient descent,

they always mean the
gradient descents where you

perform a simultaneous
update of the parameters.

If however, you were

to implement
non-simultaneous update,

it turns out it will probably
work more or less anyway.

But doing it this way isn't

really the correct
way to implement it,

is actually some other algorithm

with different properties.

I would advise you
to just stick to

the correct
simultaneous update and

not use this incorrect
version on the right.

That's gradient descent.

In the next video,

we'll go into details of

the derivative term which
you saw in this video,

but that we didn't really
talk about in detail.

Derivatives are
part of calculus,

and again, if you're
not familiar with

calculus, don't worry about it.

You don't need to know
calculus at all in order to

complete this course or
this specialization,

and you have all the
information you need

in order to implement
gradient descent.

Coming up in the next video,

we'll go over
derivatives together,

and you come away with

the intuition and
knowledge you need to

be able to implement and apply
gradient descent yourself.

I think that'll be
an exciting thing

for you to know
how to implement.

Let's go on to the next
video to see how to do that.