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The problem that we
have studied so far

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captures the essential features
of the AdWords problem,

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but it can be extended
in several ways.

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We will shortly talk
in some more detail

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about two of these, which
relate to the idea of slates

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or positions, and which relate
to the idea of personalization.

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Aside from these two
extensions, there

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are also many other
issues that Google

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deals with on a daily basis.

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One of these is related
to click-through-rates.

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In particular, how does
Google know the chance

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that a user clicks
on a given ad?

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Google does this by analyzing
large amounts of user data

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and building predictive
models, similar to those

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we studied in this class, to
predict how often users click

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on different ads when they're
shown with different queries.

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Another issue is related
to the advertisers.

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We saw earlier that the
price-per-click depends

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on how the advertisers
place their bids.

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So understanding the
behavior of advertisers

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and incorporating this behavior
in the optimization model

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is also another
important consideration.

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Let's move on to discuss
the idea of slates.

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In our example with AT&T,
T-Mobile, and Verizon,

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we assume that the search
page for each query

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has space for only one ad.

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Now typically, as
we saw in Video 1

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when we searched for
Nine Inch Nails tickets,

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there's usually
space for many ads.

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In this case,
Google has to decide

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which combination
of ads, or slate,

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to display with each query.

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Although this would seem to
be a more complicated problem,

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it can still be solved
using linear optimization.

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Before, our variables
were defined

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as x of a given advertiser
and a given query.

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But now, we would
instead define them

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as x for a given slate
and a given query.

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So for example, for our wireless
service provider example,

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if we had two spaces on our
results page, then for query 1,

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we'd still have x_A1, x_T1, and
x_V1, where here, for example,

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x_V1 is the number
of times that we

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display Verizon with query 1.

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But we would also have
x_AT1, x_AV1, and x_TV1.

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Here, for example, x_AV1,
represents the number of times

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that we display the slate
containing AT&T and Verizon

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with query 1.

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Now, this can become
even more complicated

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as the position of the ad
within the slate is important.

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For example, ads to the
right of the search results

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might not attract as many
clicks as those above the search

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results.

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In this case, we would
also consider x_TA1, x_VA1,

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and x_VT1.

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And here, the first
ad in the combination

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is the ad that is placed
in the first position.

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So, for example,
here T-Mobile is

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placed in the first
position for x_TA1

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and AT&T is placed in
the second position.

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We would formulate our
objective and our budget

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and query constraints in
the same way as before,

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but making sure that slates that
contain a certain advertiser

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use up that advertiser's budget.

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And slates in a
given query counts

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towards that query's
estimated number of requests.

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Let's now discuss the
idea of personalization.

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In addition to the query,
Google can use other information

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to decide which ad to display.

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For example, Google might
know the geographic location

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of the user as determined
from their IP address.

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Google might also know
other information,

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such as different Google
searches that the user has

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conducted, and browser
activity on Google's website.

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The question then is, how can
Google take this into account

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when deciding which ads
display for which queries?

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Well, just like slates, we
could also incorporate this

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into our linear
optimization model.

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Rather than working
with queries,

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we would work with combinations
of queries and user profiles.

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So rather than having
x defined for a given

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advertiser and a
given query, we would

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define x for a given advertiser,
a given query, and a given user

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profile.

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So here, a user profile just
describes the type of user.

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For instance, a profile
might be men aged 20 to 25

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who live in Boston,
Massachusetts in the United

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States.

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If we had three user profiles,
we could name them P1, P2, P3.

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And then for AT&T
for query 1, we

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would use x_A1P1 to
denote the number of times

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that we display
AT&T's ad with query 1

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for a user of profile P1.

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The rest of the model could
then be easily accommodated

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for this new type of
modeling consideration.

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We'll just now summarize
the salient points

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of this recitation.

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So, so far, we've
studied a small instance

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of Google's ad
allocation problem, where

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we had just three advertisers
or bidders and three queries.

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We saw how an optimization
solution increases revenue

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by 16% over a simple
common sense solution.

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What I'd like you to remember
is that in reality, this problem

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is much larger.

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For each query that Google
receives on its search engine,

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there may be
hundreds to thousands

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of advertisers bidding on it.

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In terms of dollar
amounts, in 2012,

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Google's total revenue
from advertising

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was over $40 billion.

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At this scale, the gains that
are possible from optimization

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become enormous, and I
hope this convinces you

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of the value of
linear optimization

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in online advertising.