optimization problems in internet advertising

Optimization Problems in Internet Advertising

Cliff SteinColumbia University

Google Research

Internet Advertising

Multi-billion dollar business Google purchased DoubleClick for over 3

billion dollars, 2 years ago A new paradigm for advertising Many interesting mathematical, economic,

and computational problems

Some Statistics

Vendor Ad viewersGoogle 1,118DoubleClick 1,079Yahoo 362MSN 309AOL 156Adbrite 73Total 3,087

(millions, one month in 2008)**From Wikipedia

Internet Advertising

2 main types Adwords (right column, auction) Display ads (scattered, matching)

This talk

Overview of some issues in internet advertising

Talk about two particular algorithmic results, one on adwords optimization, one on display ads

No attempt to comprehensively survey the area

Adwords

Advertisers bid to have the right to appear when a user enters a search query

Advertisers are chosen according to some kind of auction mechanism

Ads are displayed for free. Advertiser pays when a user clicks.

New Kind of Auctions Traditional auctions are for one item, or a small

number of items, and are done on a human time scale

Many types of auctions (ascending, sealed-bid, second price …) are well understood mathematically

Adwords auctions are a new type of auction, where a bidder bids on multiple items for many items on a “computer” time scale

Mathematically, it is a whole new ballgame

Technical Challenges Mechanism Design - designing rules of

a game or system to achieve a specific outcome, even though each agent may be self-interested

Technology to implement the auctions Optimization for

Advertiser (maximize clicks, minimize money spent) Internet company (maximize profit, maximize user

happiness, minimize bad publicity/lawsuits)

Basic Mechanism Design

Let’s set up an auction for

Suppose it is worth $20 to me, but $10 to Alex Rodriguez (and these values are private)

We each bid some amount: Who gets the hat? How much do they pay?

Basic Mechanism Design

Auction Mechanism

Private value

2

Private value

1

Bidders

Bid 2

Bid 1

Gives item to someoneCollects payments

Some goals in an auction

Truth revealing (bidders want to bid their values)

Revenue maximizing (auctioneer maximizes profit)

Social welfare (good for bidders)

These goals may be in conflict

First price auctions

Everyone bids, highest bidder gets item for the price he bid, others pay nothing and get nothing.

Bidders Utility = value of item received – payment.

First price auction

My utility = $20 - $20 = 0 Arod utility = $0 - $0 = 0.

Arod $10

Me$20

First PriceAuction Mechanism

Cliff gets it.Cliff pays $20Arod pays $0

Bid 20

Bid 10

Can I do better?

First price auction (2)


Arod $10

Me$20

First PriceAuction Mechanism


Bid 15

Bid 10

First Price AuctionsSuppose I bid $15, Arod bids $10.

I get item for $15, Arod gets nothing for nothing. My utility = 20- 15 = 5 Arod utility = 0-0 = 0

I am happier I am not telling the “truth” anymore My bid needs to be a function of everyone else’s bid (in

addition to my value) Auctioneer makes less money

Second Price Auctions

Everyone bids. Item goes to the highest bidder, who pays the bid of the second-highest bidder.

Bidders Utility = value of item received – payment

Second price auction


Arod $10

Me$20

Second PriceAuction Mechanism


Bid 20

Bid 10


Theorem: In a second-price auction, no bidder has any incentive to lie.

Proof: I don’t lie. If I lie any amount >= 10, nothing changes. If I lie < 10, I lose the auction and my utility

is 0. Therefore I don’t want to lie.


Theorem: In a second-price auction, noone has any incentive to lie.

Proof: Arod doesn’t lie. If he lies any amount < 20, nothing

changes for him. If he lies at x > 20, he wins for $20, but

his utility is 20 –x which is negative, so he is worse off.

Notes on Second Price Auctions

Everyone tells the truth May yield less revenue than first-price

auctions Note: we assume that I get no benefit from

seeing you pay more money.

Back to internet auctions We are not auctioning off baseball hats, or

paintings, or cars that were used in the commission of a crime….

We are auctioning off slots on a web page There are:

Multiple slots Advertisers bidding on many keywords Many auctions going on during the course of

a day

Multiple Slots: Generalized Second Price Auctions

Users are bidding for slots, where slot i is more valuable than slot i+1.

Higher slots tend to get more clicks, and therefore cost more (cost per click)

Sort bids, i’th bid gets slot i and pays bid of slot i+1.

Example of GSP Auction

Bids: $1, $0.50, $2.25, $1.20, $0.10, $2.50, $1.25

5 slots

Example 2 of GSP Auction Bids: $1,

$0.50, $2.25, $1.20, $0.10, $2.50, $1.25

5 slots

Slot Bid Payment

1 $2.50 $2.25

2 $2.25 $1.25

3 $1.25 $1.20

4 $1.20 $1.00

5 $1.00 $0.50

Some Complications from GSP We are bidding one amount, but don’t

know which slot we will win. Different advertisers have different

preferences/beliefs about slots You actually might have some incentives

to lie.

In “reality” (google), your bid is actually modified by the “quality” of your ad.

Advertisers bidding on many keywords

An advertiser sets up a campaign in which they advertise on many keywords

Each time a user issues a query that matches one of their keywords, the ad for that keyword enters the auction.

Depending on their bid (and other factors), they may get a slot in the auction

If someone clicks on their ad, they are charged

Question?

How does the advertiser control the total amount that they are charged?

They specify a budget on how much they want to spend in a day

Budgets

Advertiser specifies a daily budget B. They participate in an auction as long as

the daily budget is not spent.

Example

Advertiser Bid on “skiing”

Bid on“hiking”

Daily Budget

Joe’s outdoor store

$0.50 $1.00 $2.00

Campmor $1.00 $0.75 $3.00

Example Auction 1: Hiking. Joe wins. When click

happens, he pays $0.75


Bid on“hiking”

Daily Budget Remaining Budget


$0.50 $1.00 $2.00 $2.00

Campmor $1.00 $0.75 $3.00 $3.00




Bid on“hiking”



$0.50 $1.00 $2.00 $1.25

Campmor $1.00 $0.75 $3.00 $3.00

Example Auction 2: Skiing. Campmor. When click



Bid on“hiking”



$0.50 $1.00 $2.00 $1.25

Campmor $1.00 $0.75 $3.00 $3.00

Example Auction 2: Skiing. Campmor. When click



Bid on“hiking”



$0.50 $1.00 $2.00 $1.25

Campmor $1.00 $0.75 $3.00 $2.50




Bid on“hiking”



$0.50 $1.00 $2.00 $1.25

Campmor $1.00 $0.75 $3.00 $2.50




Bid on“hiking”



$0.50 $1.00 $2.00 $0.50

Campmor $1.00 $0.75 $3.00 $2.50

Example Auction 4: Hiking. Joe should win. But he

doesn’t have enough budget, so Campmor wins. Pays some amount < 0.75 (depends on other bidders and system minimums).


Bid on“hiking”



$0.50 $1.00 $2.00 $0.50

Campmor $1.00 $0.75 $3.00 $2.50

Lessons

Auction is not always won by the highest bidder.

Bidders may engage in strategic behavior, allow others to win at a high price so as to exhaust their budget and be removed from competition (bid jamming)

What about the advertiser?

Suppose you are an advertiser You want to bid on many keywords How should you allocate your budget

among multiple keywords?

Example: Asics Keywords:Shoe, sneaker, running shoe, gel kayano,

gel nimbus, pronating, marathon shoe, race shoe, reebok, I hate asics, sporting goods, footware, racing attire, race, wicked fast, air jordan, laces, shin splints, white sneakers, …

Budget: $100 What to bid on each one?

Who advertises adwords?

Optimization Problem Suppose that I knew

Everyone else’s bids Exactly how many times each keyword will come up The number of clicks associated with each position Google’s exact advertising mechanism

How should I bid?(Note: Think of bid as cost-per-click (cpc))

Queries vs. Keywords

asics

Gel kayano

I hateasics

Red running shoes

shoe

asics

I hate peanut butter

Red asics

Asics gel nimbush

Running shoes

Bidding Problem Bidding on multiple keywords is an NP-hard

problem (knapsack)

Knapsack: Given a set of items with sizes and values and a knapsack of size B, choose a maximum value set of objects that fit in the knapsack.

Proof of difficulty is also demonstrated by the amount that people are willing to pay to solve the problem.

How do we evaluate a bidding strategy

Objective: maximize number of clicks, subject to budget

We compare the performance of our (simple) strategy to the performance of an arbitrarily complicated strategy of an adversary, take the ratio, and minimize over all inputs

))(/)((min iOPTiAI

Simple Strategies are pretty good

Feldman, Pal, Muthukrishnan, Stein There exists one amount b, and if I bid b

on every keyword, I will get at least ½ the clicks of any strategy

There exists two numbers b1 and and b2, and if I bid either b1 or b2 on every keyword, I will get at least 63% (e/(e-1))of the clicks of any strategy

Theorem is pessimistic

Display advertising

From ALENEX 2009, with Cosmin Negruseri, Mircea Pasio, Barbara Stanley, Cristian Strat

Display Ads Publishers (e.g. newspapers, travel

agents) make on-line “real estate” available for ads

Advertisers purchase impressions (e.g. 100 appearances on CNN money page on 5/3/2009)

Users visit pages, see advertisements Market manager (e.g. google) has to

decide which ad is displayed for each user

Optimization Problem

Publisher is offering certain types of unsold “inventory” (views on pages with certain demographics)

Advertiser is looking to buy some amount of inventory

Market manager needs to quickly decide if advertisers demand can be satisfied.

Algorithmic Ideas

Push/relabel algorithms work by pushing flow over on edge at a time (pushing downhill)

Excess accumulates at vertices Vertices are relabeled, pulling them uphill. Flow is pushed over eligible edges

(pointing downhill, have residual capacity)

Previous experimental work

None that we are aware of

Synthetic Distributions Uniform Random High-Lo (chosen flow with additional edges) Rope (long paths plus some useless edges) Zipf (edge between i and j with probability

proportional to 1/(ij). Said to model real-world web graphs

First three are modifications of generators from [CG97

Experimental Questions

Can we efficiently solve the real problems we have?

On bipartite graphs, do the specialize algorithms help?

Which variants are best? Which heuristics are needed? Do these conclusions generalize to other

data?

Typical results (hi-lo)

Conclusions for display ads

Bipartite flow algorithms are worth using in practice

FIFO is usually the best variant, and rarely the worst

Heuristics (gap relabelling, exact label updates) are helpful

Data is publicly available

General Conclusions Internet advertising is an important area Interesting algorithmic and game-theoretic

problems need to be solved. There are problems for the advertiser and

for the auction maker and for the user Ongoing work – studying the online

problem of matching impressions with advertisers (e.g. Feldman, Korula, Muthukrishnan, Makroni 09)

optimization problems in internet advertising

Documents

elses bid

arod utility

arod bids

bidders utility

price auctionmy utility

truth anymoremy bid

bidder bids

price auctionssuppose