Optimal Ad Ranking for Profit Maximization

Raju Balakrishnan (Arizona State University)Subbarao Kambhampati (Arizona State University)

WebDB ‘08 Optimal Ad Ranking for Profit Maximization

Ad Ranking: State of the Art

Sort by

Bid Amount x Relevance

We Consider Ads as a Set, and ranking is based on User’s Browsing Model

Sort by

Bid Amount

Ads are Considered in Isolation, Ignoring Mutual influences.

WebDB ‘08

Mutual Influences

Optimal Ad Ranking for Profit Maximization

Three Manifestations of Mutual Influences on an Ad are1. Similar ads placed above

Reduces user’s residual relevance of the ad 2. Relevance of other ads placed above

User may click on above ads may not view the ad 3. Abandonment probability of other ads placed

above User may abandon search and not view the ad

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User’s Browsing Model

Optimal Ad Ranking for Profit Maximization

• User Browses Down Staring at First Ad

®

Abandon Browsing with Probability

Goes Down to next Ad with probability

• At every Ad he May

Process Repeats for the Ads Below With a

Reduced Probability

Click the Ad With Relevance Probability

))(|)(()( aviewaclickPaR

If is similar to residual relevance of goes down and abandonment probabilities goes up.

2a 1a2a

WebDB ‘08 Optimal Ad Ranking for Profit Maximization

Expected Profit Considering Ad Similarities

Considering Bid Amounts ( ), Residual Relevance ( ), abandonment probability ( ), and similarities the expected profit from a set of n ads is,

THEOREM: Optimal Ad Placement Considering Similarities between the ads is NP-Hard

Proof is a reduction of independent set problem to choosing top k ads considering similarities. (Refer Paper for Proof)

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i aaRaRa Expected Profit =

)( ia)( iaR)$( ia

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Dropping similarity, hence replacing Residual Relevance ( ) by Absolute Relevance ( ),

Ranking to Maximize This Expected Profit is a Sorting Problem

Optimal Ad Ranking for Profit Maximization

Expected Profit Considering other two Mutual Influences (2 and 3)

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jji

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i aaRaRa Expected Profit =

)( iaR)( iaR

WebDB ‘08 Optimal Ad Ranking for Profit Maximization

Optimal Ranking

The physical meaning RF is the profit generated for unit consumed view probability of ad

Ads above have more view probability. Placing ads producing more profit per consumed view probability is intuitively justifiable. (Refer paper for proof of optimality)

Rank ads in Descending order of:

)()$(

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aa

aRaaRF

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Comparison to Yahoo and Google

Yahoo! Assume

abandonment probability is zero

GoogleAssume

where is a constant for all ads

Optimal Ad Ranking for Profit Maximization

Assumes that the user has infinite patience to go down the results until he finds the ad he wants.

Assumes that abandonment probability is negatively proportional to relevance.

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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

15

20

25

30

35

40

Exp

ecte

d P

rofit

RFBid Amount x RelevanceBid Amount

Optimal Ad Ranking for Profit Maximization

Quantifying Expected Profit

Proposed strategy gives maximum profit for the entire range

Bid Amount Only strategy becomes optimal at í (a) = 0

45.7%35.9%

Number of ClicksZipf Random with exponent 1.5

Abandonment ProbabilityUniform Random as

RelevanceUniform Random as

Bid AmountsUniform Random

Difference in profit between RF and competing strategy is significant

10)$(0 a

1)( aR

)(0 a

WebDB ‘08 Optimal Ad Ranking for Profit Maximization

Contributions Extending Expected Profit Model of Ads

Based on Browsing Model, Considering Mutual Influences

NP-Hardness proof for placement considering similarities.

Optimal Ad Ranking Considering Mutual Influences Other than Ad Similarities.Subsumes Google and Yahoo placement as

special casesSimulation shows significant improvement in

expected profit.Hope to evaluate by assessing abandonment

probabilities (future work)