Maximizing Clicks of Sponsored Search by Integer Programming
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Maximizing Clicks of Sponsored Search by Integer
Programming
Ahmad Zainal-Abidin and Jun Wang
Department of Computer Science
University College London
Gower St, London WC1E 6BT
United Kingdom
{a.zainalabidin, jun.wang}@cs.ucl.ac.uk
ABSTRACT commonly used greedy methods.
Sponsored search enables advertisers to promote their prod-
ucts to targeted users based on the interests expressed in Categories and Subject Descriptors
the users’ web search queries. A typical search-based ad-
H.3.3 [Information Storage and Retrieval]: Information
vertisement campaign requires an advertiser to select one or
Search and Retrieval
multiple phrases (query terms) for each ad (e.g. textual data
with links to landing pages), and separately place bids for
the selected phrases in an attempt to win display slots for General Terms
the ads. A click on each ad costs the advertiser an amount Algorithms, Economics, Performance
set by a search engine through an auction and rewards the
search engine its advertising revenue.
Although advertisers and web search providers have con- Keywords
sidered the number of clicks as a practical measure of the Sponsored search, Online advertising, Optimization
effectiveness, their optimization units are, however, not nec-
essarily the same - the search providers generally focus on
clicks per query, while the advertisers are interested in clicks 1. INTRODUCTION
per ad. In this paper, we address the clicks maximization Online advertising has been growing rapidly. The large
problem from the latter point of view. To the advertiser, all volume of ad data has brought challenging problems such
ads in the campaign have potential future returns, e.g. clicks, as understanding query intent [7], personalized ad delivery
conversions, revenues, or profits, and all phrases associated [4], ad ranking [8], and optimization [21, 9]. Search-based
with the ads collectively contribute towards the overall re- advertising, display advertising, social network advertising,
turns. Additionally, each phrase has uncertain impression and email marketing are under the umbrella of online ad-
rate, click-through rate and cost per click. Due to these vertising. Search-based advertising itself, is a multi-billion
uncertainties, using a budget effectively to generate max- dollar business. It was reported that search engines’ rev-
imum possible clicks is a non-trivial task. In this paper, enues from search advertising in 2006 reached $9.4 billion, a
to consider the overall effectiveness of the selected phrases, remarkable increase of approximately $3.65 billion from the
clicks maximization is formulated as a constrained integer revenues earned in the previous year [20]. Typically, three
programming problem. parties are involved in search-based advertising: search en-
In the formulation, an overall budget and a maximum av- gines, advertisers, and users.
erage cost per click the advertiser is willing to spend are Through their advertising services, the search engines such
modeled as the constraints. Moreover, in certain practi- as Google and Yahoo! provide the mechanism to enable
cal situations, it is more useful to formulate the problem the advertisers promote their products to targeted groups of
by minimizing advertising cost given the number of clicks users. The search engines act as auctioneers selling keywords
the advertiser intends to achieve. We show that the click to the advertisers. Examples of the advertising services in-
maximization and the cost minimization formulations are clude Google AdWords1 and Yahoo! Sponsored Search2 .
mathematically equivalent. In our simulation, the proposed The advertisers require slots to place their marketing mes-
methods have yielded promising results when compared with sages (ads) on the Web. Joachims et al. [17] argue that for
each ad, the position and the result page number of the ad
have a significant influence on its click-through rate (CTR).
In the sponsored search framework, bid prices and the rel-
evancies between bid phrases and user queries influence the
Permission to make digital or hard copies of all or part of this work for slot position to be awarded. However, the bids placed by
personal or classroom use is granted without fee provided that copies are other advertisers on similar phrases are unknown. Either
not made or distributed for profit or commercial advantage and that copies
bear this notice and the full citation on the first page. To copy otherwise, to
each bid will end up winning a slot is uncertain. Motivated
republish, to post on servers or to redistribute to lists, requires prior specific by the notion that the ads displayed at higher positions are
permission and/or a fee. 1
ADKDD’10, July 25, 2010, Washington D.C., USA. http://www.google.com/adwords
2
Copyright 2010 ACM 978-1-4503-0221-0 ...$10.00. http://searchmarketing.yahoo.com/srch/index.phplikely clicked on, the advertisers typically compete to bid for age CPC. Both the click maximization and cost minimiza-
phrases that they believe to be relevant to user queries to tion problems are posed as integer programming problems.
increase the chances that their ads will be placed at higher Mathematically, the formulations for the two problems are
positions. The CTRs are arranged in a non-increasing or- equivalent and our simulation confirms this insight.
der with ads placed at higher positions have higher CTRs. The paper is organized as follows. We discuss related work
The minimum bid for an ad to stay in a certain position in Section 2, present our problem formulation and theoreti-
is therefore influenced by its CTR. Ideally, the CTR is a cal framework in Section 3, provide performance evaluation
random variable, resembling a practical scenario that its ac- in Section 4, and conclude our study in Section 5. For sim-
tual value is uncertain. However, it can be estimated by plicity, keyword(s) and phrase(s) are interchangably used.
investing a small amount of money on keywords to experi-
ment the traffic that they possibly attract. Search engines 2. RELATED WORK
companies, through their advertising services, provide infor-
In the last few years, many researches from the perspective
mation for keyword performance prediction. An ad cost per
of auctioneers (search engines) [26, 14, 5, 10] and advertisers
click (CPC) is determined through an auction [14]. Cur-
[15, 27, 13, 16, 28, 6, 25] have been conducted on auction and
rently, for each ad, each advertiser is required to choose a
bidding optimization. The views of auctioneers and adver-
set of keywords, determine the bid price for each of the cho-
tisers on sponsored search are different. For example, while
sen keywords, set a daily budget, and specify the duration
the auctioneers aim to increase revenues generated from user
of participation in the ad campaign before taking part in the
clicks on ads after issuing query terms, the advertisers are
auction.
interested in the return on investment (ROI) on their ads.
The users issue ad-hoc topics to express their information
Papers on keyword modeling, ad ranking positions, and
needs. In organic search, the relevance between a search
clicks have been discussed in [12, 3, 2, 18, 10]. Aggarwal,
topic (query) and documents on the Web is used to retrieve
Goel and Motwani [5] design an auction called laddered auc-
relevant documents. However, in search-based advertising,
tion. Unlike the next-price auction, they argue that their
ads are not retrieved purely based on relevance. The match
auction to be a truthful auction. Their approach is that,
between the search topics and the advertisers’ keywords, the
given a weight and a bid, the laddered auction assigns a
bid prices and CTRs for the keywords are among factors in
score, a ranking position and a price for the slot on auction.
deciding which ads are eventually given slots, although the
The assigned price is lower than the bid but not similar
exact method is unique from a search engine to another.
to the price assigned by the next-price auction. Edelman,
The selected ads will be displayed alongside organic search
Ostrovsky and Schwarz [14] study Internet advertising and
results. For a pay-per-click model, the advertisers will be
the generalized second-price (GSP) auction that has become
charged only if there are clicks on their displayed ads. In
successful. They compare GSP with Vickrey-Clarke-Groves
this paper, we aim at improving advertisers’ experience by
(VCG) mechanism that is truth-telling and has an equilib-
maximizing the overall impact of their ad campaigns. Some
rium dominant strategies.
common notions to measure the impact are profits, revenues,
Borgs et al. [10] study multi-unit auctions with budget-
conversions, and clicks. We use the number of clicks, a simi-
constrained bidders. Each bidder has a budget and a private
lar measure assumed in [16]. Very recently, researchers have
valuation. Their method is designed so that the revenue
started looking at the direction to improve the advertiser’s
for the auctioneer be maximized. Our proposed study also
experience in the search-based advertising ecosystem, mod-
considers budget and private valuation of a bidder, but the
eling the keyword selection as an optimization problem, con-
aim is to optimize clicks. Our focus is also different as we
strained by the budgets [23, 27, 25, 15, 16, 6].
consider the budget constrained problem from a portfolio of
In a budget constrained bidding, the advertisers specify
phrases point of view.
their advertising budgets. It is important for them to de-
In [23], Rusmevichientong and Williamson discussed CTRs
liver their marketing messages in a cost effective manner.
for various keywords over time and how to select the key-
As ads are perishable, one of the criteria that the auctioneer
words effectively. In their study, keywords with high profit-
awards display slots is when the advertisers have positive
to-cost ratio are given priorities in the selection of profitable
budgets. In a typical ad campaign, advertisers have many
keywords. Although our study involves keywords (phrases),
ads with each has multiple associated keywords. With an
we do not address the choice of keywords. We assume the
assumption that all ads have future returns, all keywords
keywords selected by advertisers are the ones they are most
associated with the ads potentially contribute towards the
interested in. Another study on CTR was done by Richard-
overall clicks. With a lot of ads to manage, setting a bid
son, Dominowska and Ragno [22] to predict CTR for new
for each keyword can be a daunting task. This motivates
ads in the advertising system. They argue that the explo-
us to view keywords as a portfolio as there has been little
ration and exploitation of new ads are crucial to enable new
previous research on how advertisers manage their ads in a
ads to have opportunities to be clicked on. Unlike ads that
portfolio of phrases mode to maximize the overall impact of
have established themselves in the advertising system, new
their campaigns. To maximize clicks, we propose a method
ads lack historical data. They propose that CTRs for new
whereby an advertiser specifies (i) an overall budget and (ii)
ads rely on the information about the ads itself. Our work
a maximum average CPC for an ad the advertiser is willing
uses CTR for clicks estimation. Ideally, CTRs are random
to spend. We argue that specifying the maximum average
variables that are obtained at the time the bidding takes
CPC for each ad eliminates the need to specify a bid for
place. Accurate CTRs provide more meaningful informa-
each keyword associated with an ad without sacrificing the
tion on how likely an ad will be clicked on.
overall total clicks that the ad can generate. We also for-
In online advertising framework, the work using linear pro-
mulate cost minimization constrained by (i) minimum clicks
gramming has been discussed in [19] by Nakamura and Abe.
an advertiser wishes to generate and (ii) a maximum aver-
However, their work focuses on the banner and pay-per-impression. Specifically, their interest leans towards schedul-
ing ad impressions. Our approach considers integer pro-
gramming but focuses on a more recent model in online ad-
vertising which is cost-per-click advertising model.
The click maximization is clearly a variant of optimization
problem. Some papers relevant to search-based advertising
discussing bid optimization from the perspective of advertis-
ers can be found in [15, 27, 16]. In their paper, Feldman et
al. [16] propose bidding technique on keywords. They apply
uniform bidding on all keywords. They claim the strategy
is able to generate at least 1 - 1/e fraction of the maxi-
mum clicks possible. Similar to their objective to maximize
clicks for a given budget, our focus is different. Our algo-
rithm does not bid uniformly for all keywords. Rather, the
algorithm uses the specified average CPC which is within
the advertiser’s control as the limit to bid on each phrase
in an attempt to maximize overall clicks. In [27], Zhou, Figure 1: An example of combinations of cost-click
Chakrabarty and Lukose model the budget-constrained op- data
timization problem as an online multiple-choice knapsack
problem. Their objective is to maximize revenues of an ad-
vertiser without the knowledge of other bidders’ bid prices budget β of 4000.00, and her valuation of maximum average
and CTRs. The problem that we address is similar in the CPC ϕ is 3.00. A greedy approach to solve the problem
sense that for each ad, an advertiser is awarded at most one will bid in such a way to be able to win the 3rd, 5th, and
slot per ad per user query. Eyal et al. [15] address a prob- 4th positions3 from Table 1(a), Table 1(b) and and Table
lem in bid optimization. Although our study is a variant of 1(c), respectively. The total number of clicks is 945; 500 for
bid optimization, their focus is more on bid optimization for phrase X, 200 for phrase Y , and 245 for phrase Z. In this
broad match auctions. example, the average CPC using greedy method is 2.68.
However, the above solution is not optimal. If the adver-
tiser A is willing to take more risks by spending more on
3. PROPOSED METHOD bids, the overall number of clicks will likely to increase. The
We describe a phrase as a single keyword (e.g. under- optimal number of clicks, given the two constraints β and ϕ,
ground ) or multiple keywords (e.g. London underground ). will be at positions 2nd, 4th, and 6th (700 + 250 + 210 =
While it is not compulsory to associate an ad with multi- 1160 clicks) for phrases X, Y , and Z respectively. The total
ple phrases, the additional phrases increase the likelihood advertising cost is 3452 which is less than β. The average
of the ad to be clicked on. In this paper, the overall gen- CPC is 2.98 which is less than ϕ. Given the two constraints
erated clicks will be the primary objective. As an illustra- and the data in Table 1, 2.98 is the closest to 3.00 it can get.
tion, consider a static model in which an advertiser A has For a small number of ad such as in the example, it is easy
an ad represented by phrases X, Y , and Z (Table 1). As- to find the optimal solution, given the advertiser’s budget
sume further that there are seven display slots available. In β and the advertiser’s valuation of average CPC ϕ. With-
practice, the total number of slots awarded per user query out ϕ the advertiser may be assigned to a more expensive
varies with different search engines implement their algo- CPC, hence the budget β becomes exhausted sooner. For
rithms differently. Table 1 provides some statistics on X, Y a large number of phrases, manually determining optimized
and Z. In this example, an ad placed lower than 7th posi- combination can be a difficult task. Some might argue why
tions on X, Y , and Z will not get displayed. In practice, would the algorithm choose to bid closer to the advertiser’s
search engines also will not display ads beyond kth posi- maximum valuation of CPC when in fact the advertiser can
tion. In the table, CP C denotes the cost per click, and save more if opting for lower bids. In practice, winning a
CT R the clickthrough rate at the given position. Assume display slot is highly uncertain as other advertisers’ bids are
that the total impressions I for phrases X, Y , and Z are unknown. Using our approach, all prices are considered as
10000, 5000 and 3500, respectively. The CTRs are in non- long as the maximum average CPC is not exceeded. We are
increasing orders in which top positions have higher CTRs. now ready to formulate the problem. It has been a practice
Generally, for n ranking positions their corresponding CTRs that search engine companies never award multiple positions
are (CT R1 ≥ CT R2 ≥ ... ≥ CT Rn ). The impression I is to an ad per user query. So, we assume that an ad is given
counted based on the number of displays associated with a at most one position at a time. Clicks and total costs are
corresponding phrase. To illustrate, the possible click-cost defined as follows:
combinations are shown in Figure 1. In the figure, given
a budget as a constraint, our method will adaptively select λij = αij ∗ γi (1)
points on the optimal curve. With the inclusion of the adver- where λij is the number of clicks at position j for phrase i,
tiser’s valuation of maximum average CPC the advertiser is αij is the clickthrough rate at position j for phrase i, and
willing to spend, the number of clicks generated for the same γi is the impression for phrase i;
budget amount is expected to be no more than the number
of clicks generated if budget is the only constraint. The τij = λij ∗ ρij (2)
maximum average CPC constraint is used as a mechanism
to control the budget exhaustion from happening sooner. 3
An advertiser bids for phrase(s). The display slot position is decided
Consider an example. Suppose that the advertiser A has a normally based on the bid price and the quality (relevance) of the adTable 1: Examples on statistics for phrases X, Y and Z
(a) Phrase X, I=10000 (b) Phrase Y, I=5000 (c) Phrase Z, I=3500
Position CPC CTR Position CPC CTR Position CPC CTR
1 3.75 0.10 1 5.15 0.09 1 4.55 0.12
2 3.15 0.07 2 4.75 0.07 2 3.65 0.10
3 2.61 0.05 3 3.95 0.06 3 3.33 0.09
4 1.59 0.03 4 3.35 0.05 4 2.75 0.07
5 1.21 0.02 5 2.75 0.04 5 2.41 0.07
6 0.98 0.02 6 2.35 0.03 6 1.95 0.06
7 0.59 0.02 7 1.65 0.03 7 1.55 0.05
where τij is the cost at position j for phrase i, and ρij is the ClickMax variant #1 is expected to perform better as it has
CPC at position j for phrase i. no limit for average CPC. The second solution is relevant to
an advertiser that has a budget but would like to have some
3.1 Click maximization control on the average CPC upper limit.
We propose two variants of click maximization in which
the first variant takes a budget β as a constraint while the 3.2 Cost minimization
other takes β and a maximum average CPC ϕ that an ad- Minimizing advertising cost can be one of business objec-
vertiser is willing to spend. tives. We propose two variants: the first variant takes mini-
mum required clicks χ as a constraint, while the other takes
3.1.1 ClickMax variant #1 χ and ϕ. The goal of these solutions is to have an insight
Given the advertiser’s budget β for the phrases in her whether the cost-click curves for ClickMax and CostMin are
portfolio, the problem is formulated as follows: identical. Our evaluations on ClickMax and CostMin are
maximize: provided in Section 4.
Xm X n
xij ∗ λij (3) 3.2.1 CostMin variant #1
i=1 j=1
Given the minimum clicks χ the advertiser expects from
subject to: the phrases she will bid, the objective function is as ex-
m X
X n pressed in Eq. 8. The constraint reflecting the inclusion of
xij ∗ τij ≤ β, (4) χ is expressed in Eq. 9. The constraints defined in Eq. 5
i=1 j=1 and Eq. 6 are also included but their definitions are not
n repeated.
minimize
X
xij ≤ 1, (5)
m X n
j=1 X
xij ∗ τij (8)
∀i, i = 1, ..., m, i=1 j=1
xij ∈ {0, 1} (6)
subject to
∀i, i = 1, ..., m and ∀j, j = 1, ..., n
m X
n
In Eq. 3 and Eq. 4, xij is either 0 or 1, reflecting at most X
1 position per phrase will be awarded. The above solution xij ∗ λij ≥ χ (9)
maximizes the number of clicks with the CPC selected varies i=1 j=1
from one phrase to another. As the only constraint is β, the
average CPC may be more than what the advertiser is will- 3.2.2 CostMin variant #2
ing to spend as the algorithm adaptively suggests the bid Given χ and ϕ, the objective function is as defined in
according to the available budget. Therefore, another con- Eq. 8. The constraints defined in Eq. 7 and Eq. 9 are
straint that should be included is the advertiser’s valuation used to reflect the inclusion of ϕ and χ, respectively. Other
of maximum average CPC ϕ in which the actual average constraints defined in Eq. 5 and Eq. 6 are also used. For
CPC should not exceed ϕ. simplicity, the definitions of Eq. 5 through Eq. 9 are not
repeated.
3.1.2 ClickMax variant #2
An alternate solution requires an advertiser to specify two 4. PERFORMANCE EVALUATION
parameters: β, and ϕ. The objective function defined in Eq.
3 and the constraints in Eq. 4, Eq. 5, and Eq. 6 are also 4.1 Experimental set-up
used. For simplicity, the definitions of those equations (Eq.3-
6) are not repeated. The additional constraint reflecting the The objective of the simulation is to measure the per-
inclusion of ϕ is expressed as follows: formance effectiveness of the proposed methods. In the
simulation, some Yahoo! Search Marketing Advertiser Bid-
Pm Pn Impression-Click [1] data are used to construct clickthrough
xij ∗ τij
i=1
Pm Pnj=1 ≤ϕ (7) and impression rates. The data set schema is as follows:
i=1 j=1 xij ∗ λij • day: the day in which an advertiser places a bid, ex-
With the assumption that within the same phrase, there pressed as an integer (e.g. 10, indicating the bid hap-
are different display slots with different CPCs, the alternate pened on the 10th day)
solution is able to select the combination of phrases to op- • anonymized account id : the anonymized account of an
timize the objective function. Comparing the two solutions, advertiser, expressed in alphanumerics.• rank : the ranking position of the phrase(s) bid by the phrase must be ≤ ϕ. The method then attempts to maxi-
advertiser mize the number of clicks for each of the phrases. In Section
• anonymized keyphrase: the phrase(s) bid by the ad- 3.2.1 and 3.2.2, the objective is to minimize costs. We use
vertiser, expressed in alphanumerics. greedy methods as our baseline to measure the performance
of our methods. The greedy solution corresponding to Cost-
• avg bid : the average bid for the bid phrase(s). Min variant #1 is defined as Greedy method variant #3 as
• impressions: the number of times the phrase(s) appear follows: for p number of phrases, the greedy method vari-
at the search engine (Yahoo!) result page ant #3 divides the minimum required clicks χ with p as the
• clicks: the number of times the advertiser’s landing minimum number of clicks to be generated by each phrase.
page associated with the bid phrase(s) have been clicked It then attempts to minimize the overall costs. In Section
on 3.2.2 the advertiser’s valuation of maximum average CPC ϕ
is required. The greedy solution corresponding to CostMin
4.2 Evaluation methodology variant #2 is defined as Greedy method variant #4 as fol-
We selected one of the longest bidding entries associated lows: for p number of phrases, the minimum required clicks
with an advertiser. Due to the anonymity of the phrases χ is divided with p as the minimum number of clicks for
per entry, we assumed that a group of phrases with similar each phrase. The max CPC for each phrase must be ≤ ϕ.
ids for all phrases within the group as a unique phrase. In The method then attempts to minimize the overall costs.
total, there were six unique phrases but we considered only
five because entries in one of the unique phrases were too
4.4 Results
few. We analyzed two-week bidding data that the advertiser
had participated in. These data were used to estimate the 4.4.1 Maximizing clicks
CTRs for different positions of each unique phrase. In our Using our proposed methods, our results show increases
observation, a phrase ranked beyond position 10th did not in the number of clicks as they are able to redistribute the
generate clicks. The CPC was not included in the data set, overall budget β on different phrases based on the statis-
so we estimated the price for each position. The price esti- tics of the different phrases. In practice, this is particularly
mated was later used for this simulation only. We observed true because different phrases are more clickable among Web
that the distribution of clicks was sparse. So, we used the users.
maximum CTR that we calculated in each phrase as a refer- Figure 2(a) shows that ClickMax variant #1 outperforms
ence to estimate the CTRs for the remaining positions. As Greedy method variant #1 in terms of the number of clicks
a guideline, the frequencies selected for each position were when β is increased by 5000 on each run. In our observation,
computed based on Yahoo!/Overture sponsored search ad- the clicks generated by ClickMax variant #1 for each β level
vertisement results available in the Atlas report [11]. Since are consistently greater than the number of clicks generated
the objective of the simulation was to maximize the overall by Greedy method variant #1. ClickMax variant #1 adap-
clicks, we applied a multiplier to balance clicks distribution tively bids to maximize the objective function as long as the
for each unique phrase. β constraint is met. There are cases whereby not all phrases
The limitation of the study is that detailed data sets spec- have been selected to gain more clicks offered by different
ifying real phrases, bid prices, clicks, revenues and profits phrases.
are difficult to have access to. At this stage, optimizing In term of budget used, Figure 2(b), ClickMax variant
ROI based on the data that we use in this sudy cannot be #1’s percentage of budget used is within the range of 80-
done. In our evaluation, the CTRs and CPCs are not readily 100% on each run. The Greedy method variant #1, uses
available. Nevertheless, the objective of the study is to eval- beween 40-65% of the budget on each run.
uate our proposed methods. The data inaccuracies due to The increase in click percentage for ClickMax variant #1
the estimations have little impact on the performance of the over Greedy method variant #1 is shown in Figure 2(c).
proposed methods. Currently, the study does not include The increase in click percentage is between 24 and 71% on
keyword interaction as the assumption is that advertisers each run. With the inclusion of an additional parameter
bid for specific phrases. Focused phrases target the ”long ϕ, the advertiser has the flexibility to set her valuation of
tail” distribution and have less likelihood of overlapping be- maximum average CPC.
tween keywords. Figure 3(a) shows the total clicks generated by ClickMax
variant #2 and Greedy method variant #2. ClickMax vari-
4.3 Evaluation baseline ant #2 outperforms the Greedy method variant #2. Click-
Recall in section 3.1.1 and section 3.1.2, the objective is to Max variant #2 is able to adaptively bid to earn itself higher
maximize clicks. We use greedy methods as our baseline to display position. The only difference with the previous eval-
measure the performance. The greedy solution correspond- uation is that with the addition of ϕ, the range of maximum
ing to ClickMax variant #1 is defined as Greedy method average CPC is set by the advertiser.
variant #1 as follows: for p number of phrases, the greedy Figure 3(b) shows the budget used by ClickMax variant
method variant #1 divides the overall budget β with p as the #2 is between 90-100%. Figure 3(c) shows the increase
budget for each phrase. It then attempts to maximize the in click percentage for ClickMax variant #2 over Greedy
number of clicks for each of the phrases. In Section 3.1.2, method variant #2. The percentages in click increase for β
the advertiser’s valuation of maximum average CPC ϕ is less than 4K are not shown as they are well beyond 300%.
required. The greedy solution corresponding to ClickMax For β ≥ 4K, the click increase is between 30-85% on each
variant #2 is defined as Greedy method #variant 2 as fol- run.
lows: for p number of phrases, the overall budget β is divided
with p as the budget for each phrase. The max CPC for each 4.4.2 Minimizing costs(a) (b) (c)
Figure 2: ClickMax variant #1 vs Greedy method variant #1 when β is the constraint. β is increased by
5000 on each run: (a) the effect on generated clicks, (b) the percentage of β used, and (c) the percentage
increase in clicks of ClickMax variant #1 over Greedy method variant #1
(a) (b) (c)
Figure 3: ClickMax variant #2 vs Greedy method variant #2 when β and ϕ are the constraints. β is increased
by 1000 and ϕ is set to be 500 on each run: (a) the effect on generated clicks, (b) the percentage of β used,
and (c) the percentage increase in clicks of ClickMax variant #2 over Greedy method variant #2
The evaluation on minimizing costs with required mini- lutions that meet the constraint (e.g. the minimum required
mum clicks χ as a constraint shows that CostMin variant clicks), CostMin will always choose the solution whose cost
#1 outperforms Greedy method variant #3 (Figure 4(a)). is the least.
In fact, on each run, the click-cost point generated by our so-
lution is optimal. Any point above the optimal curve meets 5. CONCLUSIONS
the constraint criterion but is less cost effective. Points be-
low the curve are ineffecient due to the required minimum From an advertiser point of view, a good estimation of the
clicks are not met. total clicks that an ad can generate is essential. Although
When repeated with additional constraint ϕ, similar pat- the ultimate goals is to optimize ROI, optimizing the total
tern (Figure 4(b)) shown in the previous evaluation to mini- number of clicks is a step towards that direction. The ideal
mize costs persists. CostMin variant #2 outperforms Greedy case is to generate as many conversions as possible out of the
method variant #4. The only difference is that when χ is 60, generated clicks. Later, out of the conversions, some users
no solution is found for CostMin variant #2 due to the the interact with the advertiser’s website to purchase items.
average CPC becomes too high (> 500) so the evaluation In this study we presented a theoretical insight to opti-
stops when χ is 55. mize clicks and to minimize advertising cost. We show that
Another evaluation is to have an insight whether cost-click the formulations of these two problems are mathematically
curves generated by ClickMax and CostMin are identical. equivalent. Our simulation shows that our approach (Click-
The click-cost points in ClickMax variant #1 and CostMin Max variant #1) outperforms the greedy method in maxi-
variant #1 are shown in Figure 5(a). mizing clicks. Our algorithm bids for a phrase to gain more
The cost-click points in ClickMax variant #2 and Cost- overall clicks as long as the average CPC is within the adver-
Min variant #2 are shown in Figure 5(b). Both curves are tiser’s budget. The greedy method, on the other hand, at-
almost identical. The difference is that for the same num- tempts to maximize clicks for individual phrases rather than
ber of clicks, the costs in CostMin (variant #1 and variant treating the phrases as a portfolio. Our solution resembles
#2) are slightly lower compared to the costs in ClickMax the real problem situation in which different phrases have
(variant #1 and variant #2). Since the objective function different statistics as some phrases are more popular and
in CostMin is to minimize costs, when there are multiple so- clickable among Web users. When an advertiser’s valuation
of maximum average CPC is included as a constraint, our(a) (b)
Figure 4: CostMin vs Greedy method: (a)the effects on costs on CostMin variant #1 and greedy method
variant #3 when minimum χ is increased by 5 on each run, and (b)the effects on costs on CostMin variant
#2 and greedy method variant #4 when minimum χ is increased by 5 and ϕ is set to 500 on each run
(a) (b)
Figure 5: ClickMax Vs CostMin: (a)the cost-click combinations using ClickMax variant #1 and CostMin
variant #1 when β is the constraint. β is increased by 5000 on each run, and (b)the cost-click combinations
using ClickMax variant #2 and CostMin variant #2 when β and ϕ are the constraints. β is increased by 1000
and ϕ is set to 500 on each run
method (ClickMax variant #2) allows the advertiser to pro- http://research.yahoo.com/Academic Relations.
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