Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I...
Transcript of Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I...
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Online Ad Serving: Theory and Practice
Aranyak MehtaVahab Mirrokni
June 7, 2011
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Outline of this talk
I Ad delivery for contract-based settingsI Ad ServingI Planning
I Ad serving in repeated auction settingsI General architecture.I Allocation for budget constrained advertisers.
I Other interactionsI Learning + allocationI Learning + auctionI Auction + contracts
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Contract-based Ad Delivery: Outline
I Basic InformationI Ad Serving.
I Targeting.I Online Allocation
I Ad Planning: Reservation
![Page 4: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/4.jpg)
Contract-based Online Advertising
I Pageviews (impressions) instead of queries.
I Display/Banner Ads, Video Ads, Mobile Ads.
I Cost-Per-Impression (CPM).
I Not Auction-based: offline negotiations + Online allocations.
Display/Banner Ads:
I Q1, 2010: One Trillion Display Ads in US. $2.7 billion.
I Top Advertiser: AT&T, Verizon, Scottrade.
I Ad Serving Systems e.g. Facebook, Google Doubleclick,AdMob.
![Page 5: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/5.jpg)
Contract-based Online Advertising
I Pageviews (impressions) instead of queries.
I Display/Banner Ads, Video Ads, Mobile Ads.
I Cost-Per-Impression (CPM).
I Not Auction-based: offline negotiations + Online allocations.
Display/Banner Ads:
I Q1, 2010: One Trillion Display Ads in US. $2.7 billion.
I Top Advertiser: AT&T, Verizon, Scottrade.
I Ad Serving Systems e.g. Facebook, Google Doubleclick,AdMob.
![Page 6: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/6.jpg)
Contract-based Online Advertising
I Pageviews (impressions) instead of queries.
I Display/Banner Ads, Video Ads, Mobile Ads.
I Cost-Per-Impression (CPM).
I Not Auction-based: offline negotiations + Online allocations.
Display/Banner Ads:
I Q1, 2010: One Trillion Display Ads in US. $2.7 billion.
I Top Advertiser: AT&T, Verizon, Scottrade.
I Ad Serving Systems e.g. Facebook, Google Doubleclick,AdMob.
![Page 7: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/7.jpg)
Contract-based Online Advertising
I Pageviews (impressions) instead of queries.
I Display/Banner Ads, Video Ads, Mobile Ads.
I Cost-Per-Impression (CPM).
I Not Auction-based: offline negotiations + Online allocations.
Display/Banner Ads:
I Q1, 2010: One Trillion Display Ads in US. $2.7 billion.
I Top Advertiser: AT&T, Verizon, Scottrade.
I Ad Serving Systems e.g. Facebook, Google Doubleclick,AdMob.
![Page 8: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/8.jpg)
Internet Advertising Revenues - 2010
Search
46%
Display
38%
Classified
10%
Other
6%
Internet Ad Revenues - 2010
24% increase
Total $26.0 billion
![Page 9: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/9.jpg)
Display Ad Delivery: Overview
Planning:
Display Ad Delivery
Ad Serving: Targeting: Allocation:
1. Planning: Contracts/Commitments with Advertisers.2. Ad Serving:
I Targeting: Predicting value of impressions.I Ad Allocation: Assigning Impressions to Ads Online.
I Objective Functions:I Efficiency: Users and Advertisers. Revenue of the Publisher.I Smoothness, Fairness, Delivery Penalty.
![Page 10: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/10.jpg)
Display Ad Delivery: Overview
Planning:
Display Ad Delivery
Ad Serving: Targeting: Allocation:
Strategic, Stochastic
Online, Stochastic
Offline, Online
1. Planning: Contracts/Commitments with Advertisers.2. Ad Serving:
I Targeting: Predicting value of impressions.I Ad Allocation: Assigning Impressions to Ads Online.
I Objective Functions:I Efficiency: Users and Advertisers. Revenue of the Publisher.I Smoothness, Fairness, Delivery Penalty.
![Page 11: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/11.jpg)
Display Ad Delivery: Overview
Planning:
Display Ad Delivery
Ad Serving: Targeting: Allocation:
Strategic, Stochastic
Online, Stochastic
Offline, Online Forecasting
Demand for ads
Supply of impressions
1. Planning: Contracts/Commitments with Advertisers.2. Ad Serving:
I Targeting: Predicting value of impressions.I Ad Allocation: Assigning Impressions to Ads Online.
I Objective Functions:I Efficiency: Users and Advertisers. Revenue of the Publisher.I Smoothness, Fairness, Delivery Penalty.
![Page 12: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/12.jpg)
Display Ad Delivery: Overview
Planning:
Display Ad Delivery
Ad Serving: Targeting: Allocation:
Delivery Constraints, Budget
Strategic, Stochastic
Online, Stochastic
Offline, Online Forecasting
Demand for ads
Supply of impressions
1. Planning: Contracts/Commitments with Advertisers.2. Ad Serving:
I Targeting: Predicting value of impressions.I Ad Allocation: Assigning Impressions to Ads Online.
I Objective Functions:I Efficiency: Users and Advertisers. Revenue of the Publisher.I Smoothness, Fairness, Delivery Penalty.
![Page 13: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/13.jpg)
Display Ad Delivery: Overview
Planning:
Display Ad Delivery
Ad Serving: Targeting: Allocation:
Delivery Constraints, Budget
CTR
Strategic, Stochastic
Online, Stochastic
Offline, Online Forecasting
Demand for ads
Supply of impressions
1. Planning: Contracts/Commitments with Advertisers.2. Ad Serving:
I Targeting: Predicting value of impressions.I Ad Allocation: Assigning Impressions to Ads Online.
I Objective Functions:I Efficiency: Users and Advertisers. Revenue of the Publisher.I Smoothness, Fairness, Delivery Penalty.
![Page 14: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/14.jpg)
Display Ad Delivery: Overview
Planning:
Display Ad Delivery
Ad Serving: Targeting: Allocation:
Delivery Constraints, Budget
CTR
Strategic, Stochastic
Online, Stochastic
Offline, Online Forecasting
Demand for ads
Supply of impressions
I Objective Functions:I Efficiency: Users and Advertisers. Revenue of the Publisher.I Smoothness, Fairness, Delivery Penalty.
![Page 15: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/15.jpg)
Contract-based Ad Delivery: Outline
I Basic InformationI Ad Serving.
I Targeting.I Online Ad Allocation
I Ad Planning: Reservation
![Page 16: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/16.jpg)
Targeting
Estimating Value of an impression.
I Behavioral TargetingI Interest-based Advertising.I Yan, Liu, Wang, Zhang, Jiang, Chen, 2009, How much can
Behavioral Targeting Help Online Advertising?
I Contextual TargetingI Information Retrieval (IR).I Broder, Fontoura, Josifovski, Riedel, A semantic approach to
contextual advertising
I Creative OptimizationI Experimentation
![Page 17: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/17.jpg)
Targeting
Estimating Value of an impression.I Behavioral Targeting
I Interest-based Advertising.I Yan, Liu, Wang, Zhang, Jiang, Chen, 2009, How much can
Behavioral Targeting Help Online Advertising?
I Contextual TargetingI Information Retrieval (IR).I Broder, Fontoura, Josifovski, Riedel, A semantic approach to
contextual advertising
I Creative OptimizationI Experimentation
![Page 18: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/18.jpg)
Targeting
Estimating Value of an impression.I Behavioral Targeting
I Interest-based Advertising.I Yan, Liu, Wang, Zhang, Jiang, Chen, 2009, How much can
Behavioral Targeting Help Online Advertising?
I Contextual TargetingI Information Retrieval (IR).I Broder, Fontoura, Josifovski, Riedel, A semantic approach to
contextual advertising
I Creative OptimizationI Experimentation
![Page 19: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/19.jpg)
Targeting
Estimating Value of an impression.I Behavioral Targeting
I Interest-based Advertising.I Yan, Liu, Wang, Zhang, Jiang, Chen, 2009, How much can
Behavioral Targeting Help Online Advertising?
I Contextual TargetingI Information Retrieval (IR).I Broder, Fontoura, Josifovski, Riedel, A semantic approach to
contextual advertising
I Creative OptimizationI Experimentation
![Page 20: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/20.jpg)
Predicting value of Impressions for Display Ads
I Estimating Click-Through-Rate (CTR).I Budgeted Multi-armed Bandit
I Probability of Conversion.
I Long-term vs. Short-term value of display ads?I Archak, Mirrokni, Muthukrishnan, 2010 Graph-based Models.
I Computing Adfactors based on AdGraphsI Markov Models for Advertiser-specific User Behavior
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Predicting value of Impressions for Display Ads
I Estimating Click-Through-Rate (CTR).I Budgeted Multi-armed Bandit
I Probability of Conversion.I Long-term vs. Short-term value of display ads?
I Archak, Mirrokni, Muthukrishnan, 2010 Graph-based Models.I Computing Adfactors based on AdGraphsI Markov Models for Advertiser-specific User Behavior
![Page 22: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/22.jpg)
Contract-based Ad Delivery: Outline
I Basic Information
I Ad Planning: ReservationI Ad Serving.
I Targeting.I Online Ad Allocation
![Page 23: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/23.jpg)
Outline: Online Allocation
I Online Stochastic Assignment ProblemsI Online (Stochastic) MatchingI Online Stochastic PackingI Online Generalized Assignment (with free disposal)I Experimental Results
I Online Learning and Allocation
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Online Ad Allocation
I When page arrives, assign an eligible ad.I value of assigning page i to ad a: via
I Display Ads (DA) problem:I Maximize value of ads served: max
∑i,a viaxia
I Capacity of ad a:∑
i∈A(a) xia ≤ Ca
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Online Ad Allocation
I When page arrives, assign an eligible ad.I value of assigning page i to ad a: via
I Display Ads (DA) problem:I Maximize value of ads served: max
∑i,a viaxia
I Capacity of ad a:∑
i∈A(a) xia ≤ Ca
![Page 26: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/26.jpg)
Online Ad Allocation
I When page arrives, assign an eligible ad.I revenue from assigning page i to ad a: bia
I “AdWords” (AW) problem:I Maximize revenue of ads served: max
∑i,a biaxia
I Budget of ad a:∑
i∈A(a) biaxia ≤ Ba
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General Form of LP
max∑i ,a
viaxia∑a
xia ≤ 1 (∀ i)∑i
siaxia ≤ Ca (∀ a)
xia ≥ 0 (∀ i , a)
Online Matching:via = sia = 1
Disp. Ads (DA):sia = 1
AdWords (AW):sia = via
Worst-Case Greedy: 12 ,
[KVV]: 1− 1e -aprx
[MSVV,BJN]:1− 1
e -aprx
![Page 28: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/28.jpg)
General Form of LP
max∑i ,a
viaxia∑a
xia ≤ 1 (∀ i)∑i
siaxia ≤ Ca (∀ a)
xia ≥ 0 (∀ i , a)
Online Matching:via = sia = 1
Disp. Ads (DA):sia = 1
AdWords (AW):sia = via
Worst-Case Greedy: 12 ,
[KVV]: 1− 1e -aprx
[MSVV,BJN]:1− 1
e -aprx
![Page 29: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/29.jpg)
Ad Allocation: Problems and Models
Online Matching:via = sia = 1
Disp. Ads (DA):sia = 1
AdWords (AW):sia = via
Worst Case Greedy: 12 ,
[KVV]: 1− 1e -aprx
?[MSVV,BJN]:1− 1
e -aprx
Stochastic(i.i.d.)
[FMMM09,MOS11]:0.702-aprxi.i.d with knowndistribution
?
[DH09]:1−ε-aprx,ifopt max via
Stochastic i.i.d model:
I i.i.d model with known distribution
I random order model (i.i.d model with unknown distribution)
![Page 30: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/30.jpg)
Ad Allocation: Problems and Models
Online Matching:via = sia = 1
Disp. Ads (DA):sia = 1
AdWords (AW):sia = via
Worst Case Greedy: 12 ,
[KVV]: 1− 1e -aprx
?[MSVV,BJN]:1− 1
e -aprx
Stochastic(i.i.d.)
[FMMM09,MOS11]:0.702-aprxi.i.d with knowndistribution
?
[DH09]:1−ε-aprx,ifopt max via
Stochastic i.i.d model:
I i.i.d model with known distribution
I random order model (i.i.d model with unknown distribution)
![Page 31: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/31.jpg)
Ad Allocation: Problems and Models
Online Matching:via = sia = 1
Disp. Ads (DA):sia = 1
AdWords (AW):sia = via
Worst Case Greedy: 12 ,
[KVV]: 1− 1e -aprx
?[MSVV,BJN]:1− 1
e -aprx
Stochastic(i.i.d.)
[FMMM09,MOS11]:0.702-aprxi.i.d with knowndistribution
?
[DH09]:1−ε-aprx,ifopt max via
Stochastic i.i.d model:
I i.i.d model with known distribution
I random order model (i.i.d model with unknown distribution)
![Page 32: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/32.jpg)
Ad Allocation: Problems and Models
Online Matching:via = sia = 1
Disp. Ads (DA):sia = 1
AdWords (AW):sia = via
Worst Case Greedy: 12 ,
[KVV]: 1− 1e -aprx
?[MSVV,BJN]:1− 1
e -aprx
Stochastic(i.i.d.)
[FMMM09]:0.67-aprxi.i.d with knowndistribution
?
[DH09]:1−ε-aprx,ifopt max via
![Page 33: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/33.jpg)
Ad Allocation: Problems and Models
Online Matching:via = sia = 1
Disp. Ads (DA):sia = 1
AdWords (AW):sia = via
Worst Case Greedy: 12 ,
[KVV]: 1− 1e -aprx
?[MSVV,BJN]:1− 1
e -aprx
Stochastic(i.i.d.)
[FMMM09,MOS11]:0.702-aprxi.i.d with knowndistribution
[FHKMS10,AWY]:1−ε-aprx,if opt max viaand Ca max sia
[DH09]:1−ε-aprx,ifopt max via
random order = i.i.d. model with unknown distribution
![Page 34: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/34.jpg)
Stochastic DA: Dual Algorithm
max∑i ,a
viaxia∑a
xia ≤ 1 (∀ i)∑i
xia ≤ Ca (∀ a)
xia ≥ 0 (∀ i , a)
min∑a
Caβa +∑i
zi
zi ≥ via − βa (∀i , a)
βa, zi ≥ 0 (∀i , a)
Feldman, Henzinger, Korula, M., Stein 2010Thm[FHKMS10,AWY]: W.h.p, this algorithm is a (1−O(ε))-aprx,as long as each item has low value (via ≤ εopt
m log n ), and large
capacity (Ca ≥ m log nε3
)
Fact: If optimum β∗a are known, this alg. finds optI Proof: Comp. slackness. Given β∗a , compute x∗ as follows:
x∗ia = 1 if a = argmax(via − β∗a).
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Stochastic DA: Dual Algorithm
max∑i ,a
viaxia∑a
xia ≤ 1 (∀ i)∑i
xia ≤ Ca (∀ a)
xia ≥ 0 (∀ i , a)
min∑a
Caβa +∑i
zi
zi ≥ via − βa (∀i , a)
βa, zi ≥ 0 (∀i , a)
Algorithm:I Observe the first ε fraction sample of impressions.I Learn a dual variable for each ad βa, by solving the dual
program on the sample.I Assign each impression i to ad a that maximizes via − βa.
Feldman, Henzinger, Korula, M., Stein 2010Thm[FHKMS10,AWY]: W.h.p, this algorithm is a (1−O(ε))-aprx,as long as each item has low value (via ≤ εopt
m log n ), and large
capacity (Ca ≥ m log nε3
)
Fact: If optimum β∗a are known, this alg. finds optI Proof: Comp. slackness. Given β∗a , compute x∗ as follows:
x∗ia = 1 if a = argmax(via − β∗a).
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Stochastic DA: Dual AlgorithmFeldman, Henzinger, Korula, M., Stein 2010Thm[FHKMS10,AWY]: W.h.p, this algorithm is a (1−O(ε))-aprx,as long as each item has low value (via ≤ εopt
m log n ), and large
capacity (Ca ≥ m log nε3
)
Fact: If optimum β∗a are known, this alg. finds optI Proof: Comp. slackness. Given β∗a , compute x∗ as follows:
x∗ia = 1 if a = argmax(via − β∗a).
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Stochastic DA: Dual AlgorithmFeldman, Henzinger, Korula, M., Stein 2010Thm[FHKMS10,AWY]: W.h.p, this algorithm is a (1−O(ε))-aprx,as long as each item has low value (via ≤ εopt
m log n ), and large
capacity (Ca ≥ m log nε3
)
Fact: If optimum β∗a are known, this alg. finds optI Proof: Comp. slackness. Given β∗a , compute x∗ as follows:
x∗ia = 1 if a = argmax(via − β∗a).
![Page 38: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/38.jpg)
Stochastic DA: Dual AlgorithmFeldman, Henzinger, Korula, M., Stein 2010Thm[FHKMS10,AWY]: W.h.p, this algorithm is a (1−O(ε))-aprx,as long as each item has low value (via ≤ εopt
m log n ), and large
capacity (Ca ≥ m log nε3
)
Fact: If optimum β∗a are known, this alg. finds optI Proof: Comp. slackness. Given β∗a , compute x∗ as follows:
x∗ia = 1 if a = argmax(via − β∗a).
Lemma: In the random order model, W.h.p., the sample β′a areclose to β∗a .
I Extending DH09.
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General Stochastic Packing LPs
I m fixed resources with capacity Ca
I Items i arrive online with options Oi , values vio , rsrc. use sioa.I Choose o ∈ Oi , using up capacity sioa in all a.
Thm[FHKMS10,AWY]: W.h.p, the PD algorithm is a(1−O(ε))-aprx, as long as items have low value (vio ≤ εopt
log n ) and
small size (sioa ≤ ε3Calog n ).
Other Results and Extensions (random order model):
I Agrawal, Wang, Ye: Updating dual variables by periodicsolution of the dual program: Ca ≥ m log n
ε2or sioa ≤ ε2Ca
M
I Vee, Vassilvitskii , Shanmugasundaram 2010: extension toconvex objective functions: Using KKT conditions.
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General Stochastic Packing LPs
I m fixed resources with capacity Ca
I Items i arrive online with options Oi , values vio , rsrc. use sioa.I Choose o ∈ Oi , using up capacity sioa in all a.
Thm[FHKMS10,AWY]: W.h.p, the PD algorithm is a(1−O(ε))-aprx, as long as items have low value (vio ≤ εopt
log n ) and
small size (sioa ≤ ε3Calog n ).
Other Results and Extensions (random order model):
I Agrawal, Wang, Ye: Updating dual variables by periodicsolution of the dual program: Ca ≥ m log n
ε2or sioa ≤ ε2Ca
M
I Vee, Vassilvitskii , Shanmugasundaram 2010: extension toconvex objective functions: Using KKT conditions.
![Page 41: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/41.jpg)
General Stochastic Packing LPs
I m fixed resources with capacity Ca
I Items i arrive online with options Oi , values vio , rsrc. use sioa.I Choose o ∈ Oi , using up capacity sioa in all a.
Thm[FHKMS10,AWY]: W.h.p, the PD algorithm is a(1−O(ε))-aprx, as long as items have low value (vio ≤ εopt
log n ) and
small size (sioa ≤ ε3Calog n ).
Other Results and Extensions (random order model):
I Agrawal, Wang, Ye: Updating dual variables by periodicsolution of the dual program: Ca ≥ m log n
ε2or sioa ≤ ε2Ca
M
I Vee, Vassilvitskii , Shanmugasundaram 2010: extension toconvex objective functions: Using KKT conditions.
![Page 42: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/42.jpg)
Ad Allocation: Problems and Models
Online Matching:via = sia = 1
Disp. Ads (DA):sia = 1
AdWords (AW):sia = via
Worst Case Greedy: 12 ,
[KVV]: 1− 1e -aprx
?[MSVV,BJN]:1− 1
e -aprx
Stochastic(i.i.d.)
[FMMM09,MOS11]:0.702-aprxi.i.d with knowndistribution
[FHKMS10,AWY]:1−ε-aprx,if opt max viaand Ca max sia
[DH09]:1−ε-aprx,ifopt max via
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Ad Allocation: Problems and Models
Online Matching:via = sia = 1
Disp. Ads (DA):sia = 1
AdWords (AW):sia = via
Worst Case Greedy: 12 ,
[KVV]: 1− 1e -aprx
Free Disposal[FKMMP09]:1− 1
e -aprx:if Ca max sia
[MSVV,BJN]:1− 1
e -aprx
Stochastic(i.i.d.)
[FMMM09,MOS11]:0.702-aprxi.i.d with knowndistribution
[FHKMS10,AWY]:1−ε-aprx,if opt max viaand Ca max sia
[DH09]:1−ε-aprx,ifopt max via
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DA: Free Disposal Model
0.07Ad 1: C1 = 1
0.07Ad 1: C1 = 1
0.7
I Advertisers may not complain about extra impressions, but nobonus points for extra impressions, either.
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DA: Free Disposal Model
0.07Ad 1: C1 = 1
0.07Ad 1: C1 = 1
0.7
I Advertisers may not complain about extra impressions, but nobonus points for extra impressions, either.
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DA: Free Disposal Model
0.07Ad 1: C1 = 1
0.7
0.07Ad 1: C1 = 1
0.7
I Advertisers may not complain about extra impressions, but nobonus points for extra impressions, either.
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DA: Free Disposal Model
0.07Ad 1: C1 = 1
0.7
I Advertisers may not complain about extra impressions, but nobonus points for extra impressions, either.
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DA: Free Disposal Model
0.07Ad 1: C1 = 1
0.7
I Advertisers may not complain about extra impressions, but nobonus points for extra impressions, either.
I Value of advertiser = sum of values of top Ca items she gets.
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Greedy Algorithm
Assign impression to an advertisermaximizing Marginal Gain = (imp. value - min. impression value).
I Competitive Ratio: 1/2. [NWF78]I Follows from submodularity of the value function.
1
1 + ε
Ad 1: C1 = n
Ad 2: C2 = n1
n copiesn copies
n copies
Evenly Split?
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Greedy Algorithm
Assign impression to an advertisermaximizing Marginal Gain = (imp. value - min. impression value).
I Competitive Ratio: 1/2. [NWF78]I Follows from submodularity of the value function.
1
1 + ε
Ad 1: C1 = n
Ad 2: C2 = n1
n copiesn copies
n copies
Evenly Split?
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Greedy Algorithm
Assign impression to an advertisermaximizing Marginal Gain = (imp. value - min. impression value).
I Competitive Ratio: 1/2. [NWF78]I Follows from submodularity of the value function.
1
1 + ε
Ad 1: C1 = n
Ad 2: C2 = n
n copiesn copies
1
1 + ε
Ad 1: C1 = n
Ad 2: C2 = n1
n copiesn copies
n copies
Evenly Split?
![Page 52: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/52.jpg)
Greedy Algorithm
Assign impression to an advertisermaximizing Marginal Gain = (imp. value - min. impression value).
I Competitive Ratio: 1/2. [NWF78]I Follows from submodularity of the value function.
1
1 + ε
Ad 1: C1 = n
Ad 2: C2 = n1
n copiesn copies
n copies
1
1 + ε
Ad 1: C1 = n
Ad 2: C2 = n1
n copiesn copies
n copies
Evenly Split?
![Page 53: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/53.jpg)
Greedy Algorithm
Assign impression to an advertisermaximizing Marginal Gain = (imp. value - min. impression value).
I Competitive Ratio: 1/2. [NWF78]I Follows from submodularity of the value function.
1
1 + ε
Ad 1: C1 = n
Ad 2: C2 = n1
n copiesn copies
n copies
Evenly Split?
![Page 54: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/54.jpg)
A better algorithm?
Assign impression to an advertiser amaximizing (imp. value - βa),
where βa = average value of top Ca impressions assigned to a.
1
1 + ε
Ad 1: C1 = n
Ad 2: C2 = n1
n copiesn copies
n copies
I Competitive Ratio: 12 if Ca >> 1. [FKMMP09]
I Primal-Dual Approach.
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A better algorithm?
Assign impression to an advertiser amaximizing (imp. value - βa),
where βa = average value of top Ca impressions assigned to a.
1
1 + ε
Ad 1: C1 = n
Ad 2: C2 = n1
n copiesn copies
n copies
I Competitive Ratio: 12 if Ca >> 1. [FKMMP09]
I Primal-Dual Approach.
![Page 56: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/56.jpg)
A better algorithm?
Assign impression to an advertiser amaximizing (imp. value - βa),
where βa = average value of top Ca impressions assigned to a.
1
1 + ε
Ad 1: C1 = n
Ad 2: C2 = n1
n copiesn copies
n copies
I Competitive Ratio: 12 if Ca >> 1. [FKMMP09]
I Primal-Dual Approach.
![Page 57: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/57.jpg)
An Optimal Algorithm
Assign impression to an advertiser a:maximizing (imp. value - βa),
I Greedy: βa = min. impression assigned to a.
I Better (pd-avg): βa = average value of top Ca impressionsassigned to a.
I Optimal (pd-exp): order value of edges assigned to a:v(1) ≥ v(2) . . . ≥ v(Ca):
βa =1
Ca(e − 1)
Ca∑j=1
v(j)(1 +1
Ca)j−1.
I Thm: pd-exp achieves optimal competitive Ratio: 1− 1e − ε if
Ca > O(1ε ). [Feldman, Korula, M., Muthukrishnan, Pal 2009]
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An Optimal Algorithm
Assign impression to an advertiser a:maximizing (imp. value - βa),
I Greedy: βa = min. impression assigned to a.
I Better (pd-avg): βa = average value of top Ca impressionsassigned to a.
I Optimal (pd-exp): order value of edges assigned to a:v(1) ≥ v(2) . . . ≥ v(Ca):
βa =1
Ca(e − 1)
Ca∑j=1
v(j)(1 +1
Ca)j−1.
I Thm: pd-exp achieves optimal competitive Ratio: 1− 1e − ε if
Ca > O(1ε ). [Feldman, Korula, M., Muthukrishnan, Pal 2009]
![Page 59: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/59.jpg)
An Optimal Algorithm
Assign impression to an advertiser a:maximizing (imp. value - βa),
I Greedy: βa = min. impression assigned to a.
I Better (pd-avg): βa = average value of top Ca impressionsassigned to a.
I Optimal (pd-exp): order value of edges assigned to a:v(1) ≥ v(2) . . . ≥ v(Ca):
βa =1
Ca(e − 1)
Ca∑j=1
v(j)(1 +1
Ca)j−1.
I Thm: pd-exp achieves optimal competitive Ratio: 1− 1e − ε if
Ca > O(1ε ). [Feldman, Korula, M., Muthukrishnan, Pal 2009]
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Online Generalized Assignment (with free disposal)
I Multiple Knapsack: Item i may have different value (via) anddifferent size sia for different ads a.
I DA: sia = 1, AW: via = sia.
max∑i ,a
viaxia∑a
xia ≤ 1 (∀ i)∑i
siaxia ≤ Ca (∀ a)
xia ≥ 0 (∀ i , a)
min∑a
Caβa +∑i
zi
siaβa + zi ≥ via (∀i , a)
βa, zi ≥ 0 (∀i , a)
I Offline Optimization: 1− 1e − δ-aprx[FGMS07,FV08].
I Thm[FKMMP09]: There exists a 1− 1e − ε-approximation
algorithm if Camax sia
≥ 1ε .
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Online Generalized Assignment (with free disposal)
I Multiple Knapsack: Item i may have different value (via) anddifferent size sia for different ads a.
I DA: sia = 1, AW: via = sia.
max∑i ,a
viaxia∑a
xia ≤ 1 (∀ i)∑i
siaxia ≤ Ca (∀ a)
xia ≥ 0 (∀ i , a)
min∑a
Caβa +∑i
zi
siaβa + zi ≥ via (∀i , a)
βa, zi ≥ 0 (∀i , a)
I Offline Optimization: 1− 1e − δ-aprx[FGMS07,FV08].
I Thm[FKMMP09]: There exists a 1− 1e − ε-approximation
algorithm if Camax sia
≥ 1ε .
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Proof Idea: Primal-Dual Analysis [BJN]
max∑i ,a
viaxia∑a
xia ≤ 1 (∀ i)∑i
siaxia ≤ Ca (∀ a)
xia ≥ 0 (∀ i , a)
min∑a
Caβa +∑i
zi
siaβa + zi ≥ via (∀i , a)
βa, zi ≥ 0 (∀i , a)
I Proof:
1. Start from feasible primal and dual (xia = 0, βa = 0, andzi = 0, i.e., Primal=Dual=0).
2. After each assignment, update x , β, z variables and keepprimal and dual solutions.
3. Show ∆(Dual) ≤ (1− 1e )∆(Primal).
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Proof Idea: Primal-Dual Analysis [BJN]
max∑i ,a
viaxia∑a
xia ≤ 1 (∀ i)∑i
siaxia ≤ Ca (∀ a)
xia ≥ 0 (∀ i , a)
min∑a
Caβa +∑i
zi
siaβa + zi ≥ via (∀i , a)
βa, zi ≥ 0 (∀i , a)
I Proof:
1. Start from feasible primal and dual (xia = 0, βa = 0, andzi = 0, i.e., Primal=Dual=0).
2. After each assignment, update x , β, z variables and keepprimal and dual solutions.
3. Show ∆(Dual) ≤ (1− 1e )∆(Primal).
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Ad Allocation: Problems and Models
Online Matching:via = sia = 1
Disp. Ads (DA):sia = 1
AdWords (AW):sia = via
Worst Case Greedy: 12 ,
[KVV]: 1− 1e -aprx
Free Disposal[FKMMP09]:1− 1
e -aprx: ifCa max sia
[MSVV,BJN]:1− 1
e -aprx
Stochastic(randomarrivalorder)
[FMMM09,MOS11]:0.702-aprx
[FHKMS10,AWY]:1−ε-aprx,if opt max viaand Ca max sia
[DH09]:1−ε-aprx,ifopt max via
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Outline: Online Allocation
I Online Stochastic Assignment ProblemsI Online Stochastic PackingI Online Generalized Assignment (with free disposal)I Experimental EvaluationI Online Stochastic Weighted Matching
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Dual-based Algorithms in Practice
I Algorithm:I Assign each item i to ad a that maximizes via − βa.
I More practical compared to Primal Algorithms:I Just keep one number βa per advertiser.I Suitable for Distributed Ad Serving Schemes.
I Training-based AlgorithmsI Compute βa based on historical/sample data.
I Hybrid approach (see also [MNS07]):I Start with trained βa (past history), blend in online algorithm.
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Dual-based Algorithms in Practice
I Algorithm:I Assign each item i to ad a that maximizes via − βa.
I More practical compared to Primal Algorithms:I Just keep one number βa per advertiser.I Suitable for Distributed Ad Serving Schemes.
I Training-based AlgorithmsI Compute βa based on historical/sample data.
I Hybrid approach (see also [MNS07]):I Start with trained βa (past history), blend in online algorithm.
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Dual-based Algorithms in Practice
I Algorithm:I Assign each item i to ad a that maximizes via − βa.
I More practical compared to Primal Algorithms:I Just keep one number βa per advertiser.I Suitable for Distributed Ad Serving Schemes.
I Training-based AlgorithmsI Compute βa based on historical/sample data.
I Hybrid approach (see also [MNS07]):I Start with trained βa (past history), blend in online algorithm.
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Dual-based Algorithms in Practice
I Algorithm:I Assign each item i to ad a that maximizes via − βa.
I More practical compared to Primal Algorithms:I Just keep one number βa per advertiser.I Suitable for Distributed Ad Serving Schemes.
I Training-based AlgorithmsI Compute βa based on historical/sample data.
I Hybrid approach (see also [MNS07]):I Start with trained βa (past history), blend in online algorithm.
![Page 70: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/70.jpg)
Experiments: setup
I Real ad impression data from several large publishers
I 200k - 1.5M impressions in simulation period
I 100 - 2600 advertisers
I Edge weights = predicted click probability
I Efficiency: free disposal modelI Algorithms:
I greedy: maximum marginal valueI pd-avg, pd-exp: pure online primal-dual from [FKMMP09].I dualbase: training-based primal-dual [FHKMS10]I hybrid: convex combo of training based, pure online.I lp-weight: optimum efficiency
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Experimental Evaluation: Summary
Algorithm Avg Efficiency%opt 100
greedy 69pd-avg 77pd-exp 82
dualbase 87hybrid 89
I pd-exp & pd-avg outperform greedy by 9% and 14% (withmore improvements in tight competition.)
I dualbase outperforms pure online algorithms by 6% to 12%.
I Hybrid has a mild improvement of 2% (up to 10%).
I pd-avg performs much better than the theoretical analysis.
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Other Metrics: Fairness
I Qualititative definition: advertisers are “treated equally.”
I One suggestion[FHKMS10]: Compute ”fair” solution x∗,measure `1 distance to x∗.
I Fair solution:I Each a chooses best Ca impressions (highest via)I Repeat:
I Impressions shared among those who chose them.I If some a not receiving Ca imps, a chooses an additional imp.
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Other Metrics: Fairness
I Qualititative definition: advertisers are “treated equally.”
I One suggestion[FHKMS10]: Compute ”fair” solution x∗,measure `1 distance to x∗.
I Fair solution:I Each a chooses best Ca impressions (highest via)I Repeat:
I Impressions shared among those who chose them.I If some a not receiving Ca imps, a chooses an additional imp.
![Page 74: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/74.jpg)
Other Metrics: Fairness
I Qualititative definition: advertisers are “treated equally.”
I One suggestion[FHKMS10]: Compute ”fair” solution x∗,measure `1 distance to x∗.
I Fair solution:I Each a chooses best Ca impressions (highest via)I Repeat:
I Impressions shared among those who chose them.I If some a not receiving Ca imps, a chooses an additional imp.
![Page 75: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/75.jpg)
Experiments: highlights
40 50 60 70 80 90 100
010
2030
4050
Efficiency
Fai
rnes
s
dualbasegreedy
hybrid
lp_weight
pd−avg
pd−exp
fair
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Advertiser
Effi
cien
cy (
rela
tive)
0.0
0.2
0.4
0.6
0.8
1.0
lp−weightfairdualbasepd−avg
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Experiments: highlights
70 75 80 85 90 95 100
05
1015
20
Efficiency
Fai
rnes
s
dualbasegreedy hybrid
lp_weight
pd−avg
pd−exp
fair1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Advertiser
Effi
cien
cy (
rela
tive)
0.0
0.2
0.4
0.6
0.8
1.0
lp−weightfairdualbasepd−avg
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In Production
I Smooth Delivery of Display AdsI Delivery of impressions throughout time should follow the
traffic smoothly.I Model this with multiple nested capacity constraints:
1− 1/e-competitive algorithm for this extension.I Bhalgat, Feldman, M., 2011
I Combined Allocation with Ad ExchangeI Yield Optimization of Display Advertising with Ad ExchangeI Belsairo, Feldman, M., Muthukrishnan, 2011
I Re-act adaptively and quickly to changes in traffic:I Use a control loop on the dual variable.I Assymptotically optimal policy: B. Tan and R. Srikant, 2011
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In Production
I Smooth Delivery of Display AdsI Delivery of impressions throughout time should follow the
traffic smoothly.I Model this with multiple nested capacity constraints:
1− 1/e-competitive algorithm for this extension.I Bhalgat, Feldman, M., 2011
I Combined Allocation with Ad ExchangeI Yield Optimization of Display Advertising with Ad ExchangeI Belsairo, Feldman, M., Muthukrishnan, 2011
I Re-act adaptively and quickly to changes in traffic:I Use a control loop on the dual variable.I Assymptotically optimal policy: B. Tan and R. Srikant, 2011
![Page 79: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/79.jpg)
In Production
I Smooth Delivery of Display AdsI Delivery of impressions throughout time should follow the
traffic smoothly.I Model this with multiple nested capacity constraints:
1− 1/e-competitive algorithm for this extension.I Bhalgat, Feldman, M., 2011
I Combined Allocation with Ad ExchangeI Yield Optimization of Display Advertising with Ad ExchangeI Belsairo, Feldman, M., Muthukrishnan, 2011
I Re-act adaptively and quickly to changes in traffic:I Use a control loop on the dual variable.I Assymptotically optimal policy: B. Tan and R. Srikant, 2011
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Online Ad Allocation: Interesting Problems
I Online Stochastic DAI Simultaneous online worst-case & stochastic optimization.I Tradeoff between delivery penalty and efficiency: Covering
Constraints?I More complex stochastic modeling (drift, seasonality, etc.)
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Outline: Online Allocation
I Online Stochastic Ad AllocationI Online Stochastic PackingI Online Generalized Assignment (with free disposal)I Experimental ResultsI Online Stochastic Weighted Matching
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Online Stochastic Weighted Matching
“ALG is α-approximation?” if E [ALG(H)]E [OPT(H)] ≥ α
Power of Two ChoicesI Offline:
1. Find an optimal fractional solution x∗e to a discountedmatching LP, where xe ≤ 1− 1
e .2. Sample a matching Ms from x∗.3. Let M ′ = M1\Ms where M1 is the maximum weighted
matching.
I Online: try the edge in Ms first, and if it doesn’t work, try M ′.
I Thm: Approximation factor is better than 0.66.
(Haeupler, M., ZadiMoghaddam, 2011).
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Online Stochastic Weighted Matching
“ALG is α-approximation?” if E [ALG(H)]E [OPT(H)] ≥ α
Power of Two ChoicesI Offline:
1. Find an optimal fractional solution x∗e to a discountedmatching LP, where xe ≤ 1− 1
e .2. Sample a matching Ms from x∗.3. Let M ′ = M1\Ms where M1 is the maximum weighted
matching.
I Online: try the edge in Ms first, and if it doesn’t work, try M ′.
I Thm: Approximation factor is better than 0.66.
(Haeupler, M., ZadiMoghaddam, 2011).
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Open Problems
I Online Stochastic Display Ad AllocationI Simultaneous online worst-case & stochastic optimization.I Tradeoff between delivery penalty and efficiency: Covering
Constraints?I More complex stochastic modeling (drift, seasonality, etc.)
I Online Stochastic Weighted MatchingI Online Stochastic Matching: Close gap between 0.703 & 0.81.I Online Stochastic Weighted Matching: Power of many
choices? Better lower bound?I Online Weighted Matching (with Free Disposal): Is
1− 1/e-approximation possible?
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Contract-based Ad Delivery: Outline
I Basic InformationI Ad Serving.
I Targeting.I Online Allocation
I Ad Planning: Reservation
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Display Ad Delivery: Overview
Planning:
Display Ad Delivery
Ad Serving: Targeting: Allocation:
Delivery Constraints, Budget
CTR
Strategic, Stochastic
Online, Stochastic
Offline, Online Forecasting
Demand for ads
Supply of impressions
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Ad Planning: Research Issues
Which set of contracts should we accept?
Related Research Issues.I Pricing Uncertain Inventory.
I Stochastic Supply and DemandI Bundling Opportunities
I Online Mechanisms for Signing Contracts.
I Contracts with Delivery Penalty.
I Offline Optimization of Contracts.
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Ad Planning: Research Issues
Which set of contracts should we accept?Related Research Issues.
I Pricing Uncertain Inventory.I Stochastic Supply and DemandI Bundling Opportunities
I Online Mechanisms for Signing Contracts.
I Contracts with Delivery Penalty.
I Offline Optimization of Contracts.
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General Ad Planning: Weighted Matching
I n advertisers, and set Y of impressions (items).I Each advertiser i
I Interested in a set Ji of impressions, (e.g, young women inSeattle),
I Needs di impressions (Demand),I Value vit (or Bid bi ) for each impression t,
Jjdi = 4
bj
Ji
biAdvertisers
Impressions
(Ji, bi, di)
Efficiency (or Revenue) Maximization: Find an assignment withthe maximum value.
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Contracts with Delivery Penalty
If we don’t meet the demand of an advertiser this month, weshould give him/her free impressions in the next month.
I Each advertiser iI Needs di impressions,I Bids bi for each impression,I Penalty λbi for not satisfying each unit (Guaranteed Delivery).
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Contracts with Delivery Penalty
If we don’t meet the demand of an advertiser this month, weshould give him/her free impressions in the next month.
I Each advertiser iI Needs di impressions,I Bids bi for each impression,I Penalty λbi for not satisfying each unit (Guaranteed Delivery).
![Page 92: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/92.jpg)
Ad Planning With Penalties
I n advertisers, and set Y of impressions (items).I Each advertiser i
I Interested in set Ji of impressions, (e.g, young women inSeattle),
I Bids bi for each impression,I Needs di impressions,I Penalty λbi for not satisfying each unit (Guaranteed Delivery).
Jjdi = 4
bj
Ji
biAdvertisers
Impressions
(Ji, bi, di)
Goal: Choose a set T of advertisers to maximize revenue, f (T ).
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Ad Planning With Penalties
I n advertisers, and set Y of impressions (items).I Each advertiser i
I Interested in set Ji of impressions, (e.g, young women inSeattle),
I Bids bi for each impression,I Needs di impressions,I Penalty λbi for not satisfying each unit (Guaranteed Delivery).
Jjdi = 4
bj
Ji
biAdvertisers
Impressions
(Ji, bi, di)
Goal: Choose a set T of advertisers to maximize revenue, f (T ).
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Relation to Weighted MatchingIf we give q items to advertiser i , we get
qbi − λbi (di − q) = q(1 + λ)bi − diλbi = q(1 + λ)bi − ci
If we commit to a set T of advertisers:
f (T ) = P(T )−∑
i∈T ci = P(T )− C (T ).
I C (T ) =∑
i∈T ci where ci = diλbi .
I P(T ) be the maximum weighted matching in the followingbipartite graph with (1 + λ)bi as weights of edges.
I Advertiser i ∈ T needs at most di ads.I Each ad can go to at most one advertiser.
Advertisers
Impressions
T
Maximum weighted matching for this graph.
(1 + λ)bj(1 + λ)bi
P (T ) =
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Relation to Weighted MatchingIf we give q items to advertiser i , we get
qbi − λbi (di − q) = q(1 + λ)bi − diλbi = q(1 + λ)bi − ci
If we commit to a set T of advertisers:
f (T ) = P(T )−∑
i∈T ci = P(T )− C (T ).
I C (T ) =∑
i∈T ci where ci = diλbi .
I P(T ) be the maximum weighted matching in the followingbipartite graph with (1 + λ)bi as weights of edges.
I Advertiser i ∈ T needs at most di ads.I Each ad can go to at most one advertiser.
Advertisers
Impressions
T
Maximum weighted matching for this graph.
(1 + λ)bj(1 + λ)bi
P (T ) =
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Discussion Summary
Given a set T of advertisers, maximizing f (T ) is easy as it is amaximum weighted matching.
Challenge: Which set of advertisers T should we accept tomaximize f (T )?
Note:
I Offline Optimization.
I Can be used in a negotiation process.
I Can have different penalty factors λi for each advertiser i .
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Discussion Summary
Given a set T of advertisers, maximizing f (T ) is easy as it is amaximum weighted matching.
Challenge: Which set of advertisers T should we accept tomaximize f (T )?
Note:
I Offline Optimization.
I Can be used in a negotiation process.
I Can have different penalty factors λi for each advertiser i .
![Page 98: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/98.jpg)
Discussion Summary
Given a set T of advertisers, maximizing f (T ) is easy as it is amaximum weighted matching.
Challenge: Which set of advertisers T should we accept tomaximize f (T )?
Note:
I Offline Optimization.
I Can be used in a negotiation process.
I Can have different penalty factors λi for each advertiser i .
![Page 99: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/99.jpg)
Ad Planning with Penalties
Feige, Immorlica, M., Nazerzadeh, 2008.
I Hardness: No Constant-factor Approximation.I Heuristic Greedy Algorithms:
I Simple Greedy Algorithm: Bicriteria Approximation.I At each step, add the advertiser with the maximum
profit-per-impression fixing the existing assignment.
Theorem: This is a good approximation compared to theoptimum with larger penalty factor.
I Greedy-Rate Algorithm: Structural Approximation.
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Ad Planning with Penalties
Feige, Immorlica, M., Nazerzadeh, 2008.
I Hardness: No Constant-factor Approximation.I Heuristic Greedy Algorithms:
I Simple Greedy Algorithm: Bicriteria Approximation.I At each step, add the advertiser with the maximum
profit-per-impression fixing the existing assignment.
Theorem: This is a good approximation compared to theoptimum with larger penalty factor.
I Greedy-Rate Algorithm: Structural Approximation.
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Ad Planning with Penalties
Feige, Immorlica, M., Nazerzadeh, 2008.
I Hardness: No Constant-factor Approximation.I Heuristic Greedy Algorithms:
I Simple Greedy Algorithm: Bicriteria Approximation.I At each step, add the advertiser with the maximum
profit-per-impression fixing the existing assignment.
Theorem: This is a good approximation compared to theoptimum with larger penalty factor.
I Greedy-Rate Algorithm: Structural Approximation.
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Greedy Algorithms
Greedy-Rate Algorithm:
I At each step, add the advertiser with the maximummarginal-profit per marginal-cost ratio.
T : Set of advertisers we committed to (initialized to ∅)I At each step, add an advertiser i ∈ X\S to T that maximizes
P(S∪i)−P(S)ci
, if P(S ∪ i)− P(S)− ci > 0.
Theorem: The greedy-rate algorithm achieves the best structuralapproximation.Proof: Uses submodularity of P(T ), and f (T ).
I The approximation factor of the algorithm is a function of the
structure of the solution, i.e., a Signature: α = C(OPT)
P(OPT).
I Greedy-rate algorithm achieves at least factor1−α−α ln 1
α1−α
(improving factor 1 + α− 2√α).
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Greedy Algorithms
Greedy-Rate Algorithm:
I At each step, add the advertiser with the maximummarginal-profit per marginal-cost ratio.
T : Set of advertisers we committed to (initialized to ∅)I At each step, add an advertiser i ∈ X\S to T that maximizes
P(S∪i)−P(S)ci
, if P(S ∪ i)− P(S)− ci > 0.
Theorem: The greedy-rate algorithm achieves the best structuralapproximation.Proof: Uses submodularity of P(T ), and f (T ).
I The approximation factor of the algorithm is a function of the
structure of the solution, i.e., a Signature: α = C(OPT)
P(OPT).
I Greedy-rate algorithm achieves at least factor1−α−α ln 1
α1−α
(improving factor 1 + α− 2√α).
![Page 104: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/104.jpg)
Greedy Algorithms
Greedy-Rate Algorithm:
I At each step, add the advertiser with the maximummarginal-profit per marginal-cost ratio.
T : Set of advertisers we committed to (initialized to ∅)I At each step, add an advertiser i ∈ X\S to T that maximizes
P(S∪i)−P(S)ci
, if P(S ∪ i)− P(S)− ci > 0.
Theorem: The greedy-rate algorithm achieves the best structuralapproximation.
Proof: Uses submodularity of P(T ), and f (T ).
I The approximation factor of the algorithm is a function of the
structure of the solution, i.e., a Signature: α = C(OPT)
P(OPT).
I Greedy-rate algorithm achieves at least factor1−α−α ln 1
α1−α
(improving factor 1 + α− 2√α).
![Page 105: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/105.jpg)
Greedy Algorithms
Greedy-Rate Algorithm:
I At each step, add the advertiser with the maximummarginal-profit per marginal-cost ratio.
T : Set of advertisers we committed to (initialized to ∅)I At each step, add an advertiser i ∈ X\S to T that maximizes
P(S∪i)−P(S)ci
, if P(S ∪ i)− P(S)− ci > 0.
Theorem: The greedy-rate algorithm achieves the best structuralapproximation.Proof: Uses submodularity of P(T ), and f (T ).
I The approximation factor of the algorithm is a function of the
structure of the solution, i.e., a Signature: α = C(OPT)
P(OPT).
I Greedy-rate algorithm achieves at least factor1−α−α ln 1
α1−α
(improving factor 1 + α− 2√α).
![Page 106: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/106.jpg)
Ad Planning with Delivery Penalty
Online
Banner Ad Delivery
Planning:Which
ads/advertisersshould wecommit to?
Strategic
Stochastic
FIMN’08
Constraints: Guaranteed Delivery, Fairness, ...
BHK 09
CFMP 09
Banner Ad Delivery
• Babaiof, Hartline, Kleinberg: Online Algorithms with Buyback
• Special cases: Single item, Matroid, Knapsack
• Constantin, Feldman, Muthkrishnan, Pal: Ad slotting with Cancellations.
• Special case: Demand=1, Truthful Mechanism: Constant-factor
Interesting Algorithmic Problem:I Online mechanism for general ad planning with delivery
penalty: bicriteria approximation?
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Ad Planning with Delivery Penalty
Online
Banner Ad Delivery
Planning:Which
ads/advertisersshould wecommit to?
Strategic
Stochastic
FIMN’08
Constraints: Guaranteed Delivery, Fairness, ...
BHK 09
CFMP 09
Banner Ad Delivery
• Babaiof, Hartline, Kleinberg: Online Algorithms with Buyback
• Special cases: Single item, Matroid, Knapsack
• Constantin, Feldman, Muthkrishnan, Pal: Ad slotting with Cancellations.
• Special case: Demand=1, Truthful Mechanism: Constant-factor
Interesting Algorithmic Problem:I Online mechanism for general ad planning with delivery
penalty: bicriteria approximation?
![Page 108: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/108.jpg)
Ad Planning: Offline Optimization of Contracts
I Fast Algorithms to Verify Feasibility of Contracts:I Lopsided Bipartite Graphs.I Improved Algorithms for Bipartite Network Flow: Ahuja, Orlin,
Stein, Tarjan 94I Faster Algorithm for max-flow: running time depends on the
size of smaller part.
I Sampling for Max-Cardinality Matching: Charles, Chickering,Devanur, Jain, Sanghi 2010,
I Sampling and Concise Allocation.I Algorithm: Iteratively assign nodes, and minimize the future
failure probability.I WHP verifies if there exists a feasible matching.
I Online algorithms for accepting contracts: Alaei, Arcuate,Khuller, Ma, Malekian, Tomlin 2009
I Utility model to combine contract-based advertisers &sales-based advertisers.
I Online algorithm for accepting contracts (under assumptions)
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Ad Planning: Offline Optimization of Contracts
I Fast Algorithms to Verify Feasibility of Contracts:I Lopsided Bipartite Graphs.I Improved Algorithms for Bipartite Network Flow: Ahuja, Orlin,
Stein, Tarjan 94I Faster Algorithm for max-flow: running time depends on the
size of smaller part.
I Sampling for Max-Cardinality Matching: Charles, Chickering,Devanur, Jain, Sanghi 2010,
I Sampling and Concise Allocation.I Algorithm: Iteratively assign nodes, and minimize the future
failure probability.I WHP verifies if there exists a feasible matching.
I Online algorithms for accepting contracts: Alaei, Arcuate,Khuller, Ma, Malekian, Tomlin 2009
I Utility model to combine contract-based advertisers &sales-based advertisers.
I Online algorithm for accepting contracts (under assumptions)
![Page 110: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/110.jpg)
Ad Planning: Offline Optimization of Contracts
I Fast Algorithms to Verify Feasibility of Contracts:I Lopsided Bipartite Graphs.I Improved Algorithms for Bipartite Network Flow: Ahuja, Orlin,
Stein, Tarjan 94I Faster Algorithm for max-flow: running time depends on the
size of smaller part.
I Sampling for Max-Cardinality Matching: Charles, Chickering,Devanur, Jain, Sanghi 2010,
I Sampling and Concise Allocation.I Algorithm: Iteratively assign nodes, and minimize the future
failure probability.I WHP verifies if there exists a feasible matching.
I Online algorithms for accepting contracts: Alaei, Arcuate,Khuller, Ma, Malekian, Tomlin 2009
I Utility model to combine contract-based advertisers &sales-based advertisers.
I Online algorithm for accepting contracts (under assumptions)
![Page 111: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/111.jpg)
Outline of this talk
I Ad delivery for contract based settingsI PlanningI Ad Serving
I Ad serving in repeated auction settingsI General architecture.I Allocation for budget constrained advertisers.
I Other interactionsI Learning + allocationI Learning + auctionI Auction + contracts
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Outline of this talk
I Ad delivery for contract based settingsI PlanningI Ad Serving
I Ad serving in repeated auction settingsI General architecture.I Allocation for budget constrained advertisers.
I Other interactionsI Learning + allocationI Learning + auctionI Auction + contracts
![Page 113: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/113.jpg)
Three main theory/practice problems
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Combined Allocation with AdX: Objective
Short-term: boost revenue from AdXVS
Long-term: prioritize quality of guaranteed contracts.
Find allocation policy to maximize
yield = revenue(AdX) + γ · quality(advertisers),
where γ ≥ 0 is a tradeoff paramater (or Lagrange multiplier).
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Publisher’s Decisions
Impression n-tharrives withquality Qn
Assign to an advertiser or discard
Submit to AdXwith price p
Obtain payment
Assign to anadvertiser ordiscard
accept
reject
Optimal to always test the exchange!
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Publisher’s Decisions
Impression n-tharrives withquality Qn
Assign to an advertiser or discard
Submit to AdXwith price p
Obtain payment
Assign to anadvertiser ordiscard
accept
reject
Optimal to always test the exchange!
![Page 117: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/117.jpg)
Impact of AdX
400
500
600
700
800
900
1000
350 370 390 410 430 450
Quality
Advert
isers
Revenue AdX
∞
Pareto efficient frontier
I γ = 0: maximum revenue from AdX.
I γ =∞: maximum placement quality for contracts.
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Display Ad Delivery
Planning:
Display Ad Delivery
Ad Serving: Targeting: Allocation:
Delivery Constraints, Budget
CTR
Strategic, Stochastic
Online, Stochastic
Offline, Online Forecasting
Demand for ads
Supply of impressions
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Display Ad Delivery
Planning:
Display Ad Delivery
Ad Serving: Targeting: Allocation:
Delivery Constraints, Budget
CTR
Strategic, Stochastic
Online, Stochastic
Offline, Online
Feedback
Forecasting
Demand for ads
Supply of impressions
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Online Learning & Allocation
I Value: Estimated Click-Through-Rate (CTR).
I Combined online capacity planning & learning?I Budgeted Active Learning
I Madani, Lizotte, Greiner 2004, Active Model Selection.
I Bayesian Budgeted Multi-armed Bandits:I Guha, Munagala, Multi-armed Bandits with Metric Switching
Costs.I Goel, Khanna, Null, The Ratio Index for Budgeted Learning,
with Applications.I Guha, Munagala, Pal, Multi-armed Bandit with Delayed
Feedback.
I Budgeted Unknown-CTR Multi-armed BanditI Pandey, Olston 2007, Handling Advertisement of Unknown
Quality.
![Page 121: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/121.jpg)
Online Learning & Allocation
I Value: Estimated Click-Through-Rate (CTR).I Combined online capacity planning & learning?
I Budgeted Active LearningI Madani, Lizotte, Greiner 2004, Active Model Selection.
I Bayesian Budgeted Multi-armed Bandits:I Guha, Munagala, Multi-armed Bandits with Metric Switching
Costs.I Goel, Khanna, Null, The Ratio Index for Budgeted Learning,
with Applications.I Guha, Munagala, Pal, Multi-armed Bandit with Delayed
Feedback.
I Budgeted Unknown-CTR Multi-armed BanditI Pandey, Olston 2007, Handling Advertisement of Unknown
Quality.
![Page 122: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/122.jpg)
Online Learning & Allocation
I Value: Estimated Click-Through-Rate (CTR).I Combined online capacity planning & learning?
I Budgeted Active LearningI Madani, Lizotte, Greiner 2004, Active Model Selection.
I Bayesian Budgeted Multi-armed Bandits:I Guha, Munagala, Multi-armed Bandits with Metric Switching
Costs.I Goel, Khanna, Null, The Ratio Index for Budgeted Learning,
with Applications.I Guha, Munagala, Pal, Multi-armed Bandit with Delayed
Feedback.
I Budgeted Unknown-CTR Multi-armed BanditI Pandey, Olston 2007, Handling Advertisement of Unknown
Quality.
![Page 123: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/123.jpg)
Online Learning & Allocation
I Value: Estimated Click-Through-Rate (CTR).I Combined online capacity planning & learning?
I Budgeted Active LearningI Madani, Lizotte, Greiner 2004, Active Model Selection.
I Bayesian Budgeted Multi-armed Bandits:I Guha, Munagala, Multi-armed Bandits with Metric Switching
Costs.I Goel, Khanna, Null, The Ratio Index for Budgeted Learning,
with Applications.I Guha, Munagala, Pal, Multi-armed Bandit with Delayed
Feedback.
I Budgeted Unknown-CTR Multi-armed BanditI Pandey, Olston 2007, Handling Advertisement of Unknown
Quality.
![Page 124: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/124.jpg)
Online CTR Learning: Mixed Explore/Exploit
I Pandey, Olston 2007, Handling Advertisement of UnknownQuality.
I Algorithm: Revised GreedyI Upon arrival of query of type i , assign it to an ad a maximizing
Pia = (cia +√
2 ln ninia
)bia
where cia is the current estimate of CTR, nia is the number oftimes i has been assigned to a, ni is the number of queries oftype i so far.
I Thm[PO07]: ALG ≥ opt2 − O(ln n) where n is the number of
arrivals.
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Online CTR Learning: Mixed Explore/Exploit
I Pandey, Olston 2007, Handling Advertisement of UnknownQuality.
I Algorithm: Revised GreedyI Upon arrival of query of type i , assign it to an ad a maximizing
Pia = (cia +√
2 ln ninia
)bia
where cia is the current estimate of CTR, nia is the number oftimes i has been assigned to a, ni is the number of queries oftype i so far.
I Thm[PO07]: ALG ≥ opt2 − O(ln n) where n is the number of
arrivals.
![Page 126: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/126.jpg)
Online CTR Learning: Mixed Explore/Exploit
I Pandey, Olston 2007, Handling Advertisement of UnknownQuality.
I Algorithm: Revised GreedyI Upon arrival of query of type i , assign it to an ad a maximizing
Pia = (cia +√
2 ln ninia
)bia
where cia is the current estimate of CTR, nia is the number oftimes i has been assigned to a, ni is the number of queries oftype i so far.
I Thm[PO07]: ALG ≥ opt2 − O(ln n) where n is the number of
arrivals.
![Page 127: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/127.jpg)
Hybrid ad serving: Contracts + Spot Auctions
Given a page view, and two types of advertisers:
I Contract-based.
I Auction-based.
I Decide who wins and how much do they pay.I Requirements:
I For each contract-advertiser, meet its demand.I Implement the scheme using proxy-bidding for
contract-advertisers in the spot auction.
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Hybrid ad serving: Contracts + Spot Auctions
Given a page view, and two types of advertisers:
I Contract-based.
I Auction-based.
I Decide who wins and how much do they pay.I Requirements:
I For each contract-advertiser, meet its demand.I Implement the scheme using proxy-bidding for
contract-advertisers in the spot auction.
![Page 129: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/129.jpg)
Hybrid ad serving: Contracts + Spot Auctions
I Naive solution: If a contract-adv is eligible and has notfinished demand, then let it win the spot. Bid infinity for allauctions.
I Optimize for revenue: If the auction pressure (price) is lowthen let the contract-adv win. Bid a low bid for all auctions.
I Unfair to contract-adv, since low auction-price ⇒ it is a lowervalue impression.
I Ideally:I Provide contract-adv with a representative allocation, an equal
slice of impressions from each price-point.I A price-oblivious scheme, i.e., bid without seeing the auction
bids.I Revenue per auction: average auction-price of impressions
given away to contract-advertisers is at most some target t.
![Page 130: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/130.jpg)
Hybrid ad serving: Contracts + Spot Auctions
I Naive solution: If a contract-adv is eligible and has notfinished demand, then let it win the spot. Bid infinity for allauctions.
I Optimize for revenue: If the auction pressure (price) is lowthen let the contract-adv win. Bid a low bid for all auctions.
I Unfair to contract-adv, since low auction-price ⇒ it is a lowervalue impression.
I Ideally:I Provide contract-adv with a representative allocation, an equal
slice of impressions from each price-point.I A price-oblivious scheme, i.e., bid without seeing the auction
bids.I Revenue per auction: average auction-price of impressions
given away to contract-advertisers is at most some target t.
![Page 131: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/131.jpg)
Hybrid ad serving: Contracts + Spot Auctions
I Naive solution: If a contract-adv is eligible and has notfinished demand, then let it win the spot. Bid infinity for allauctions.
I Optimize for revenue: If the auction pressure (price) is lowthen let the contract-adv win. Bid a low bid for all auctions.
I Unfair to contract-adv, since low auction-price ⇒ it is a lowervalue impression.
I Ideally:I Provide contract-adv with a representative allocation, an equal
slice of impressions from each price-point.I A price-oblivious scheme, i.e., bid without seeing the auction
bids.I Revenue per auction: average auction-price of impressions
given away to contract-advertisers is at most some target t.
![Page 132: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/132.jpg)
Hybrid ad serving: Contracts + Spot Auctions
I Naive solution: If a contract-adv is eligible and has notfinished demand, then let it win the spot. Bid infinity for allauctions.
I Optimize for revenue: If the auction pressure (price) is lowthen let the contract-adv win. Bid a low bid for all auctions.
I Unfair to contract-adv, since low auction-price ⇒ it is a lowervalue impression.
I Ideally:I Provide contract-adv with a representative allocation, an equal
slice of impressions from each price-point.I A price-oblivious scheme, i.e., bid without seeing the auction
bids.I Revenue per auction: average auction-price of impressions
given away to contract-advertisers is at most some target t.
![Page 133: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/133.jpg)
Obtaining representative allocationsTwo main ideas:
1. Can implement any decreasing function a(p) for fraction ofimpressions of auction-price p.
2. Solve the system for well chosen distance functions:
Minimize dist(U, a)
s.t.:
∫pa(p)f (p)dp = d∫
ppa(p)f (p)dp ≤ td
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Obtaining representative allocationsTwo main ideas:
1. Can implement any decreasing function a(p) for fraction ofimpressions of auction-price p.
2. Solve the system for well chosen distance functions:
Minimize dist(U, a)
s.t.:
∫pa(p)f (p)dp = d∫
ppa(p)f (p)dp ≤ td
![Page 135: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/135.jpg)
Online Learning & Auction Incentives
[Devanur,Kakade’09, Babaioff,Sharma,Slivkins’09]
I Multi-Armed Bandit algorithms achieve an “implicit”exploration-exploitation tradeoff to get a regret of O(
√T )
(e.g., UCB).
I Can these be run in tandem with truthful auctions? (e.g., 2ndprice for a single slot).
I A naive explore-exploit method gets O(T 2/3) regret:I Explore ads for the first phase, giving them out for free.I Fix the CTRs thus learned in the first phase.I Run 2nd price auction for the 2nd phase.
I Can you do better that this simpe decoupling?
I No!
Theorem[DK09,BSS09] For every truthful auction (under certainassumptions), there exist bids, ctrs, s.t. regret = Ω(T 2/3).
![Page 136: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/136.jpg)
Online Learning & Auction Incentives
[Devanur,Kakade’09, Babaioff,Sharma,Slivkins’09]
I Multi-Armed Bandit algorithms achieve an “implicit”exploration-exploitation tradeoff to get a regret of O(
√T )
(e.g., UCB).
I Can these be run in tandem with truthful auctions? (e.g., 2ndprice for a single slot).
I A naive explore-exploit method gets O(T 2/3) regret:I Explore ads for the first phase, giving them out for free.I Fix the CTRs thus learned in the first phase.I Run 2nd price auction for the 2nd phase.
I Can you do better that this simpe decoupling?
I No!
Theorem[DK09,BSS09] For every truthful auction (under certainassumptions), there exist bids, ctrs, s.t. regret = Ω(T 2/3).
![Page 137: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/137.jpg)
Online Learning & Auction Incentives
[Devanur,Kakade’09, Babaioff,Sharma,Slivkins’09]
I Multi-Armed Bandit algorithms achieve an “implicit”exploration-exploitation tradeoff to get a regret of O(
√T )
(e.g., UCB).
I Can these be run in tandem with truthful auctions? (e.g., 2ndprice for a single slot).
I A naive explore-exploit method gets O(T 2/3) regret:I Explore ads for the first phase, giving them out for free.I Fix the CTRs thus learned in the first phase.I Run 2nd price auction for the 2nd phase.
I Can you do better that this simpe decoupling?
I No!
Theorem[DK09,BSS09] For every truthful auction (under certainassumptions), there exist bids, ctrs, s.t. regret = Ω(T 2/3).
![Page 138: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/138.jpg)
Display Ad Delivery
Planning:
Display Ad Delivery
Ad Serving: Targeting: Allocation:
Delivery Constraints, Budget
CTR
Strategic, Stochastic
Online, Stochastic
Offline, Online
Feedback
Feedback
Forecasting
Demand for ads
Supply of impressions
Open Problems:I Optimal combined online allocation & learning.I Feature selection and correlation in learning CTR.I Optimal combined stochastic planning and serving?
![Page 139: Online Ad Serving: Theory and Practice · I Display/Banner Ads, Video Ads, Mobile Ads. I Cost-Per-Impression (CPM). I Not Auction-based:o ine negotiations+ Online allocations. Display/Banner](https://reader033.fdocuments.us/reader033/viewer/2022042911/5f4532a233140b5ca3776cae/html5/thumbnails/139.jpg)
Thank You