Online Matching and Ad Allocation

2016/07/21

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8. Online Submodular Welfare Maximization

V U n ufu : 2V R+

V 2V

stream u Vu Vu

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maxuU fu(Vu) f

S T V, f(U) f(T ) f(V )

X,Y : f(X Y ) + f(X Y ) f(X) + f(Y )

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X,Y : f(X Y ) + f(X Y ) f(X) + f(Y ) X Y, i / Y : f(X {i}) f(X) f(Y {i}) f(Y )

X, Y X Y = Z,X = Z {x} (x / Y )

f(Z) + f(Y {x}) f(Z {x}) + f(Y ) f(Y {x}) f(Y ) f(Z {x}) f(Z)

Z Y, x / Z, x / Y 5/ 30

http://tasusu.hatenablog.com/entry/2015/12/01/000608

(Cont.)

f

v V

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S T V, x / T : f(S + x) f(S) f(T + x) f(T )

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f GREEDY

GREEDYmarginal gain

Vu u U v V fu(Vu {v}) fu(Vu) u

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Theorem 8.1GREEDYAdversarial 1

2

5.2

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4.2marginal gain (ru) = 1 eru1ru [0, 1] Perturbed GreedyAlgorithm 71 1

e

5.2marginal gain (xu) = 1 exu1 MSVVAlgorithm 10 1 1

e

6Algorithm 13Algorithm 11

small bit assamption

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Display Ad

Adwords Display Ad 6 Free Disposal FKMMP09Algorithm 17 1 1

e

cu

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Theorem 8.2 1

2

small bit assamption

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Open Question 10

small bit assamption Adwords free disposal Display Ad

Open Question 11

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Unknown IID

Theorem 8.3Unknown IIDGREEDY 1 1

e

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9.Applications

9.1bid-scalingsmall bit assumption

9.2 9.3 bid-scaling 9.4 9.5Throttling

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9.1 A Unified View: Bid-Scaling Algorithms

Bid-Scaling Algorighms

MSVV Perturbed Greedy

MSVV FKMMP09

Perturbed Greedy MSVV FKMMP09

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GREEDY GREEDY

CPU

bid CPU

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Adversarial

AdversarialGREEDY

6.2

GREEDY LP

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9.2 Objective Functions Used in Practice

efficiency

efficiency

Return on InvestmentROI

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Quality =

iI qi/|I| I qi i quality scoreCTRi qi CTR CTR

ROI =

iI CTRiCVRiViiI CTRiCPCi

Vi ROI =

iI CTRiCVRi(ViCPCi)

iI CTRiCPCi

Revenue =

iI CTRiCPCi

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fairness

Open Question 12

efficiencyonline matching problem

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9.3 Published Results from the Industry

bid-scaling algorithm Display Ad Display Ad

X impressionY impression capacity

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Google

Adwords Problem: Online Keyword Matching with Budgeted Bidders underRandom PermutationsDisplay Ad

5 MSVVargmin

{uU uBu +

vV maxu xuv(1 u)

}xuv(1 u) uBu u

Adwords Display Ad free disposal 1 mm m

Efficiency GREEDY 10% fairness

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http://research-srv.microsoft.com/en-us/um/people/nikdev/pubs/Adwords.pdfhttp://research-srv.microsoft.com/en-us/um/people/nikdev/pubs/Adwords.pdf

Google

Online Stochastic Packing applied to Display Ad Allocation fairness u(x) =

vV wuvxuvV (x) =

uU u(x)

offline x fairness =

uU

V (x)V (x) u(x) u(x) onlineofflineEfficiency

fairness Efficiency online Efficiency

fairness 0

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https://arxiv.org/pdf/1001.5076.pdf

Google Cont.

pd-avgimppd-expMSVVhybrid1% pd-avglp weightofflinefairoffline fairdualbase

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GoogleCont.

maximum possible efficiency MSVV Efficiency fairness

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Microsoft

Display Ad impressioncapacityWaterlevel

5 Balance bid Fast Algorithms for Finding Matchings in Lopsided Bipartite Graphs withApplications to Display Ads

Microsoft CTR*CPC Waterlevel

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http://research.microsoft.com/en-us/um/people/nikdev/pubs/waterlevel.pdfhttp://research.microsoft.com/en-us/um/people/nikdev/pubs/waterlevel.pdf

Microsoft

Real-Time Bidding Algorithms for Performance-Based Display Ad Allocation SlideShare CyberAgent Tatsuki Sugio SlideShare RTB bid CTRimpression

bidGREEDY imp

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http://www.msr-waypoint.net/en-us/um/people/nikdev/pubs/rtb-perf.pdfhttp://www.slideshare.net/JUJU4607/real-time-bidding-algorithms-for-performance-based-displayadallocation

Yahoo!

Optimal Online Assignment with Forecasts 6

0 Lagrangian

KKT

6

free disposal

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http://theory.stanford.edu/~sergei/papers/ec10-lagrange.pdf

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Applications