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The Roles of Uncertainty and Randomness in Online Advertising. Raga Gopalakrishnan. 2 nd Year Graduate Student (Computer Science), Caltech. Eric Bax. Ragavendran Gopalakrishnan. Product Manager (Marketplace Design), Yahoo!. Display Advertising. AD-SLOT. - PowerPoint PPT Presentation
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The Roles of Uncertainty and Randomness in Online Advertising
Ragavendran Gopalakrishnan
Eric Bax
Raga Gopalakrishnan2nd Year Graduate Student (Computer Science), Caltech
Product Manager (Marketplace Design), Yahoo!
AD-SLOT Display Advertising
Simple Model for Display Advertising
AD-SLOT
AD SELECTION ALGORITHM
ad callsads w/
bids
resultant matching (selected ad for
each ad call)
implement
feedback
webpage
Objective Make Money!
0 and subject to
maxarg
1
1
i
n
ii
n
iiii
kimk
sbkk ?
m ad callsad slot
ad 1 ad 2 ad n
k1 k2 kn
b1 b2 bn
s1 s2 sn
. . .
. . .Bid Value
Response Rate
• May not be the right thing to do, for two reasons:– Reason 1: Not Incentive Compatible– Reason 2: Coming up…
The Caveat
• The response rate is not known, it has to be estimated.
• The actual revenue differs from the estimated expected revenue due to two factors:– Uncertainty (error in estimating response rates si)– Randomness (fluctuations around the response
rate: )
n
iiii sbk
1
estRevenue Expected Estimated
),(~responses# iii skB
billion ad calls per day
AD 1 AD 2
ad slot
$1 per response $1 per response
0.001 w/ prob 1 0.0007 w/ prob ½ 0.0013 w/ prob ½
$1 million $1 million
$1000 (0.1%) $0.3 million (30%)
Bid Value
Estimated Response Rate
Estimated Expected Revenue
Standard Deviation of Revenue
How bad can Uncertainty be?
How can we combat it?How much time do we have?
Long-Term Short-Term
LEARNING RISKSPREADING
MAIN FOCUS
?Future Work
• Again, these solutions are not automatically incentive compatible.
m ad callsad slot
ad 1 ad 2 ad n
k1 k2 kn
b1 b2 bn
S1
. . .
. . .Bid Value
Response Rate S2 Sn
Revenue X1(S1) X2(S2) Xn(Sn)Xi(Si)
X1i(Si) X2i(Si) Xmi(Si)
. . . . . .
. . .
n
i
kk
kkhihi
i
i
SXXSkr1
1
11
)(),,(
Model for Variance of
Revenue
Model for Variance (contd.)• The variance of the revenue can
be derived as:
• Independent Returns Case:
),,( ,
XSkrVarXS
n
iiiXSi
n
i
n
jjjXiiXSSji SXVarEkSXESXECovkk
iijiji11 1
, )()](),([
UNCERTAINTY RANDOMNESS
n
iiiXSiiiXSi SXVarEkSXEVark
iiii1
2 )()]([
ad 1
S
k ad calls
Mean = p Std. Dev. = d*p
X(S) is Bernoulli w/ parameter S
)1( Variance 222 pkppdk
n
iiiXSiiiXSi SXVarEkSXEVark
iiii1
2 )()]([
12
2
pkd
pkd
Fraction of Variance Due to Uncertainty is
Factors affecting Variance
Uncertainty or Randomness?
1~y uncertaint todue Variance ofFraction
2
2
pkd
pkd
Bottom LineUncertainty can be really bad
Real World – Uncertainty dominates
Long-Term Short-Term
LEARNING RISKSPREADING
SOLUTION
ad 1v learning ad calls u responses
preal : Real response rate (unknown)
Estimate preal as p = u/v
v
)p-(1pσ realreal
p
vp
1~
p
σd
realreal
p
ad 1 k ‘real’ ad calls
12
2
pkd
pkd
Fraction of Variancedue to Uncertainty is
1vkvk
Effect of Learning
Bottom LineUncertainty can be really bad
Real World – Uncertainty dominates
Long-Term Short-Term
LEARNING RISKSPREADING
SOLUTION
AD 1 AD 2
$1 per response $1 per response
0.001 w/ prob 1 0.0007 w/ prob ½ 0.0013 w/ prob ½
$1 million $1 million
$1000 (0.1%) $0.3 million (30%)
Bid Value
Estimated Response Rate
Estimated Expected Revenue
Standard Deviation of Revenue
billion ad calls per day
0 + 1000000 90000000000 + 1000000Variance of Revenue
New Strategy: Use each of a billion ads iid to AD 2 on each ad callVariance of revenue = 90 + 1000000
Effect of Risk Sharing
Formalize Risk-Sharing
• The goal of sharing risk and bringing the variance down motivates the following optimization problem:
mk
ki
dXSkrVar
XSkrEk
n
ii
i
XS
XS
1
,
,
0
),,( subject to
),,( max
mk
ki
XSkrEqXSkrVark
n
ii
i
XSXS
1
,,
0 subject to
),,( ),,( min
generateresponse rates
Normal Distributionm = 0.001, s =
0.0001
10“CPC” ADS
generateresponse rates
Normal Distributionm = 0.0001, s =
0.00001
10“CPA” ADS
Bid$1
Bid$10
Simulations
• Start with an assumed prior (uniform, approximate or exact)• All 20 ads are given 100000 learning ad calls each, responses are counted,
corresponding posteriors are obtained using Bayes’ Rule• Method 1 (Portfolio): Compute the optimal portfolio and allocate ad calls accordingly• Method 2 (Single Winner): Allocate all ad calls to the ad with the highest estimated
expected revenue• Compare Results
Estimated Expected Revenue
Uniform Prior – Actual Expected Revenue
Uniform Prior – Efficiency
Uniform Prior – Allocation by share of ad calls
Uniform Prior – Allocation by actual expected revenue
Exact Prior – Actual Estimated Revenue
Exact Prior – Allocation by share of ad calls
Exact Prior – Allocation by actual expected revenue
Approximate Prior – Actual Expected Revenue
Approximate Prior – Allocation by share of ad calls
Approximate Prior – Allocation by actual expected revenue
A Word of Caution – Covariance• Randomness is usually uncorrelated over
different ad calls.• More often than not, uncertainty is correlated
over multiple ads, as their response rates could be estimated through a common learning algorithm.
• Covariance can be estimated from empirical data, using models that are specific to the contributing factors (e.g., specific learning methods used).
Summary• Actual Revenue differs from Estimated Expected
Revenue for two reasons – uncertainty and randomness.
• Uncertainty can be very bad, and dominates randomness in most cases.
• Learning helps reduce uncertainty in the long run, but in the short run, portfolio optimization (risk distribution) is one way to combat uncertainty.
• Simulations show that actual revenue can improve as an important side effect of reducing uncertainty.
Further Directions…• Can we tie up the long term and short term solutions?– Example: Consider the explore-exploit family of learning
methods.– After every explore step, we have better estimates of
response rates, but they may still be bad. So the exploit phase could be replaced with the portfolio optimization step!
– Side Effect: Additional exploration in the “exploit” phase.– Is this an optimal way of mixing the two?
• Financial Markets – does it make sense for risk-neutral investors to employ portfolio optimization?
• Incentive Compatibility – can we deal with it?
Thank You
• Questions?
