Managing Risk of Bidding in Display Advertising

1. Managing Risk of Bidding
in Display Advertising
9 Feb 2017, WSDM17
Haifeng Zhang, Wenxin Li
Peking University
Weinan Zhang, Kan Ren
Shanghai JiaoTong University
Yifei Rong
YOYI Inc
Jun Wang
UCL, MediaGamma Ltd

2. Display advertising
http://www.nytimes.com/

3. The Scale of Real-Time Bidding (RTB) based Display Advertising
DSP/Exchange Daily traffic
RTB advertising iPinYou, China 18 billion impressions
YOYI, China 5 billion impressions
Fikisu, US 32 billion impressions
Appnexus, US 100+billion impressions
Web search Google search
~3.5 billion
searches/impressions
Financial markets New York stock exchange 12 billion shares daily
Shanghai stock exchange 14 billion shares daily
Shen, Jianqiang, et al. "From 0.5 Million to 2.5 Million: Efficiently Scaling up Real-Time Bidding." Data Mining (ICDM), 2015 IEEE
International Conference on. IEEE, 2015.
http://www.internetlivestats.com/google-search-statistics/

4. Real-time machine bidding
• Design bidding algorithms to make the best match
between the advertisers and Internet users with
economic constraints

5. 0.4 0.6 0.8 1.0
CTR
TR Distribution, q=30
µ=0
µ=-0.1
µ=-0.2
0.4 0.6 0.8 1.0
CTR
TR Distribution, µ=-0.1
q=5
q=30
q=100
on of the proposed CTR distribution
µ and q in Eq. (12).
= ln ˆy − ln(1 − ˆy) is monotonic and
, 1), so we obtain the closed-form of
i q−1
i xi
e
−
(σ−1(ˆy)− i µixi)2
2 i q
−1
i
xi , (12)
0.0 0.2 0.4 0.6 0.8 1.0
CTR
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
p(y)
CTR Distribution
CTR y
0 50 100 150 200 250 300
Market Price
0.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
0.016
0.018
p(z)
Market Price Distribution
Market Price z
100 50 0 50 100 150 200 250
Profit. P(vy-z < 0 | b=84)=16.5%
0.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
0.016
0.018
p(vy-z)
Profit Distribution
Profit vy− z
Figure 2: An example of CTR, market price and profit
distribution when bidding the expected utility value. The
profit p.d.f. on 0 is the probability of losing the auction,
resulting in a peak.
The risk in machine bidding
• Risk 1: CTR is a random
variable: p(CTR)
• Risk 2: market price: p(z)
• As a result, reward/profit is
also a random variable
𝑅 𝑏 = $
0, 𝑏 ≤ 𝑧 (𝑙𝑜𝑠𝑒)
𝑣 · ŷ − 𝑏, 𝑏 > 𝑧 (𝑤𝑖𝑛)
This peak is caused by the losing bids.
0.4 0.6 0.8 1.0
CTR
Distribution, q=30
µ=0
µ=-0.1
µ=-0.2
0.4 0.6 0.8 1.0
CTR
istribution, µ=-0.1
q=5
q=30
q=100
of the proposed CTR distribution
nd q in Eq. (12).
n ˆy − ln(1 − ˆy) is monotonic and
, so we obtain the closed-form of
i q−1
i xi
e
−
(σ−1(ˆy)− i µixi)2
2 i q
−1
i
xi , (12)
0.0 0.2 0.4 0.6 0.8 1.0
CTR
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
p(y)
CTR Distribution
CTR y
0 50 100 150 200 250 300
Market Price
0.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
0.016
0.018
p(z)
Market Price Distribution
Market Price z
100 50 0 50 100 150 200 250
Profit. P(vy-z < 0 | b=84)=16.5%
0.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
0.016
0.018
p(vy-z)
Profit Distribution
Profit vy− z
Figure 2: An example of CTR, market price and profit
distribution when bidding the expected utility value. The
profit p.d.f. on 0 is the probability of losing the auction,
0.4 0.6 0.8 1.0
CTR
R Distribution, q=30
µ=0
µ=-0.1
µ=-0.2
0.4 0.6 0.8 1.0
CTR
Distribution, µ=-0.1
q=5
q=30
q=100
of the proposed CTR distribution
and q in Eq. (12).
ln ˆy − ln(1 − ˆy) is monotonic and
1), so we obtain the closed-form of
i q−1
i xi
e
−
(σ−1(ˆy)− i µixi)2
2 i q
−1
i
xi , (12)
cit CTR p.d.f. To our best knowl-
0.0 0.2 0.4 0.6 0.8 1.0
CTR
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
p(y)
CTR Distribution
CTR y
0 50 100 150 200 250 300
Market Price
0.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
0.016
0.018
p(z)
Market Price Distribution
Market Price z
100 50 0 50 100 150 200 250
Profit. P(vy-z < 0 | b=84)=16.5%
0.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
0.016
0.018
p(vy-z)
Profit Distribution
Profit vy− z
Figure 2: An example of CTR, market price and profit
distribution when bidding the expected utility value. The
profit p.d.f. on 0 is the probability of losing the auction,
resulting in a peak.Value at Risk (VaR): What is the reward given the downside risk we are willing to take?

6. Click-Through Rate(CTR) distribution estimation
• Existing CTR estimation solution
– Point estimation: LR, Tree models,
etc.
– Distribution estimation: Bayesian
probit model (doesn’t have
closed-form)
• Our solution
– Assumption: feature weight 𝑤8 is
from Gaussian i.i.d.,thus
𝑤8~𝑁 𝜇8, 𝑞8
=> .
– Closed-form: 𝑝ŷ ŷ =
>
(ŷ=ŷ@) ABCDE
𝑒
=
(GDE ŷ DH)@
@IDE
, where
𝜇 = ∑ 𝜇8 𝑥88 , 𝑞=> = ∑ 𝑞8
=> 𝑥88
and σ is the sigmoid function.
0.0 0.2 0.4 0.6 0.8 1.0
CTR
0
1
2
3
4
5
6
7
8
p(CTR)
CTR Distribution, q=30
µ=0
µ=-0.1
µ=-0.2
0.0 0.2 0.4 0.6 0.8 1.0
CTR
0
1
2
3
4
5
6
7
p(CTR)
CTR Distribution, µ=-0.1
q=5
q=30
q=100

7. Experiment results
LR VaR
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
ROI
LR VaR
0
20
40
60
80
100
Profit (USD)
LR VaR
0
20
40
60
80
100
120
140
Budget Spent (USD)
LR VaR
0
2
4
6
8
10
12
Winning Rate (%)
LR VaR
0.0
0.5
1.0
1.5
2.0
2.5
3.0
CTR ( )
LR VaR
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
CPM (USD)
• Offline test: effect on Profit VaR vs LR 11%↑ RMP vs LR 15%↑
• Online A/B test: the VaR strategy achieves 17.5% higher profit than LR
LR
λ =0.0 λ =0.2 λ =0.4 λ =0.0 λ =0.2 λ =0.4
0.6
0.8
1.0
1.2
1.4
ROI
LR VaR
λ =0.0
VaR
λ =0.2
VaR
λ =0.4
RMP
λ =0.0
RMP
λ =0.2
RMP
λ =0.4
3.0
3.2
3.4
3.6
4.0
LR VaR
λ =0.0
VaR
λ =0.2
VaR
λ =0.4
RMP
λ =0.0
RMP
λ =0.2
RMP
λ =0.4
0.75
3
LR VaR
λ =0.0
VaR
λ =0.2
VaR
λ =0.4
RMP
λ =0.0
RMP
λ =0.2
RMP
λ =0.4
4.0
4.5
5.0
5.5
6.0
6.5
7.0
LR VaR
λ =0.0
VaR
λ =0.2
VaR
λ =0.4
RMP
λ =0.0
RMP
λ =0.2
RMP
λ =0.4
4.5
5.0
5.5
6.0
6.5
7.0
7.5
LR VaR
λ =0.0
VaR
λ =0.2
VaR
λ =0.4
RMP
λ =0.0
RMP
λ =0.2
RMP
λ =0.4
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
Figure 8: Overall non-budgeted test performance.
ROI
LR
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
ROI
LR
0
20
40
60
LR VaR
0
2
4
6
LR
0.0
0.5
2.0
2.5
3.0
Figure 10: Online re
posed strategies filtered out t
always with high uncertaint
rate, VaR reduced the CPM
dent cases and highering th
tuning φ); RMP did not gu
sought the bid yielding the h
profit.
Offline test Online A/B test
.4
LR VaR
λ =0.0
VaR
λ =0.2
VaR
λ =0.4
RMP
λ =0.0
RMP
λ =0.2
RMP
λ =0.4
3.0
3.2
3.4
3.6
4.0
P
.4
LR VaR
λ =0.0
VaR
λ =0.2
VaR
λ =0.4
RMP
λ =0.0
RMP
λ =0.2
RMP
λ =0.4
4.0
4.5
5.0
5.5
6.0
6.5
7.0
4.0
4.5
5.0
5.5
6.0
LR
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
ROI
LR VaR
0
20
40
60
LR VaR
0
20
40
60
LR VaR
0
2
4
6
LR VaR
0.0
0.5
2.0
2.5
3.0
LR VaR
0.00
0.02
0.03
0.04
0.05
0.06
0.07
Figure 10: Online results from YOYI DSP.
posed strategies filtered out the low-value cases, which were

8. Summary
• Online advertising is a good case study of information
matching with economic constraints
• Developed value-at-risk bidding strategies in order to
handle the randomness of estimated CTR and market
price
• CTR distribution is modeled in closed-form
Zhang, H., Zhang, W., Rong, Y., Ren, K., Li, W., & Wang, J. (2017). Managing Risk of
Bidding in Display Advertising. WSDM17
Wang, Jun, Weinan Zhang, and Shuai Yuan. "Display Advertising with Real-Time
Bidding (RTB) and Behavioural Targeting." arXiv preprint arXiv:1610.03013 (2016).
Foundations and Trends® in Information Retrieval, Now Publishers (to appear)