Managing Risk of Bidding in Display Advertising

9 Feb 2017, WSDM17

Haifeng Zhang, Wenxin LiPeking University

Weinan Zhang, Kan RenShanghai JiaoTong University

Yifei RongYOYI Inc

Jun WangUCL, MediaGamma Ltd

Displayadvertising

http://www.nytimes.com/

TheScaleofReal-TimeBidding(RTB)basedDisplayAdvertising

DSP/Exchange Dailytraffic

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/

Real-timemachinebidding

• Designbiddingalgorithms tomakethebestmatchbetweentheadvertisersandInternetuserswitheconomicconstraints

0.0 0.2 0.4 0.6 0.8 1.0CTR

012345678

p(CT

R)

CTR Distribution, q=30µ=0µ=-0.1µ=-0.2

0.0 0.2 0.4 0.6 0.8 1.0CTR

01234567

p(CT

R)

CTR Distribution, µ=-0.1

q=5q=30q=100

Figure 1: An illustration of the proposed CTR distributionagainst its parameters µ and q in Eq. (12).

In our case, σ−1(y) = ln y − ln(1 − y) is monotonic anddifferentiable within (0, 1), so we obtain the closed-form ofy’s p.d.f.

py(y) =1

(y − y2)!

2π"

i q−1i xi

e−

(σ−1(y)−!

i µixi)2

2!

i q−1i

xi , (12)

which provides an explicit CTR p.d.f. To our best knowl-edge, the above proposed solution has not been studied inprevious literature [41, 13, 36]. To understand the natureof the model, Figure 1 plots the CTR distribution againstits parameters µ and q, where x = 110. As observed, thep.d.f. presents a single-peak shape in [0, 1] which is similarwith the shapes of beta distributions.

It is straightforward to see from Figure 1 that µ and qjointly determine the peak location and sharpness of theCTR p.d.f. and specifically µ influences more on the peaklocation while q influences more on the distribution sharp-ness. To understand how it models the CTR prediction un-certainty/confidence, from Eq. (8), we see each time a datainstance with feature xi is observed, the precision qi willbe updated with a higher value, which in turn contributesa sharper CTR p.d.f. in Eq. (12). Therefore, for the adimpression with frequent (similar) features, the predictedCTR is of low uncertainty, and vice versa.

4. RISK-AWARE BIDDING STRATEGIESWith our CTR distribution model in Eq. (12), we next

investigate the conditional distribution of a utility given aspecific bid price for an input bid request. By considering arisk-aware utility as an optimization target, we are ready toderive the corresponding risk-aware bidding strategy. Notethat alternative CTR distribution models can also be incor-porated in our solution framework.

Specifically, we start from the theoretic derivation of aBayesian truth-telling bidding strategy and provide an anal-ysis of its risk in Section 4.1. Then we will propose twosolutions, discussed in Sections 4.2 and 4.3 respectively.

4.1 Analysis: Bayesian Truth-telling BiddingThe utility r of an ad impression could be defined based

on the advertiser’s value v on a specific user action, e.g.,click or conversion. For example, if the value v is on eachclick, given an impression with CTR y distributed as inEq. (12), the utility r and its p.d.f. of this impression are

r = v · y, pr(r) = py(y)/v. (13)

Moreover, the cost to win the ad impression comes fromthe highest bid from other competitors, defined as marketprice z [5]. The profit of winning this impression is then cal-

0.0 0.2 0.4 0.6 0.8 1.0CTR

0.00.51.01.52.02.53.03.54.0

p(y)

CTR DistributionCTR y

0 50 100 150 200 250 300Market Price

0.0000.0020.0040.0060.0080.0100.0120.0140.0160.018

p(z)

Market Price DistributionMarket Price z

100 50 0 50 100 150 200 250Profit. P(vy-z < 0 | b=84)=16.5%

0.0000.0020.0040.0060.0080.0100.0120.0140.0160.018

p(vy

-z)

Profit Distribution

Profit vy− z

Figure 2: An example of CTR, market price and profitdistribution when bidding the expected utility value. Theprofit p.d.f. on 0 is the probability of losing the auction,resulting in a peak.

culated as the utility r minus the cost z, which is set as theoptimization target of performance-driven campaigns [39].In a general setting, considering both the estimated CTR

y and cost z are stochastic variables: y ∼ py(y) and z ∼pz(z), the bid optimization problem is to find the optimalbid price to the auction.Let us first consider a simple case without considering the

uncertainty of our estimation, where the goal is to maximizethe expected profit R(b) by marginalizing out y and z:

b∗ = argmaxb

E[R(b)] (14)

= argmaxb

#

y

# b

z=0

(v · y − z)pz(z)dz · py(y)dy. (15)

Take the derivative w.r.t. b and set it to 0:

∂E[R(b)]∂b

=∂∂b

# b

z=0

pz(z)

#

y

(v · y − z)py(y)dydz (16)

= pz(b)

#

y

(v · y − b)py(y)dy = 0 (17)

⇒ b∗ =

#

y

v · y · py(y)dy = v · E[y] = E[r]. (18)

We see that the optimal bid price is the product of the ac-tion value and the estimated CTR y, which is independentof the market price distribution. If we assume y is knownand fixed, i.e., py(y) focuses its mass on a single point, thenthe optimal bid price is v · y. Note that the optimality oftruth-telling bidding is for one-shot auction. When consid-ering campaign budget and auction volume, a coefficient φis commonly added to Eq. (18) as φ · E[r].

Discussion of Risk. The above classic bidding solutionis built on maximizing the expectation of the profit R(b),regardless of its uncertainty. However, a potential problemis that there is a chance a bid is won, but v · y is less thanz, in which case R(b) will be negative. We can obtain the

Theriskinmachinebidding• Risk1: CTRisarandom

variable:p(CTR)

• Risk2:marketprice:p(z)

• Asaresult,reward/profitisalsoarandomvariable

𝑅 𝑏 = $0, 𝑏 ≤ 𝑧(𝑙𝑜𝑠𝑒)𝑣 · ŷ − 𝑏, 𝑏 > 𝑧(𝑤𝑖𝑛)

This peak is caused by the losing bids.

0.0 0.2 0.4 0.6 0.8 1.0CTR

012345678

p(CT

R)

CTR Distribution, q=30µ=0µ=-0.1µ=-0.2

0.0 0.2 0.4 0.6 0.8 1.0CTR

01234567

p(CT

R)

CTR Distribution, µ=-0.1

q=5q=30q=100

Figure 1: An illustration of the proposed CTR distributionagainst its parameters µ and q in Eq. (12).

In our case, σ−1(y) = ln y − ln(1 − y) is monotonic anddifferentiable within (0, 1), so we obtain the closed-form ofy’s p.d.f.

py(y) =1

(y − y2)!

2π"

i q−1i xi

e−

(σ−1(y)−!

i µixi)2

2!

i q−1i

xi , (12)

which provides an explicit CTR p.d.f. To our best knowl-edge, the above proposed solution has not been studied inprevious literature [41, 13, 36]. To understand the natureof the model, Figure 1 plots the CTR distribution againstits parameters µ and q, where x = 110. As observed, thep.d.f. presents a single-peak shape in [0, 1] which is similarwith the shapes of beta distributions.

It is straightforward to see from Figure 1 that µ and qjointly determine the peak location and sharpness of theCTR p.d.f. and specifically µ influences more on the peaklocation while q influences more on the distribution sharp-ness. To understand how it models the CTR prediction un-certainty/confidence, from Eq. (8), we see each time a datainstance with feature xi is observed, the precision qi willbe updated with a higher value, which in turn contributesa sharper CTR p.d.f. in Eq. (12). Therefore, for the adimpression with frequent (similar) features, the predictedCTR is of low uncertainty, and vice versa.

4. RISK-AWARE BIDDING STRATEGIESWith our CTR distribution model in Eq. (12), we next

investigate the conditional distribution of a utility given aspecific bid price for an input bid request. By considering arisk-aware utility as an optimization target, we are ready toderive the corresponding risk-aware bidding strategy. Notethat alternative CTR distribution models can also be incor-porated in our solution framework.

Specifically, we start from the theoretic derivation of aBayesian truth-telling bidding strategy and provide an anal-ysis of its risk in Section 4.1. Then we will propose twosolutions, discussed in Sections 4.2 and 4.3 respectively.

4.1 Analysis: Bayesian Truth-telling BiddingThe utility r of an ad impression could be defined based

on the advertiser’s value v on a specific user action, e.g.,click or conversion. For example, if the value v is on eachclick, given an impression with CTR y distributed as inEq. (12), the utility r and its p.d.f. of this impression are

r = v · y, pr(r) = py(y)/v. (13)

Moreover, the cost to win the ad impression comes fromthe highest bid from other competitors, defined as marketprice z [5]. The profit of winning this impression is then cal-

0.0 0.2 0.4 0.6 0.8 1.0CTR

0.00.51.01.52.02.53.03.54.0

p(y)

CTR DistributionCTR y

0 50 100 150 200 250 300Market Price

0.0000.0020.0040.0060.0080.0100.0120.0140.0160.018

p(z)

Market Price DistributionMarket Price z

100 50 0 50 100 150 200 250Profit. P(vy-z < 0 | b=84)=16.5%

0.0000.0020.0040.0060.0080.0100.0120.0140.0160.018

p(vy

-z)

Profit Distribution

Profit vy− z

Figure 2: An example of CTR, market price and profitdistribution when bidding the expected utility value. Theprofit p.d.f. on 0 is the probability of losing the auction,resulting in a peak.

culated as the utility r minus the cost z, which is set as theoptimization target of performance-driven campaigns [39].In a general setting, considering both the estimated CTR

y and cost z are stochastic variables: y ∼ py(y) and z ∼pz(z), the bid optimization problem is to find the optimalbid price to the auction.Let us first consider a simple case without considering the

uncertainty of our estimation, where the goal is to maximizethe expected profit R(b) by marginalizing out y and z:

b∗ = argmaxb

E[R(b)] (14)

= argmaxb

#

y

# b

z=0

(v · y − z)pz(z)dz · py(y)dy. (15)

Take the derivative w.r.t. b and set it to 0:

∂E[R(b)]∂b

=∂∂b

# b

z=0

pz(z)

#

y

(v · y − z)py(y)dydz (16)

= pz(b)

#

y

(v · y − b)py(y)dy = 0 (17)

⇒ b∗ =

#

y

v · y · py(y)dy = v · E[y] = E[r]. (18)

We see that the optimal bid price is the product of the ac-tion value and the estimated CTR y, which is independentof the market price distribution. If we assume y is knownand fixed, i.e., py(y) focuses its mass on a single point, thenthe optimal bid price is v · y. Note that the optimality oftruth-telling bidding is for one-shot auction. When consid-ering campaign budget and auction volume, a coefficient φis commonly added to Eq. (18) as φ · E[r].

Discussion of Risk. The above classic bidding solutionis built on maximizing the expectation of the profit R(b),regardless of its uncertainty. However, a potential problemis that there is a chance a bid is won, but v · y is less thanz, in which case R(b) will be negative. We can obtain the

0.0 0.2 0.4 0.6 0.8 1.0CTR

012345678

p(CT

R)

CTR Distribution, q=30µ=0µ=-0.1µ=-0.2

0.0 0.2 0.4 0.6 0.8 1.0CTR

01234567

p(CT

R)

CTR Distribution, µ=-0.1

q=5q=30q=100

Figure 1: An illustration of the proposed CTR distributionagainst its parameters µ and q in Eq. (12).

In our case, σ−1(y) = ln y − ln(1 − y) is monotonic anddifferentiable within (0, 1), so we obtain the closed-form ofy’s p.d.f.

py(y) =1

(y − y2)!

2π"

i q−1i xi

e−

(σ−1(y)−!

i µixi)2

2!

i q−1i

xi , (12)

which provides an explicit CTR p.d.f. To our best knowl-edge, the above proposed solution has not been studied inprevious literature [41, 13, 36]. To understand the natureof the model, Figure 1 plots the CTR distribution againstits parameters µ and q, where x = 110. As observed, thep.d.f. presents a single-peak shape in [0, 1] which is similarwith the shapes of beta distributions.

It is straightforward to see from Figure 1 that µ and qjointly determine the peak location and sharpness of theCTR p.d.f. and specifically µ influences more on the peaklocation while q influences more on the distribution sharp-ness. To understand how it models the CTR prediction un-certainty/confidence, from Eq. (8), we see each time a datainstance with feature xi is observed, the precision qi willbe updated with a higher value, which in turn contributesa sharper CTR p.d.f. in Eq. (12). Therefore, for the adimpression with frequent (similar) features, the predictedCTR is of low uncertainty, and vice versa.

4. RISK-AWARE BIDDING STRATEGIESWith our CTR distribution model in Eq. (12), we next

investigate the conditional distribution of a utility given aspecific bid price for an input bid request. By considering arisk-aware utility as an optimization target, we are ready toderive the corresponding risk-aware bidding strategy. Notethat alternative CTR distribution models can also be incor-porated in our solution framework.

Specifically, we start from the theoretic derivation of aBayesian truth-telling bidding strategy and provide an anal-ysis of its risk in Section 4.1. Then we will propose twosolutions, discussed in Sections 4.2 and 4.3 respectively.

4.1 Analysis: Bayesian Truth-telling BiddingThe utility r of an ad impression could be defined based

on the advertiser’s value v on a specific user action, e.g.,click or conversion. For example, if the value v is on eachclick, given an impression with CTR y distributed as inEq. (12), the utility r and its p.d.f. of this impression are

r = v · y, pr(r) = py(y)/v. (13)

Moreover, the cost to win the ad impression comes fromthe highest bid from other competitors, defined as marketprice z [5]. The profit of winning this impression is then cal-

0.0 0.2 0.4 0.6 0.8 1.0CTR

0.00.51.01.52.02.53.03.54.0

p(y)

CTR DistributionCTR y

0 50 100 150 200 250 300Market Price

0.0000.0020.0040.0060.0080.0100.0120.0140.0160.018

p(z)

Market Price DistributionMarket Price z

100 50 0 50 100 150 200 250Profit. P(vy-z < 0 | b=84)=16.5%

0.0000.0020.0040.0060.0080.0100.0120.0140.0160.018

p(vy

-z)

Profit Distribution

Profit vy− z

Figure 2: An example of CTR, market price and profitdistribution when bidding the expected utility value. Theprofit p.d.f. on 0 is the probability of losing the auction,resulting in a peak.

culated as the utility r minus the cost z, which is set as theoptimization target of performance-driven campaigns [39].In a general setting, considering both the estimated CTR

y and cost z are stochastic variables: y ∼ py(y) and z ∼pz(z), the bid optimization problem is to find the optimalbid price to the auction.Let us first consider a simple case without considering the

uncertainty of our estimation, where the goal is to maximizethe expected profit R(b) by marginalizing out y and z:

b∗ = argmaxb

E[R(b)] (14)

= argmaxb

#

y

# b

z=0

(v · y − z)pz(z)dz · py(y)dy. (15)

Take the derivative w.r.t. b and set it to 0:

∂E[R(b)]∂b

=∂∂b

# b

z=0

pz(z)

#

y

(v · y − z)py(y)dydz (16)

= pz(b)

#

y

(v · y − b)py(y)dy = 0 (17)

⇒ b∗ =

#

y

v · y · py(y)dy = v · E[y] = E[r]. (18)

We see that the optimal bid price is the product of the ac-tion value and the estimated CTR y, which is independentof the market price distribution. If we assume y is knownand fixed, i.e., py(y) focuses its mass on a single point, thenthe optimal bid price is v · y. Note that the optimality oftruth-telling bidding is for one-shot auction. When consid-ering campaign budget and auction volume, a coefficient φis commonly added to Eq. (18) as φ · E[r].

Discussion of Risk. The above classic bidding solutionis built on maximizing the expectation of the profit R(b),regardless of its uncertainty. However, a potential problemis that there is a chance a bid is won, but v · y is less thanz, in which case R(b) will be negative. We can obtain the

Value at Risk (VaR): What is the reward given the downside risk we are willing to take?

Click-ThroughRate(CTR)distributionestimation• ExistingCTRestimationsolution

– Pointestimation:LR,Treemodels,etc.

– Distributionestimation:Bayesianprobit model(doesn’thaveclosed-form)

• Oursolution– Assumption:featureweight𝑤8 is

fromGaussiani.i.d.,thus𝑤8~𝑁 𝜇8, 𝑞8=> .

– Closed-form:𝑝ŷ ŷ =>

(ŷ=ŷ@) ABCDE� 𝑒=(GDE ŷ DH)@

@IDE ,where

𝜇 = ∑ 𝜇8𝑥8�8 , 𝑞=> = ∑ 𝑞8=>𝑥8�

8andσ isthesigmoidfunction.

0.0 0.2 0.4 0.6 0.8 1.0CTR

012345678

p(C

TR)

CTR Distribution, q=30

µ=0µ=-0.1µ=-0.2

0.0 0.2 0.4 0.6 0.8 1.0CTR

01234567

p(C

TR)

CTR Distribution, µ=-0.1

q=5q=30q=100

Experimentresults

LR VaR0.00.10.20.30.40.50.60.70.8 ROI

LR VaR0

20

40

60

80

100 Profit (USD)

LR VaR0

20406080

100120140Budget Spent (USD)

LR VaR02468

1012 Winning Rate (%)

LR VaR0.00.51.01.52.02.53.0

CTR ( )

LR VaR0.000.010.020.030.040.050.060.070.080.09 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

LRλ =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

1.4ROI

LR VaRλ =0.0

VaRλ =0.2

VaRλ =0.4

RMPλ =0.0

RMPλ =0.2

RMPλ =0.4

3.03.23.43.6

4.0

LR VaRλ =0.0

VaRλ =0.2

VaRλ =0.4

RMPλ =0.0

RMPλ =0.2

RMPλ =0.4

0.75

3

LR VaRλ =0.0

VaRλ =0.2

VaRλ =0.4

RMPλ =0.0

RMPλ =0.2

RMPλ =0.4

4.04.55.05.56.06.57.0

LR VaRλ =0.0

VaRλ =0.2

VaRλ =0.4

RMPλ =0.0

RMPλ =0.2

RMPλ =0.4

4.55.05.56.06.57.07.5

LR VaRλ =0.0

VaRλ =0.2

VaRλ =0.4

RMPλ =0.0

RMPλ =0.2

RMPλ =0.4

2.53.03.54.04.55.05.56.0

Figure 8: Overall non-budgeted test performance.

LRλ =0.0

LRλ =0.2

LRλ =0.4λ =0.0 λ =0.2 λ =0.4λ =0.0 λ =0.2 λ =0.4

0.6

0.8

1.0

1.2

1.4

ROI

LRλ =0.0

LRλ =0.2

LRλ =0.4

VaRλ =0.0

VaRλ =0.2

VaRλ =0.4

RMPλ =0.0

RMPλ =0.2

RMPλ =0.4

3.03.23.43.6

4.0

LRλ =0.0

LRλ =0.2

LRλ =0.4

VaRλ =0.0

VaRλ =0.2

VaRλ =0.4

RMPλ =0.0

RMPλ =0.2

RMPλ =0.4

3

LRλ =0.0

LRλ =0.2

LRλ =0.4

VaRλ =0.0

VaRλ =0.2

VaRλ =0.4

RMPλ =0.0

RMPλ =0.2

RMPλ =0.4

4.0

4.5

5.0

5.5

6.0

LRλ =0.0

LRλ =0.2

LRλ =0.4

VaRλ =0.0

VaRλ =0.2

VaRλ =0.4

RMPλ =0.0

RMPλ =0.2

RMPλ =0.4

5.0

5.5

6.0

6.5

7.0

LRλ =0.0

LRλ =0.2

LRλ =0.4

VaRλ =0.0

VaRλ =0.2

VaRλ =0.4

RMPλ =0.0

RMPλ =0.2

RMPλ =0.4

2.5

3.0

3.5

4.0

4.5

Figure 9: Performance with budget constraint (1/2 budget).

uncertainty cases to low-uncertainty ones, which does notmean the average CTR should get lower.

5.7 Bidding with Budget ConstraintsFollowing the previous section, we sought the tangent

points which maximized CP-Profit with various λ’s. Theselected models are highlighted with red circles in Figure 5.There might be overlapped red circles as the CP-Profit withdifferent λ’s still selected the same model.

Figure 9 provides the overall performance over 9 iPinYoucampaigns with budget constraint (1/2 budget setting). Thebaseline is LR with λ = 0, i.e., simply selecting φ yieldingthe highest profit on validation dataset. We found that:(i) For small λ settings, VaR and RMP were both betterthan LR on profit, which verified the claim that the risk-aware bidding strategies successfully yield higher profit viacontrolling the risk. Specifically, risk-aware bidding strate-gies performed better on yielding profit for the campaignswith poorer LR estimators. (ii) All proposed methods, i.e.,LR with non-zero λ model selection and VaR/RMP withvarious λ’s, yielded higher ROI than the baseline LR withλ = 0. Some strategies (VaR and RMP with λ = 0, 0.2)yielded both higher profit and higher ROI. (iii) All risk-aware bidding strategies provided higher CTR (except forthe conservative VaR with λ = 0.4), which meant the pro-

LR0.00.10.20.30.40.50.60.70.8 ROI

LR VaR0

204060

LR VaR0

204060

LR VaR0246

LR VaR0.00.5

2.02.53.0

LR VaR0.00

0.020.030.040.050.060.07

Figure 10: Online results from YOYI DSP.

posed strategies filtered out the low-value cases, which werealways with high uncertainty. (iv) For CPM and winningrate, VaR reduced the CPM by lowering bids on unconfi-dent cases and highering the bids on confident ones (viatuning φ); RMP did not guarantee any low bid as it justsought the bid yielding the highest value of risk-controlledprofit.

6. ONLINEDEPLOYMENTANDA/BTESTOnline Environment. We have deployed our biddingstrategies on YOYI Platform, which is a mainstream DSPin the global RTB market. The total daily bid request vol-ume received by YOYI was about 5 billion. Among thereceived bid requests, about 200M (4%) met YOYI’s bidtarget rules of cost-per-click (CPC) campaigns, for whichYOYI would return a valid bid. Each of our tested strate-gies was allocated with 1.5% bid request volume from 10CPC campaigns, i.e. about 3M bid opportunities daily.For training our models, we collected the impression andclick data of 7 consecutive days just before the A/B testingin Jan. 2016, which contained 424M ad impressions, 532Kclicks and 47.2K US dollars (USD) expense. The eCPCon the training data is 0.087 USD. A 2% negative instancedown sampling was performed by YOYI system. The ad-vertisers of tested CPC campaigns paid a fixed amount forevery user landing action, i.e., valid click. The landing valuev was set to be 0.054 USD, which was the average CPC ofall campaigns.

Test Setting. We tested two strategies for 7 days in Jan.2016: (i) The baseline LR strategy. It consists of a lo-gistic regression whose AUC is 88% and a linear biddingfunction with fixed φ = 0.56 set by YOYI operation staff.(ii) The proposed VaR strategy. The parameter α acquiredfrom the training was a positive value that slightly varieddaily, which meant the trained bidding strategy risk-averse.The parameter φ was set to be greater than LR. Thus thetwo parameters had opposite effects on bid price, which re-sulted in an average bid price close to that of LR. Strategieswere tested with the same bid volume constraint. The bidvolume for each strategy was 19.5M. The whole test livevolume contained 39M auctions resulting in 3.3M impres-sions and 7.4K user landings. VaR spent 12% more budgetthan LR since φ was learned from training thus there wasno guarantee of equivalent budget spending for A/B test.

Result Discussion. The online results are presented inFigure 10. We show the performance over six metrics. Fromthe results, we found that: (i) Our VaR strategy outper-formed baseline LR on ROI by about 5%, which demon-strated the efficacy of our risk-aware bidding strategy. (ii)VaR achieved 17.5% higher profit than LR. Although this

Offline test Online A/B test

LRλ =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

1.4ROI

LR VaRλ =0.0

VaRλ =0.2

VaRλ =0.4

RMPλ =0.0

RMPλ =0.2

RMPλ =0.4

3.03.23.43.6

4.0

LR VaRλ =0.0

VaRλ =0.2

VaRλ =0.4

RMPλ =0.0

RMPλ =0.2

RMPλ =0.4

0.75

3

LR VaRλ =0.0

VaRλ =0.2

VaRλ =0.4

RMPλ =0.0

RMPλ =0.2

RMPλ =0.4

4.04.55.05.56.06.57.0

LR VaRλ =0.0

VaRλ =0.2

VaRλ =0.4

RMPλ =0.0

RMPλ =0.2

RMPλ =0.4

4.55.05.56.06.57.07.5

LR VaRλ =0.0

VaRλ =0.2

VaRλ =0.4

RMPλ =0.0

RMPλ =0.2

RMPλ =0.4

2.53.03.54.04.55.05.56.0

Figure 8: Overall non-budgeted test performance.

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Figure 9: Performance with budget constraint (1/2 budget).

uncertainty cases to low-uncertainty ones, which does notmean the average CTR should get lower.

5.7 Bidding with Budget ConstraintsFollowing the previous section, we sought the tangent

points which maximized CP-Profit with various λ’s. Theselected models are highlighted with red circles in Figure 5.There might be overlapped red circles as the CP-Profit withdifferent λ’s still selected the same model.

Figure 9 provides the overall performance over 9 iPinYoucampaigns with budget constraint (1/2 budget setting). Thebaseline is LR with λ = 0, i.e., simply selecting φ yieldingthe highest profit on validation dataset. We found that:(i) For small λ settings, VaR and RMP were both betterthan LR on profit, which verified the claim that the risk-aware bidding strategies successfully yield higher profit viacontrolling the risk. Specifically, risk-aware bidding strate-gies performed better on yielding profit for the campaignswith poorer LR estimators. (ii) All proposed methods, i.e.,LR with non-zero λ model selection and VaR/RMP withvarious λ’s, yielded higher ROI than the baseline LR withλ = 0. Some strategies (VaR and RMP with λ = 0, 0.2)yielded both higher profit and higher ROI. (iii) All risk-aware bidding strategies provided higher CTR (except forthe conservative VaR with λ = 0.4), which meant the pro-

LR0.00.10.20.30.40.50.60.70.8 ROI

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Figure 10: Online results from YOYI DSP.

posed strategies filtered out the low-value cases, which werealways with high uncertainty. (iv) For CPM and winningrate, VaR reduced the CPM by lowering bids on unconfi-dent cases and highering the bids on confident ones (viatuning φ); RMP did not guarantee any low bid as it justsought the bid yielding the highest value of risk-controlledprofit.

6. ONLINEDEPLOYMENTANDA/BTESTOnline Environment. We have deployed our biddingstrategies on YOYI Platform, which is a mainstream DSPin the global RTB market. The total daily bid request vol-ume received by YOYI was about 5 billion. Among thereceived bid requests, about 200M (4%) met YOYI’s bidtarget rules of cost-per-click (CPC) campaigns, for whichYOYI would return a valid bid. Each of our tested strate-gies was allocated with 1.5% bid request volume from 10CPC campaigns, i.e. about 3M bid opportunities daily.For training our models, we collected the impression andclick data of 7 consecutive days just before the A/B testingin Jan. 2016, which contained 424M ad impressions, 532Kclicks and 47.2K US dollars (USD) expense. The eCPCon the training data is 0.087 USD. A 2% negative instancedown sampling was performed by YOYI system. The ad-vertisers of tested CPC campaigns paid a fixed amount forevery user landing action, i.e., valid click. The landing valuev was set to be 0.054 USD, which was the average CPC ofall campaigns.

Test Setting. We tested two strategies for 7 days in Jan.2016: (i) The baseline LR strategy. It consists of a lo-gistic regression whose AUC is 88% and a linear biddingfunction with fixed φ = 0.56 set by YOYI operation staff.(ii) The proposed VaR strategy. The parameter α acquiredfrom the training was a positive value that slightly varieddaily, which meant the trained bidding strategy risk-averse.The parameter φ was set to be greater than LR. Thus thetwo parameters had opposite effects on bid price, which re-sulted in an average bid price close to that of LR. Strategieswere tested with the same bid volume constraint. The bidvolume for each strategy was 19.5M. The whole test livevolume contained 39M auctions resulting in 3.3M impres-sions and 7.4K user landings. VaR spent 12% more budgetthan LR since φ was learned from training thus there wasno guarantee of equivalent budget spending for A/B test.

Result Discussion. The online results are presented inFigure 10. We show the performance over six metrics. Fromthe results, we found that: (i) Our VaR strategy outper-formed baseline LR on ROI by about 5%, which demon-strated the efficacy of our risk-aware bidding strategy. (ii)VaR achieved 17.5% higher profit than LR. Although this

Summary• Onlineadvertisingisagoodcasestudyofinformationmatchingwitheconomicconstraints

• Developedvalue-at-riskbiddingstrategiesinordertohandletherandomnessofestimatedCTRandmarketprice

• CTRdistributionismodeledinclosed-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)