1. 1 Traffic Shaping to Optimize Ad Delivery Deepayan Chakrabarti Erik Vee

2. Traffic Shaping 2 Which article summary should be picked? Ans: The one with highest expected CTR Which ad should be displayed? Ans: The ad that minimizes underdelivery Article pool

3. Underdelivery Advertisers are guaranteed some impressions (say, 1M) over some time (say, 2 months)  only to users matching their specs  only when they visit certain types of pages  only on certain positions on the page An underdelivering ad is one that is likely to miss its guarantee 3

4. Traffic Shaping 4 Which article summary should be picked? Ans: The one with highest expected CTR Which ad should be displayed? Ans: The ad that minimizes underdelivery Goal: Combine the two

5. Traffic Shaping Goal: Bias the article summary selection to  reduce under-delivery  but insignificant drop in CTR  AND do this in real-time

6. Outline Formulation as an optimization problem Real-time solution Empirical results 6

7. Formulation j:(ads) ℓ: (user, article, position) “Fully Qualified Impression” i:(user, article) k:(user) ℓ j i k Goal: Infer traffic shaping fractions w ki Supply s k CTR c ki Traffic shaping fraction w ki Demand d j Ad delivery fraction φ ℓj

8. Formulation Full traffic shaping graph:  All forecasted user traffic X all available articles  arriving at the homepage,  or directly on article page Goal: Infer w ki  But forced to infer φ ℓj as well Full Traffic Shaping Graph A B C Traffic shaping fraction w ki Ad delivery fraction φ ℓj CTR c ki

9. Outline Formulation as an optimization problem Real-time solution Empirical results 9

10. Formulation Reformulation: {w ki, φ ℓj }→ z ℓj Convex program  can be solved optimally 10

11. Formulation But we have another problem  At runtime, we must shape every incoming user without looking at the entire graph Solution:  Periodically solve the convex problem offline  Store a cache derived from this solution  Reconstruct the optimal solution for each user at runtime, using only the cache 11

12. Real-time solution 12 Cache these Reconstruct using these All constraints can be expressed as constraints on σ ℓ

13. Results Data:  Historical traffic logs from April, 2011  25K user nodes Total supply weight > 50B impressions  100K ads 13

14. Lift in impressions Lift in impressions delivered to underperforming ads Fraction of traffic that is not shaped Nearly threefold improvement via traffic shaping 14

15. Average CTR Average CTR (as percentage of maximum CTR) Fraction of traffic that is not shaped CTR drop < 10% 15

16. Results Data:  Historical traffic logs from April, 2011  25K user nodes Total supply weight > 50B impressions  100K ads 3x underdelivery reduction with <10% CTR drop 16

17. Summary 3x underdelivery reduction with <10% CTR drop 2.6x reduction with 4% CTR drop Runtime application needs only a small cache 17

18. Underdelivery How can underdelivery be computed?  Need user traffic forecasts  Depends on other ads in the system An ad-serving system will try to minimize under-delivery on this graph 18 Forecasted impressions (user, article, position) Ad inventory Supply s ℓ Demand d j ℓ j

19. Real-time solution 19 1 2 σ ℓ = 0 unless Σz ℓj = max ℓ Σz ℓj 3 Σ ℓ σ ℓ = constant for all i connected to k Σz ℓj UiUi LiLi σℓσℓ 3 KKT conditions Shape depends on the cached duals α j ℓ j k i

20. Real-time solution 20 1 2 σ ℓ = 0 unless Σz ℓj = max ℓ Σz ℓj 3 Σ ℓ σ ℓ = constant for all i connected to k ℓ j k i Σz ℓj UiUi LiLi σℓσℓ Algo  Initialize σ ℓ = 0  Compute Σz ℓj from (1)  If constraints unsatisfied, increase σ ℓ while satisfying (2) and (3)  Repeat  Extract w ki from z ℓj

21. Comparison with other methods 21

22. Key Transformation This allows a reformulation solely in terms of new variables z ℓj  z ℓj = fraction of supply that is shown ad j, assuming user always clicks article 22

23. Results Data:  Historical traffic logs from April, 2011  25K user nodes Total supply weight > 50B impressions  100K ads We compare our model to a scheme that  picks articles to maximize expected CTR, and  picks ads to display via a separate greedy method 23

24. Formulation 24 ℓ j i k underdelivery Total user traffic flowing to j (accounting for CTR loss) demand (Satisfy demand constraints) sksk w ki c ki

25. Formulation 25 ℓ j i k (Bounds on traffic shaping fractions) (Shape only available traffic) (Satisfy demand constraints) (Ad delivery fractions)