PVLDB'17 Revenue Maximization in Incentivized Social Advertising

1. Revenue Maximization in
Incentivized Social Advertising
Cigdem Aslay1, Francesco Bonchi1, Laks VS Lakshmanan2, Wei Lu3

2. • Given
• a directed social network G = (V,E)
• a propagation model m
• a cardinality budget k
• Define
• S: initial set of k (seed) nodes to start the propagation
• σm(S): expected size of the influence propagation from S
• Find
S⇤
= argmax
S✓V,|S|=k
m(S)
Influence Maximization
* Kempe et al., “Maximizing the spread of influence through a social network”, KDD 2003 2
Discrete Optimization Problem*

3. Influence Propagation Models
Independent Cascade (IC) Model
• Each arc (u,v) is associated with an influence probability puv
• A node u activated at time t tries to influence each inactive neighbor v, with a
success probability puv
Topic-aware Independent Cascade (TIC) Model*
• An item i described as a distribution over K topics:
• Topic specific influence probabilities on arcs:
• Item specific success probabilities on arcs:
*N. Barbieri, F. Bonchi and G. Manco, “Topic-aware Social Influence Propagation Models”, ICDM 2012 3

4. Complexity and Approximation
• Influence Maximization is NP-Hard under IC model
• TIC boils down to IC on the probabilistic graph Gi = (V,A,pi)
• Reduction from the Set Cover problem
• Greedy algorithm
• (1 – 1/e)-approximation* using monotonicity1 and submodularity2
4
#P-hard
*Nemhauser et al., “An analysis of approximations for maximizing submodular set functions I”, Mathematical Programming 1978

5. 5
A market that did not exist until Facebook launched its first advertising
service in May 2005, projected to generate $11 billion revenue by 2017*
Social Advertising
https://www.emarketer.com/Article/Social-Network-Ad-Spending-Hit-2368-Billion-Worldwide-2015/1012357
http://www.unified.com/historyofsocialadvertising/

6. nice ad! indeed!
6
Social Advertising
Promoted Posts
• Implemented by online social networking platforms
• Similar to organic posts from friends in the social network
• Contain an advertising message: text, image or video
• Can propagate to friends via social actions: “likes”, “shares”

7. Incentivized Social Advertising

8. seed user
incentive
(cost)
ad-engagement
revenue (cpe)
budget
Incentivized Social Advertising

9. Incentivized Social Advertising
CPE Model with Seed User Incentives
9
• Advertiser
• Pays a fixed CPE to host for each
engagement
• Pays monetary incentive to each seed user
promoting its ad
• Net payment subject to its budget
• Host
• Selects initial endorsers (seed users) for each ad participating in the campaign
• Seed users take a cut from the social advertising budget in exchange
• Sells the resulting ad-engagements to advertisers
 Bi.

10. Revenue Maximization
• Given
• a social graph G = (V,E)
• TIC propagation model
• h advertisers with budget Bi and CPE(i) for each ad i
• seed user incentives ci(u) for each user u∈V and for each ad i
• Find an allocation S = (S1, …, Sh) that maximizes the
overall revenue of the host from the allocation:
10
X
i
⇡i =
X
i
cpe(i) · i(Si).

11. Theoretical Analysis
• Revenue-Maximization problem is NP-hard
• Restricted special case with h = 1:
• NP-Hard Submodular-Cost Submodular-Knapsack (SCSK)
problem*
11*Iyer et al., “Submodular optimization with submodular cover and submodular knapsack constraints”, NIPS 2013.
Partition matroid
Submodular knapsack constraints
• Family 𝘊 of feasible solutions form an Independence System

12. Theoretical Analysis
• Cost-Agnostic Greedy Algorithm (CA-Greedy)
• Selects (node,ad) pair giving the max. marginal increase in revenue
12
Two greedy approximation algorithms w/ different sensitivity to seed user
incentives during the node selection
• Cost-Sensitive Greedy Algorithm (CS-Greedy)
• Selects the feasible (node,ad) pair giving the max. rate of marginal
gain in revenue per marginal gain in payment
#P-Hard!

13. Theoretical Analysis
• Cost-Agnostic Greedy Algorithm (CA-Greedy)
• Theorem: Approximation guarantee follows* from the fact that 𝘊
forms an independence system
where
• R and r are, respectively, upper and lower rank of 𝘊
• κπ is the curvature of total revenue function π(.)
13
* Conforti et al., "Submodular set functions, matroids and the greedy algorithm: tight worst-case bounds and some
generalizations of the Rado-Edmonds theorem.", Discrete Applied Mathematics 1984

14. Theoretical Analysis
• Cost-Agnostic Greedy Algorithm (CA-Greedy)
• Tightness of cost-agnostic bound.
14
Optimal solution
• T = {a,c} with 𝜋(T) = 6
CA-Greedy solution
• S = {b} with 𝜋(S) = 3
B = 7, cpe = 1
r = 1, R = 2
κ 𝜋 = 1

15. Theoretical Analysis
• Cost-Sensitive Greedy Algorithm (CS-Greedy)
• Theorem: Approximation guarantee obtained
where
• ρmax and ρmin are, respectively, max. and min. singleton payments
• κρi is the curvature of ad i’s payment function ρi(.)
15
Tightness of cost-sensitive approximation is open.

16. Scalable Algorithms
Two-Phase Iterative Revenue Maximization
• Built on TIM algorithm [Tang et al. SIGMOD 2014]; uses
Reverse-Reachable sets [Borgs et al. SODA 2014].
Random RR-Set:
• Sample a possible world X from G: remove every edge (u,v) with
probability 1 – puv
• Pick a target node v from G uniformly at random
• RR-set of v = {nodes that can reach v via out-links in X}
TIM Algorithm:
• Estimates influence spread for the most influential “s” nodes from a
random sample of (RR-Sets) of size
16
= L(s, ✏)

17. Scalable Algorithms
Two-Phase Iterative Revenue Maximization
* Tang et al., “Influence maximization: Near-optimal time complexity meets practical efficiency”, SIGMOD 2014
Two-Phase Influence Maximization (TIM) Algorithm*
• Accurately estimates the influence spread of any set S of at most “s”
nodes from a random sample R of “L(s,ε)” RR-Sets
• L(s,ε): Lower bound on the statistically sufficient sample size required
• Unbiased estimator:
TIM cannot be directly employed: requires
predefined seed set size s
Built on the Reverse Influence Sampling framework of TIM
17

18. Scalable Algorithms
Two-Phase Iterative Revenue Maximization
• Built on the Reverse Influence Sampling framework of TIM*
• Latent seed set size estimation
• Start with a safe initial seed set size si
• Sample L(si,ε) RR sets required for si
• Update si based on current payment
• Revise L(si,ε), sample additional RR sets, revise estimates
18
Two-Phase Iterative Cost-Agnostic
Revenue Maximization (TI-CARM)
* Tang et al., “Influence maximization: Near-optimal time complexity meets practical efficiency”, SIGMOD 2014
Scalable CA-Greedy
Two-Phase Iterative Cost-Sensitive
Revenue Maximization (TI-CSRM)
Scalable CS-Greedy
• Theorem: Deterioration in the approximation guarantees (see paper).

19. Datasets and Parameters
19
TIC EM
Learning
TIC WC
Model
WC
Model
WC
Model
Peer influence
probabilities:
Experiments

20. Algorithms Tested
20
Experiments
}• TI-CARM
• TI-CSRM
• PageRank-GR
• For each ad i, find the best candidate user wrt Pagerank ordering
• Among those, select the (user, ad) pair giving maximum marginal increase in the
revenue of the host
• PageRank-RR
• For each ad i, find the best candidate user wrt Pagerank ordering
• Use round-robin ordering of advertisers to select the (user, ad) pair
• ε set to 0.1 for quality experiments on FLIXSTER and EPINIONS
• ε set to 0.3 for scalability experiments on DBLP and LIVEJOURNAL

21. Seed Incentives Models
21
Experiments
• Linear incentives
• Proportional to the node’s ad-specific singleton influence spread
• Constant incentives
• Proportional to the average ad-specific singleton influence spread
• Sublinear incentives
• Proportional to the logarithm of node's ad-specific singleton influence spread

22. 22
Total Revenue

23. 23
Total Seeding Cost

24. 24
Revenue vs Running Time Trade-off

25. 25
Scalability Results - Running Time

26. 26
Scalability Results - Memory (GB)

27. • TI-C*RM could be built on top of more recent
approximation algorithms — IMM and Stop & Stare.
• Further scalability?
• All these algorithms require significant memory usage,
which limits scalability.
• Hard competition?
• Adaptive revenue maximization?
• Tightness of cost-sensitive approximation?
Tang et al. SIGMOD 2015.
Nguyen et al. arXiv 2016-2017; Keke et al. PVLDB 2017.
27
†
†
‡
‡
Open Problems

28. Thank you!