Viral Marketing Meets Social Advertising: Ad Allocation with Minimum Regret

Cigdem Aslay1,3, Wei Lu2, Francesco Bonchi3, Amit Goyal4, Laks VS Lakshmanan2

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Roadmap

•  Background: Influence Maximization

•  Social Advertising and Viral Ad Allocation

•  Regret Minimization Problem

•  Scalable Algorithms

•  Experimental Results

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Influence Maximization Business goal (Viral Marketing) •  exploit the “word of mouth” effect in a social network to achieve

marketing objectives through self-replicating viral processes

* Kempe et al., “Maximizing the spread of influence through a social network”, KDD 2003

Discrete optimization problem* •  Given

§  a directed social network G = (V,E) §  a propagation model §  a budget k

•  Define §  S: initial set of k (seed) nodes to start the propagation §  σ(S): expected size of the influence propagation spreading from S

•  Goal §  Find the seed set S such that σ(S) is maximized

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Social Advertising Promoted Posts

•  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” –  Each click to a promoted post produces social proof to friends

nice ad! indeed!

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Social Advertising Cost per Engagement (CPE) Model

•  The social network platform owner (a.k.a. host) –  Provides social advertising service –  Inserts promoted posts to the social feed of users likely to click –  Sells these “ad-engagements” (“clicks”) to advertisers •  Advertiser –  Willing to pay a fixed price, called cost-per-engagement (cpe), to host

for each user clicking his ad – whether the ad is inserted to his social feed by the host or propagated from a friend who clicked the ad

Allocation Problem •  Strategically allocate users to advertisers, leveraging social

influence and the propensity of ads to propagate

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Viral Ad Allocation Challenges

•  Balance between intrinsic relevance in the absence of social proof and peer influence

•  Topic-dependent interests and influence •  Balance between limited advertiser budget and virality of ads

•  Limited attention span of users

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Viral Ad Allocation Challenges

•  Balance between intrinsic relevance in the absence of social proof and peer influence

•  Topic-dependent interests and influence •  Balance between limited advertiser budget and virality of ads

•  Limited attention span of users

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TIC-CTP Propagation Model for Viral Ads Extension from TIC* model with Click-Through-Probabilities •  Each ad i is mapped to a distribution over K topics

•  Topic-aware peer influence probabilities on each arc: piu,v

•  Ad-specific CTP for each user: δ(u,i)

–  Probability that user u will click ad i in the absence of social proof

•  Reduces to TIC model by defining CTP as piH,u

–  When δ(u,i) = 1 for all u and i, TIC = TIC-CTP

TIC

v

u

w H puw

puv

pHv

pHw

pHu

* N. Barbieri, F. Bonchi and G. Manco, “Topic-aware Social Influence Propagation Models”, ICDM 2012 8 of 25

Viral Ad Allocation Challenges

•  Balance between intrinsic relevance in the absence of social proof and peer influence ✔

•  Topic-dependent interests and influence ✔ •  Balance between limited advertiser budget and virality of ads

•  Limited attention span of users

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Budget and Regret •  Host:

–  Owns directed social graph G = (V,E) and TIC-CTP propagation model –  Sets user attention bound κu for each user u ∊ V

•  Advertiser i: agrees to pay cpe(i) for each click up to his budget Bi

•  Expected revenue of the host from allocating seed set Si to advertiser i:

min(σi(Si) × cpe(i), Bi)

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Budget and Regret •  Host:

–  Owns directed social graph G = (V,E) and TIC-CTP propagation model –  Sets user attention bound κu for each user u ∊ V

•  Advertiser i: agrees to pay cpe(i) for each click up to his budget Bi

•  Expected revenue of the host from allocating seed set Si to advertiser i:

min(σi(Si) × cpe(i), Bi)

•  σi(Si) × cpe(i) < Bi : Lost revenue opportunity for the host

•  σi(Si) × cpe(i) > Bi : Free service to the advertiser Regret!!

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Budget and Regret •  (Raw) Allocation Regret •  Regret of the host from allocating seed set Si to advertiser i:

Ri(Si) = |Bi − σi(Si) × cpe(i)|

•  Overall allocation regret:

R(S1, …, Sh) = Ri(Si)

i=1

h

∑

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Budget and Regret •  (Raw) Allocation Regret •  Regret of the host from allocating seed set Si to advertiser i:

Ri(Si) = |Bi − σi(Si) × cpe(i)|

•  Overall allocation regret:

R(S1, …, Sh) = Ri(Si)

i=1

h

∑

•  Penalized Allocation Regret •  λ: penalty to discourage selecting large number of poor quality seeds

•  Regret of the host with seed set size penalization

Ri(Si) = |Bi − σi(Si) × cpe(i)| + λ × |Si|

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Regret Minimization •  Given

–  a social graph G = (V,E) –  TIC-CTP propagation model –  h advertisers with budget Bi and cpe(i) for each advertiser i –  attention bound κu for each user u ∊ V –  penalty parameter λ ≥ 0

•  Find a valid allocation S = (S1, …, Sh) that minimizes the overall regret of the host from the allocation S:

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Approximation

•  Regret-Minimization is NP-hard and is NP-hard to approximate –  Reduction from 3-PARTITION for the special case λ = 0 –  No theoretical guarantees w.r.t. “optimal” overall regret

•  Regret function is neither monotone nor submodular

–  Mon. decreasing and submodular for πi(Si) < Bi and πi(Si U {u}) < Bi

–  Mon. increasing and submodular for πi(Si) > Bi and πi(Si U {u}) > Bi

–  Neither monotone nor submodular for πi(Si) < Bi and πi(Si U {u}) > Bi

Bi

πi(Si) πi(Si U {u})

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Approximation

•  A Greedy Algorithm –  Select the (ad i, user u) pair that gives the max. reduction in regret at

each iteration

•  Stop the allocation to i when Ri(Si) starts to increase

•  Stop the allocation to u when he receives κu ads

•  Approximation guarantee w.r.t. the total budget of all advertisers: Theorems 2 & 3 & 4 in the paper!

–  Theorem 2: for λ > 0, details omitted

–  Theorem 3: for λ = 0: R(S) ≤

–  Theorem 4: for λ = 0: R(S) ≤

maxi∈[h],u∈V

cpe(i) ×σ i ({u})Bi

#

$%

&

'(× Bi

i=1

h

∑

13× Bi

i=1

h

∑

#P-Hard!

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Scalable Algorithms Two-Phase Iterative Regret Minimization (TIRM)

•  Built on Reverse-Reachable (RR) Set Sampling based TIM algorithm proposed by Tang et al.* for Influence Maximization

* Y. Tang, X. Xiao, and Y. Shi., “Influence maximization: Near-optimal time complexity meets practical efficiency”, SIGMOD 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 •  Form RR-set of v from the nodes that can reach v via out-going links

in X

TIM Algorithm: •  Estimates influence spread for the most influential “s” nodes from a

random sample of “θ(s)” RR-Sets θ(s): statistically sufficient sample size for unbiased influence spread estimation of s nodes

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Scalable Algorithms TIM cannot be directly extended for minimizing the regret ①  Requires predefined seed set size s ②  Does not handle CTPs

For each advertiser i:

•  Start with a “safe” initial seed set size si •  Sample θi(si) RR sets required for si •  Update si based on current regret •  Revise θi(si), sample additional RR sets, revise estimates

(1) Iterative Seed Set Size Estimation

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Scalable Algorithms TIM cannot be directly extended for minimizing the regret ①  Requires predefined seed set size s ✔ ②  Does not handle CTPs

(2) RR-sets sampling under TIC-CTP model: RRC-sets •  Sample a random RR set R for advertiser i •  Remove every node u in R with probability 1 – δ(u,i) •  Form “RRC-set” from the remaining nodes

Scalability compromised! •  Requires at least 2 orders of magnitude bigger sample

size for CTP = 0.01.

Theorem 5: MG(u | S) in IC-CTP = δ(u) * MG(u | S) in IC 19 of 25

Experimental Results Datasets and Parameters

TIC EM Learning

Exponential Distribution

WC Model

WC Model

sampled uniformly at random from [0.01, 0.03]

Peer influence probabilities:

CTPs:

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Experimental Results Algorithms Tested

•  MYOPIC: Top κu ads for which u has the highest δ(u,i) * cpe(i)

•  MYOPIC+: Budget-aware MYOPIC enhancement

•  Greedy-IRIE: Instantiation of the Greedy algorithm with IRIE* heuristic

•  TIRM:

–  ε set to 0.1 for quality experiments on FLIXSTER and EPINIONS

–  ε set to 0.2 for scalability experiments on DBLP and LIVEJOURNAL

* K. Jung, W. Heo, and W. Chen, "IRIE: Scalable and Robust Influence Maximization in Social Networks", ICDM 2012 21 of 25

2.5%

26%

122%

141% O

vera

ll R

egre

t

6.5% 16% 145%

205%

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Seed Set Size vs Users’ Attention Bound

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Scalability Experiments – Running Time

16 min.s (47 seeds)

5 hours (4649 seeds)

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Thank you! Poster Session: September 3rd, 17:15

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