TiSA: Time-Dependent Social Network Advertising

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1 TiSA: Time-Dependent Social Network Advertising Wei Wang, Linlin Yang, Qing Liao, Xiang Zh, Qian Zhang Department of Compter Science and Engineering, Fok Ying Tng Gradate School, Hong Kong University of Science and Technology College of Compter, National University of Defense Technology {gswwang, lyangah, qnatre, Abstract Mch of today s online social network (OSN) system relies on advertising for financial spport. To improve the effectiveness of advertising, online advertisers tend to leverage inflential sers to deliver ads. Most of existing efforts on online advertising have focsed on single-shot scenarios or assme static OSN models, while they overlook the fact that actions of advertising affect sers behaviors. In this paper, we investigate the behaviors of Sina Weibo sers over three months, and make the observation that advertising affects the behaviors of the ser s followers, which in trn has an impact on the effectiveness of ftre advertising. Based on this observation, we propose TiSA, a time-dependent advertising framework, which considers the ftre impact of advertising. Under this framework, the advertiser and the ser make their decisions based on their instant tilities as well as ftre tilities. We also devise a learning algorithm with provable convergence to obtain the optimal policies. Evalations sing three month traces of 975 Sina Weibo sers have been condcted, and the reslts validate the effectiveness of the proposed framework by showing that the tilities of all entities are significantly improved compared with traditional systems. I. INTRODUCTION Social network advertising provides financial spport for a large portion of today s online social network (OSN) ecosystem, and is displayed in a variety of forms embedded in web sites. As the behavior of a ser is affected by others via perceived relationships and received information from online friends, organizations, and societies, online advertisers tend to leverage the power of inflential people in OSNs to increase brand awareness and inflence people s prchasing actions [], [2]. Many companies like IBM, Microsoft, and Walmart have adopted this advertising strategy, and distribted advertisements (ads) among inflential people who are willing to post the ads. To improve the effectiveness of social network advertising, many efforts have been devoted to identifying inflential people [3] and targeted advertising [4], [5]. However, most of these stdies focs on single-shot scenarios or assme static OSN models, while the correlations and interactions between sers inflence and advertising in a long-term perspective have not yet been investigated. The motivation behind this is the profond impact of advertising on sers ftre behaviors in OSNs. For example, a ser contining posting ads within a short time may annoy some of its followers and even drive them away, which in trn affects the effectiveness of advertising in ftre. Withot considering this ftre impact, the advertising strategies are myopic and fail to maximize advertisers profits in a long-term perspective. The target of this paper is to fill the gaps in long-term social network advertising. In this paper, we arge that the impact of advertising on sers ftre behaviors shold be considered. We first characterize the impact of advertising in OSNs by investigating Sina Weibo, which is the largest microblogging social network in China. We observe that freqent advertising has a negative impact on the ser s nmber of followers, which ndermines the advertising effectiveness in ftre. Therefore, the advertiser and the sers shold careflly choose their policies to strike a balance between the instant tilities and ftre tilities. To obtain long-term advertising policies, we propose TiSA, a Time-dependent Social network Advertising framework that considers the dynamics of OSNs and the impact of advertising. In TiSA, we model the strategic and dynamic interactions between a ser and an advertiser as a stochstic game, where both players concern abot their long-term tilities. In each time slot, both the ser and the advertiser observe the crrent nmber of the ser s followers, as well as the nmbers of followers in the past, and then take their actions based on their policies. Specifically, the ser decides the nmber of ads to post in each time slot, while the advertiser determines the price it pays the ser for posting each ad. To obtain the optimal policies of the ser and the advertiser, we design a learning algorithm for TiSA with provable convergence. The main contribtions of this paper are smmarized as follows. We investigate the behaviors of 975 Sina Weibo sers over three months, and characterize the impact of advertising in OSNs. These observations have profond implications on the design of long-term advertising systems in OSNs. We propose a time-dependent advertising framework that maximizes the long-term tilities of the advertiser and the ser. To the best of or knowledge, this is the first advertising framework that considers the impact of advertising and the dynamics of followers. We model the dynamic interactions between the advertiser and the ser as a stochastic game, and derive the

2 Ad Inflential ser.8 Advertiser Profits Reward Ad Posting ad in the OSN CDF.6.4 Interested followers Uninterested followers Fig.. Social network advertising system. optimal policies via a learning algorithm with provable convergence. We evalate or framework sing three-month traces of 975 sers. Promisingly, the reslts show that TiSA otperforms baseline schemes in terms of long-term tilities. The reminder of this paper is strctred as follows. We begin in Section II with the advertising system model in social networks, and then characterize the impact of advertising by investigating Sina Weibo. Section III describes the detailed time-dependent advertising problem formlation, and presents a learning algorithm to obtain the optimal policies. Evalation of TiSA is presented in Section IV. Section V reviews related work, followed by conclsion in Section VI. II. CHARACTERIZING ADVERTISING IN ONLINE SOCIAL NETWORKS In this section, we first describe the advertising system in online social networks by introdcing the ser model, the advertiser model, and their interactions. Then, we investigate the impact of advertising in social networks by analyzing the ser behaviors in Sina Weibo. A. Advertising System in Online Social Networks An advertising system in an OSN consists of an advertiser, inflential sers who post ads in the OSN for the advertiser, and the followers of the inflential sers. The inflential sers refer to the sers connect directly or indirectly with a massive nmber of sers. In the OSN, a ser can post messages which can be seen by its followers. In this paper, the relationship of following and being followed can be either reciprocal (e.g., friend-relationship in Facebook) or non-reciprocal (e.g., relationship in Twitter and Sina Weibo). In the OSN, the advertiser delivers its ads to sers via inflential sers, who post ads forwarded by the advertiser. In trn, the advertiser pays a certain amont of reward to the inflential sers for posting ads. The ads posted by the inflential sers can be seen by their followers. Among these followers, there may be interested sers who are potential byers, from whom the advertiser earns profits. However, there may exist followers who are not interested in the ads, or may even regard them as spams. In this case, the ninterested sers can be annoyed by freqent appearance of ads in their incoming messages, and nfollow the sers posting lots of Cont NRMSE x Fig. 2. CDF of NRMSE for linear regression Normalized residal error Fig. 3. Distribtion of normalized residal error. ads. As the ser s inflence largely depends on the nmber of followers, the nfollowing action ndermines the inflential ser s inflence, thereby impairing the ser s ftre payoff. Therefore, the inflential sers need to careflly strike a balance between the crrent payoff and ftre payoffs. To characterize the impact of advertising on ser s followers, we take a case stdy on Sina Weibo. B. Impact of Advertising in Online Social Networks We characterize the follower increment sing the ser traces in Sina Weibo. We crawled and collected profiles of 22,54,394 sers and their posts starting from September 2 to September 24. In order to collect sers profiles and posts, we started with inflential sers who have millions of followers, and then crawled breadth-first along the direction of the sers followers and followings. As or stdy reqires complete post records of active sers, we select 975 sers with complete records over 9 days. These sers continos post new messages each day. To avoid ad recognition errors, we manally categorize all messages into ads and non-advertising messages. We first investigate how the nmber of followers varies over time for

3 955 sers who have not posted ads over the 9 days. We regard the nmber of followers as a fnction of time (one day as a time slot), and the corresponding crve exhibits strong linear properties. To validate this observation, we adopt linear regression for crve fitting. Fig. 2 draws the cmlative distribtion fnction (CDF) of normalized root-mean-sqare error (NRMSE) for linear regression. The NRMSEs of over 98% sers are smaller than 5 3, which demonstrates that linear crves tightly fit the nmber of follower variances. For the reside errors incrred by crve fitting, we plot a histogram in Fig. 3, which consists of residal errors of all sers. We see that the residal error can be well fit by a Gassian distribtion (the red crve in the figre), where the NRMSE is merely.682. Therefore, for sers withot posting ads, the nmber of followers variance over time can be modeled by n t = at + b + δ, () where n t is the nmber of followers in time slot t, a, b the parameters learned by linear regression, δ the random variable following a Gassian distribtion. () implies that the expectation of the follower increment, i.e., E[n t+ n t ]= E[a + δ t+ δt ]=a, is a constant over time. In the following, we show that this observation does not stand for sers who post ads: the follower increment of a ser varies when the ser posts different nmber of ads. Next, we stdy the advertising impact of 2 inflential sers who have posted ads in 9 days. Fig. 4 shows the scatter plot of daily follower increments with the nmbers of ads posted in the corresponding days. The reslts reveal that the large follower increment occrs only when the nmber of ads is small. The follower increment diminishes as the nmber of ads increases. Fig. 5 depicts the CDF of Pearson correlation coefficient ρ between the follower increment and the nmber of ads. In the figre, we compte ρ for each ser. The reslts report that ρ is negative for 9% sers, and ρ<.5 for more than 5% sers, which frther validates the negative impact of advertising on follower increment. The above case stdy provides the following implication: withot considering the impact of advertising on follower increment, single-shot strategy based advertising systems are not sstainable for long-term operation. This observation motivates the design of TiSA, a time-dependent advertising framework that takes the impact of advertising into accont, so as to maximize the long-term tilities of both the advertiser and the ser. III. TIME-DEPENDENT ADVERTISING FRAMEWORK In this section, we design TiSA, a time-dependent advertising framework in OSNs. We first formlate the advertising problem as a twp-player stochastic game, and then develop a learning algorithm to derive optimal policies for TiSA. A. Problem Formlation Recall that the nmber of followers is a random variable that depends on the ser s advertising behaviors, and the nmber of followers determines the effectiveness of advertising. Ths, Follower increment 8 x Nmber of Ads Fig. 4. Follower increments nder different nmbers of dailyposted ads. CDF ρ Fig. 5. CDF of Pearson correlation coefficient between follower increment and nmber of daily-posted ads. the interactions in social network advertising can be modeled as stochastic game between the ser and the advertiser. System state. In each time slot, a ser has a certain nmber of followers, which is an essential factor that determines the ser s inflence in the OSN. Therefore, the nmber of followers is considered as the system state. The nmber of followers at time t is denoted as n t N, and the system state at time t is defined by S t = n t. Actions. After observing the state S t at each stage, both the ser and the advertiser decides their actions for the crrent stage. As we observed in Sina Weibo, sers sally repeatedly post the same ad mltiple times to make it easier to be seen by other sers. Hence, in each time slot, the ser controls the nmber of posts for each ad forwarded by the advertiser. Formally, the action of the ser at time t is defined as a t = {m t,..., m t M }, where mt i [, ] is the fraction of the ser s posts that contain ad i within the time slot t, and M is the total nmber of ads. As the total nmber of posts that contain ads cannot exceed the nmber of all posts, we have the following

4 constraints for m t i. m t i, i m t i, i. (2) On the other hand, the advertiser decides the nit prices it pays to the ser who posts its ads. Mathematically, the adversary s actions at time t are defined as a t = {p t,..., p t M }, where p t i (,U p] is the nit price for ad i and U p is the pper bond for nit price. State transitions. The system state S t is ncertain and depends on the actions of the ser and the advertiser. Ths, the state transition probability can be compted by Pr[S t+ S t, a t, a t a]=pr[n t+ n t, a t, a t a]. (3) Stage payoffs. After defining the states and actions, we give a concrete expression of stage payoffs. The payoff fnction of the ser is defined to be reward earned by posting ads with weighted penalty on inflence loss, which is expressed as r (S t, a t, a t a)=w (a t, a t a) ω L(S t, a t ), (4) where W (a t, a t a) is the reward paid by the advertiser for ad posting, ω the eqivalent economic loss cased by nit inflence loss, and L(S t, a t ) the inflence loss. Recall that The advertiser determines the price a t a for each ad posted by the ser. Ths, we have W (a t, a t a)=m t a t a t a, where M t is the total nmber all posts in time slot t. L(S t, a t ) is the measre of the ninterested followers degree of dissatisfaction with the ndesired ads posted by the ser they follow, which is considered as a negative impact of posting ads. Sigmoid fnction has been widely sed to approximate the ser s satisfaction/dissatisfaction with respect to service qalities [6]. Concretely, L(a t,s t ) is measred as L(a t,s t )= +e, (5) α(at nt η l ) where α determines the steepness of the qality of service satisfactory crve, η l the satisfaction threshold below which the followers have very limited dissatisfaction (the fnction crve is convex) and above which the followers dissatisfaction rapidly approaches an asymptotic vale (the fnction crve is concave). In this paper, we consider sers who are active in the OSN for a long time. Ths, the ser cares abot the crrent as well as the ftre payoffs. Normally, a recent payoff is more valable than a payoff that will be received in the faraway ftre. Thereby, the ser s tility is the expected sm of disconted stage payoffs [ ] U = E γ t r (S t, a t, a t a), (6) t= where γ t is the discont factor of the advertising payoff. The ser s objective is to derive an optimal policy that maximizes U. On the other hand, the advertiser s payoff is determined by the profit it earned mins the amont of payment W (a t, a t a) to the ser, which is written as r a (S t, a t, a t a)=p (S t, a t ) W (a t, a t a), (7) where P (S t, a t ) is the profit the advertiser earned from advertising, which has been widely modeled as sigmoid fnction [7]. Note that the advertiser earns more profit when i) the ser who posts ads have more followers, and ii) the ser posts more ads. Then, the advertising profit P (S t, a t ) can be measred as P (a t,s t θ )= +e, (8) β(at nt η p) where θ is the advertiser s valation for advertising profit with respect to the payment W (a t, a t a), β and η p the steepness and threshold of the sigmoid crve. Analogos to the ser s tility, the advertiser s tility can be expressed as [ ] U a = E γ t r a (S t, a t, a t a). (9) t= B. Learning the Optimal Advertising Policy After formlating the time-dependent advertising game, we now elaborate the algorithm to obtain the Nash Eqilibrim (NE) of the advertising game, so as to derive the optimal advertising policy. Optimal Policies in TiSA. We denote the set of system states as S, and the ser s and advertiser s policies as π,π a, respectively. For a system state s S, the ser s tility can be written in the form of state vale V π (s) V π (s) = γ t E[r (S t, a t, a t a) π,π a,s = s] t= =r (s, a π, a π a)+γ s Pr[s s, a π, a π a]v π (s ), () where a π, a π a are the actions determined by π,π a. Similarly, the advertiser s tility can be written as V π a (s) =r a (s, a π, a π a)+γ s Pr[s s, a π, a π a]v π a (s ). () The optimal policies {π,π a} are obtained at the NE point, which is defined as follows. Definition (NE in TiSA) In the stochastic game for TiSA, an NE point is a pair of policies π = {π,π a}, sch that for all state s S, V π (s) V πa (s) and Va π (s) Va π (s), (2) where π a = {π,π a}, π, and π = {π,π a }, π a. The learning algorithm for TiSA. Note that the minimax algorithm [8], [9] can be sed to learn the optimal policies in zero-sm stochastic game, while the minimax algorithm cannot be applied to TiSA as the ser s and the advertiser s payoffs are not the opposite of each other. Therefore, we

5 Algorithm State Vale Learning Algorithm in TiSA Inpt: System state set S, state transition probability Pr[S t+ S t, a t, a t a], stage payoffs r (S t, a t, a t a),r a (S t, a t, a t a) Otpt: π,π a //. initialization : t ; 2: For all s S, V (s),va (s) ; 3: Initialize policies π,π a, which is the mixed strategy NE soltion of the stage game V (s),va (s); // 2. iteration 4: repeat 5: Select an action pair a t,a t a} based on π,π t a; t 6: Update S t+ after both players take their actions a t,a t a}; 7: Update state vales according to (3); 8: Update policies pair π t+,πa t+ according to Definition sch that V π (s) V πa 9: t t +; : ntil π t,π t a converge : π,π a π t,π t a; (s) and Va π (s) Va π (s); (4) propose a new learning algorithm for TiSA to derive the optimal policies. In order to obtain the optimal policies {π,π a }, the ser and the advertiser in TiSA pdate their state vales according to the following rle. V t+ (s) =( α t+ )V(s) t +α t+ (r (s, a π, a π a)+γ s Pr[s s, a π, a π a]v π (s )), Va t+ (s) =( α t+ )Va t (s) +α t+ (r a (s, a π, a π a)+γ s Pr[s s, a π, a π a]va π (s )), (3) where V(s),V t (s) t are approximates of V π (s),va π (s), α t [, ) the learning rate. In or algorithm, we set α t =/t. The pdate rle (3) iteratively pdate V(s),V t (s) t ntil they converge to V π (s),va π (s). The detail of or learning algorithm is stated in. First, Algorithm initializes policies and state vales for t =. Then, it iteratively pdates policies and state vales according to (3) and Definition ntil they converge to optimal vales. IV. EVALUATION In this section, we evalate TiSA sing trace-driven simlations. We feed Sina Weibo dataset into or simlations as the dynamic OSN model, and evalate the effectiveness of different policies. A. Setp Dataset. We collected the Sina Weibo data throgh the API provided by Sina Weibo. The Sina company provides abot 2% of the most reliable data available in China. We collected the data of 22,54,394 sers from September 2 to September 24 (3 days in total), from which we select a sbset of 975 active sers who continos post new pdates each day within a three months dration. System parameters. We extract the follower variance from the Sina Weibo dataset, which is sed to emlate the state transitions in or evalation. Unless explicitly otherwise stated, we se the following system parameters in or evalation. The pper bond for nit price U p is set to, total nmber of ads set to 5, satisfaction thresholds η l,η p set to.7, steepness α, β parameters set to., discont factor γ set to.8. Baselines. We compare the performance of TiSA with two typical advertising systems, i.e., single-shot advertising and static advertising. The single-short advertising strategy aims to maximize the instant tilities, and obtains policies by solving each stage game independently. The static advertising strategy se static policies for all stages. The static policies are obtained by solving the first stage game. B. Reslts We first compare the overall performance of all advertising systems in Fig. 6 and Fig. 7. Fig. 6 shows the ser s sm of disconted payoffs U nder nmbers of stages. The sms of disconted payoffs nder all policies converge to constant vales as the nmber of stages increase. We see that advertising policies obtained TiSA and single-shot achieve higher sms of disconted payoffs than static policies. This is becase TiSA and single-shot systems adjst actions over time based on the ser s nmber of followers, while the static system takes actions only based on the initial state. Moreover, TiSA otperforms single-shot system in all stages. The reason is that TiSA also considers the ftre impact of advertising actions when learning the policies. Fig. 7 depicts the advertiser s sm of disconted payoffs in different advertising systems. Similar to the reslts in Fig. 6, TiSA otperforms the other two systems in all stages. Hence, when advertisers rely on inflential sers in OSNs for advertising, the best strategy is to take the dynamics of the OSNs into accont when making decisions. Fig. 8 reports the advertiser s sms of disconted payoffs nder different satisfaction threshold η p. When η p is smaller, the advertiser earns more profits for each posted ad. Ths, for all systems, the advertiser s sms of disconted payoffs diminish when the satisfaction threshold grows. We also see that the differences between the sms of disconted payoffs achieved by TiSA and the other two systems grow larger as the satisfaction threshold increases. The reason is that when the satisfaction threshold is very low, high profits can be easily earned by posting a small nmber of ads. As sch, the profit part dominates the advertiser s tility, and stays relatively the same over different actions. Based on this observation, we conclde that the merits of TiSA is more significant in the case of high satisfaction threshold, where the advertiser s total payoff is very sensitive to different policies. Hence, the advertising system with high satisfaction threshold shold be

6 U.5.5 single shot static TiSA U a 2.5 static single shot TiSA U a static single shot TiSA Nmber of stages Nmber of stages Satisfaction threshold Fig. 6. User s sm of disconted payoffs nder different policies. Fig. 7. Advertiser s sm of disconted payoffs nder different policies. Fig. 8. Advertiser s sm of disconted payoffs nder different satisfaction thresholds. careflly designed to strike a balance between instant tility and ftre tility. V. RELATED WORK Targeted advertising. The aim of targeted advertising is to devise effective advertising systems to find interested sers or potential byers. Chakrabarti et al. [] propose a new class of models to display relevant ads to web pages of different contents. Kodialam et al. [4] devise a privacy-preserving protocol to deliver ads to privacy-sensitive sers, who send falsified click information to an ad broker according to predetermined rles. These systems focs on single-shot scenarios and cannot be applied to long-term advertising in OSNs where a ser s advertising behaviors affect its ftre tilities. Social inflence and advertising. Recently, online social networks are considered as a new dimension for marketing. The notion of social network advertising is first proposed as an important motivations for social inflence stdies. Bakshy et al. [3] condcted several field experiments to investigate how social inflence affects sers responses to social network advertising, which provides profond implications for ad optimization and ser interface design. Provost et al. Ning et al. [] stdy the problem of ad dissemination mobile social networks, and devise an incentive scheme to motivate sers to forward ads. A privacy-friendly framework is proposed in [2] to deliver different ads to sers based on their browsing behaviors. The fndamental difference between these works and TiSA is that TiSA considers the time-dependency in social network when making advertising policies. VI. CONCLUSION This paper presents TiSA, the first time-dependent advertising system that considers the impact of advertising on followers ftre behaviors. We first investigate the impact of advertising by taking a case stdy on Sina Weibo. Based on the model extracted from Sina Weibo dataset, we formlate the advertising problem as a stochastic game, which considers the dynamics of followers and ftre impacts of the ser s and advertiser s actions. Frthermore, we devise a learning algorithm to obtain the optimal policies that maximizes longterm tilities. We hope that or investigation on the impact of advertising and the proposed time-dependent framework can provide some implications for ftre advertising system designs. ACKNOWLEDGMENT The research was spport in part by grants from 973 project 23CB3296, China NSFC nder Grant 67356, RGC nder the contracts CERG 62263, 62274, HKUST6/CRF/2R, and M-HKUST69/3, as well as the grant from Hawei-HKUST joint lab. REFERENCES [] S. Milstein, B. Lorica, R. Magolas, G. Hochmth, A. Chowdhry, and T. O Reilly, Twitter and the micro-messaging revoltion: Commnication, connections, and immediacy 4 characters at a time. O Reilly Media, Incorporated, 28. [2] W. Wang, L. Yang, Y. Chen, and Q. Zhang, A privacy-aware framework for targeted advertising, Elsevier Compter Networks, vol. 79, pp. 7 29, 25. [3] E. Bakshy, D. Eckles, R. Yan, and I. Rosenn, Social inflence in social advertising: evidence from field experiments, in ACM Proc. EC, 22. [4] M. Kodialam, T. Lakshman, and S. Mkherjee, Effective ad targeting with concealed profiles, in Proc. IEEE INFOCOM, 22. [5] T. Ning, Z. Yang, H. W, and Z. Han, Self-interest-driven incentives for ad dissemination in atonomos mobile social networks, in Proc. IEEE INFOCOM, 23. [6] H. Lin, M. Chatterjee, S. Das, and K. Bas, Arc: an integrated admission and rate control framework for competitive wireless cdma data networks sing noncooperative games, IEEE Trans. Mobile Compt., vol. 4, no. 3, pp , 25. [7] J. K. Johansson, Advertising and the s-crve: A new approach, JSTOR Jornal of Marketing Research, pp , 979. [8] B. Wang, Y. W, K. R. Li, and T. C. Clancy, An anti-jamming stochastic game for cognitive radio networks, IEEE J. Sel. Areas Commn., vol. 29, no. 4, pp , 2. [9] W. Wang and Q. Zhang, A stochastic game for privacy preserving context sensing on mobile phone, in Proc. IEEE INFOCOM, 24, pp [] D. Chakrabarti, D. Agarwal, and V. Josifovski, Contextal advertising by combining relevance with click feedback, in Proc. ACM WWW, 28. [] M. Kodialam, T. Lakshman, and S. Mkherjee, Self-interest-drive incentives for ad dissemination in atonomos mobile social networks, in Proc. IEEE INFOCOM, 23. [2] F. Provost, B. Dalessandro, R. Hook, X. Zhang, and A. Mrray, Adience selection for on-line brand advertising: privacy-friendly social network targeting, in Proc. ACM SIGKDD, 29.