Notes for Offline Optimal Ads Allocation in Social Network Advertising

Social network sites (SNS) such as Facebook, Google+ and Twitter have attracted hundres of millions of users daily since their appearance [1]. In modern social networks (SNS), users expose many personal behaviors and connect to each other based on real world relationships, both of which makes SNS ideal for target advertising [2, 3]. Advertisers bid a target user group satisfying a set of criterias matching advertising objective and publish their product advertisements within social networks via advertisement agents (e.g. Facebook, Google+, Twitter), who allocate each advertisement (Ad) to users impressions (i.e. when user is reading a page) and charge certain prices, often based on number of clicks, impressions or engagements. In social network advertising, the cost-per-mille model is often used, where the advertisement agents receive the commission for one thousand user impressions displaying the Ad. The Ad allocation problem is a central problem for advertisement agents: how to maximize its revenue while respecting advertisers bids and budgets constraints. The advertising mechanism used by online advertisement agents, including social network websites, is essentially large auctions where advertisers place bids on user impressions, and specify their daily or total budget [4]. What makes social network advertising different from other Internet advertising is it is able to diffuse the advertisement and reach potentially larger audience through users’ engagements (e.g. ‘like’ in Facebook, ‘reteeet’ in Twitter, ‘+1’ in Google+). Previous research is mainly focusing on search engine settings, where the matching is ad-hoc and associated with search queries. Let the advertisers be A, each advertiser ai ∈ A has a budget Bi, and let the queries be Q and each qj ∈ Q can only be placed to one ad. Given the bidding matrix b, bij denoting how much money advertiser ai willing to pay for query keyword qj, the offline ad allocation problem in this setting is choose the allocation M to maximize the revenue of Ad agent: