Optimal advertisement allocation in online social media feeds

We study the problem of optimal native advertisement placement in the social media post feed of a user. A feed, or timeline is a set of displayed posts such as news, updates, photos, videos. There exist fundamental differences between native and traditional web-search ads, which warrant a fresh view on native advertisement selection and allocation. We seek the ad allocation policy that maximizes the total expected profit for the online platform, which depends on the profit per click and the click probability for each ad. In our model, the click probability depends on the relevance of the ad to the preceding post, and on the distance between consecutively projected ads; i.e., the fewer the intervening posts between two ads, the smaller the click probability is, due to user saturation. If ads may be repeated in the feed, we show that the problem of maximizing total expected profit becomes an instance of a shortest-path problem on a weighted directed acyclic graph. If ads are not repeatable in the feed, the problem becomes a resource-constrained shortest-path problem and is NP-Hard. For the latter case, we present two heuristic algorithms. The first one uses Lagrangian relaxation and solves the dual problem of maximizing the Lagrangian function through a coordinate-ascent method. The second one is based on iteratively solving two subproblems: (i) ad selection and assignment at fixed positions using max-weight matching on a bipartite graph, and (ii) position perturbation for given set of ads. We show through numerical evaluation on real posts that the algorithms approach the optimal solution and trade complexity for approximation accuracy.