Online Influence Maximization (Extended Version)

Social networks are commonly used for marketing purposes. For example, free samples of a product can be given to a few influential social network users (or "seed nodes"), with the hope that they will convince their friends to buy it. One way to formalize marketers' objective is through influence maximization (or IM), whose goal is to find the best seed nodes to activate under a fixed budget, so that the number of people who get influenced in the end is maximized. Recent solutions to IM rely on the influence probability that a user influences another one. However, this probability information may be unavailable or incomplete. In this paper, we study IM in the absence of complete information on influence probability. We call this problem Online Influence Maximization (OIM) since we learn influence probabilities at the same time we run influence campaigns. To solve OIM, we propose a multiple-trial approach, where (1) some seed nodes are selected based on existing influence information; (2) an influence campaign is started with these seed nodes; and (3) users' feedback is used to update influence information. We adopt the Explore-Exploit strategy, which can select seed nodes using either the current influence probability estimation (exploit), or the confidence bound on the estimation (explore). Any existing IM algorithm can be used in this framework. We also develop an incremental algorithm that can significantly reduce the overhead of handling users' feedback information. Our experiments show that our solution is more effective than traditional IM methods on the partial information.Comment: 13 pages. To appear in KDD 2015. Extended versio

Online Influence Maximization in Non-Stationary Social Networks

Social networks have been popular platforms for information propagation. An important use case is viral marketing: given a promotion budget, an advertiser can choose some influential users as the seed set and provide them free or discounted sample products; in this way, the advertiser hopes to increase the popularity of the product in the users' friend circles by the world-of-mouth effect, and thus maximizes the number of users that information of the production can reach. There has been a body of literature studying the influence maximization problem. Nevertheless, the existing studies mostly investigate the problem on a one-off basis, assuming fixed known influence probabilities among users, or the knowledge of the exact social network topology. In practice, the social network topology and the influence probabilities are typically unknown to the advertiser, which can be varying over time, i.e., in cases of newly established, strengthened or weakened social ties. In this paper, we focus on a dynamic non-stationary social network and design a randomized algorithm, RSB, based on multi-armed bandit optimization, to maximize influence propagation over time. The algorithm produces a sequence of online decisions and calibrates its explore-exploit strategy utilizing outcomes of previous decisions. It is rigorously proven to achieve an upper-bounded regret in reward and applicable to large-scale social networks. Practical effectiveness of the algorithm is evaluated using both synthetic and real-world datasets, which demonstrates that our algorithm outperforms previous stationary methods under non-stationary conditions.Comment: 10 pages. To appear in IEEE/ACM IWQoS 2016. Full versio

Factorization Bandits for Online Influence Maximization

We study the problem of online influence maximization in social networks. In this problem, a learner aims to identify the set of "best influencers" in a network by interacting with it, i.e., repeatedly selecting seed nodes and observing activation feedback in the network. We capitalize on an important property of the influence maximization problem named network assortativity, which is ignored by most existing works in online influence maximization. To realize network assortativity, we factorize the activation probability on the edges into latent factors on the corresponding nodes, including influence factor on the giving nodes and susceptibility factor on the receiving nodes. We propose an upper confidence bound based online learning solution to estimate the latent factors, and therefore the activation probabilities. Considerable regret reduction is achieved by our factorization based online influence maximization algorithm. And extensive empirical evaluations on two real-world networks showed the effectiveness of our proposed solution.Comment: 11 pages (including SUPPLEMENT

Online Influence Maximization under Independent Cascade Model with Semi-Bandit Feedback

We study the online influence maximization problem in social networks under the independent cascade model. Specifically, we aim to learn the set of "best influencers" in a social network online while repeatedly interacting with it. We address the challenges of (i) combinatorial action space, since the number of feasible influencer sets grows exponentially with the maximum number of influencers, and (ii) limited feedback, since only the influenced portion of the network is observed. Under a stochastic semi-bandit feedback, we propose and analyze IMLinUCB, a computationally efficient UCB-based algorithm. Our bounds on the cumulative regret are polynomial in all quantities of interest, achieve near-optimal dependence on the number of interactions and reflect the topology of the network and the activation probabilities of its edges, thereby giving insights on the problem complexity. To the best of our knowledge, these are the first such results. Our experiments show that in several representative graph topologies, the regret of IMLinUCB scales as suggested by our upper bounds. IMLinUCB permits linear generalization and thus is both statistically and computationally suitable for large-scale problems. Our experiments also show that IMLinUCB with linear generalization can lead to low regret in real-world online influence maximization.Comment: Compared with the previous version, this version has fixed a mistake. This version is also consistent with the NIPS camera-ready versio

Budgeted online influence maximization

Virtual conferenceInternational audienceWe introduce a new budgeted framework for on-line influence maximization, considering the total cost of an advertising campaign instead of the common cardinality constraint on a chosen influ-encer set. Our approach models better the real-world setting where the cost of influencers varies and advertizers want to find the best value for their overall social advertising budget. We propose an algorithm assuming an independent cascade diffusion model and edge-level semi-bandit feedback, and provide both theoretical and experimental results. Our analysis is also valid for the cardinality-constraint setting and improves the state of the art regret bound in this case