Online Influence Maximization (Extended Version) (1506.01188v1)

Abstract: 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.

Online Influence Maximization

The paper "Online Influence Maximization" explores the intricate problem of maximizing influence dissemination in social networks, especially under the constraints of incomplete information about influence probabilities. This research addresses a critical challenge in marketing strategies within digital platforms, where advertisers aim to maximize their reach by identifying strategic individuals or seed nodes to initiate product promotions.

The traditional Influence Maximization (IM) techniques rely heavily on pre-known influence probabilities between nodes in a network, executed through complex offline algorithms. However, the reality of marketing operations in new or dynamic social environments often leads to scenarios where such probabilities are either inaccessible or non-existent. Here, the authors present a versatile solution termed Online Influence Maximization (OIM), which emphasizes learning influence probabilities concurrently with campaign execution.

Framework for OIM

OIM is presented as a strategic framework operating over multiple influence trials. The framework includes three main operations in each trial:

1. Seed Selection: The OIM deploys various strategies like Explore--Exploit (EE) to dynamically choose seed nodes based on current influence probability estimates. The EE strategy utilizes mechanisms such as the $$-greedy approach and Confidence-Bound (CB) algorithm to navigate the exploration (learning new influence probabilities) versus exploitation (utilizing known probabilities) trade-off.
2. Execution and Feedback: After seed selection, an influence campaign is conducted, the results of which are collected as feedback in the form of activated nodes and edge interaction logs. This real-world feedback becomes pivotal in refining node influence probabilities for subsequent trials.
3. Graph Update: The framework leverages sophisticated updates, including local and global influencing parameter adaptations via Maximum Likelihood Estimation (MLE) and Least-Squares Estimation (LSE). These update methods ensure that each trial progressively refines its influence graph towards a more accurate reflection of actual network dynamics.

Algorithm Efficiency and Incremental Solutions

The paper introduces an incremental solution to further enhance the efficiency of OIM. Noting the computational load of state-of-the-art offline IM algorithms due to extensive sampling requirements, the researchers propose an optimized sample-management system. This system stores samples from each trial for potential reuse, leveraging local and global checks to verify sample validity post-update. This optimization substantially reduces computational overhead, a benefit particularly notable in larger social graphs like DBLP with millions of edges.

Insights and Implications

The proposed OIM framework and strategies showcase high potential in practical marketing scenarios where influence probability is a dynamic or incompletely known entity. This flexibility is crucial for social marketers aiming to utilize limited promotional budgets efficiently across diverse social landscapes. The paper’s experimental results validate the framework’s efficacy, with CB-based explore-exploit strategies showing favorable outcomes over traditional heuristics.

Future Directions

While the OIM framework effectively mitigates influence uncertainty, the authors recognize avenues for further enhancements. These include handling variable budgets across trials, integrating community/topic-based influence models, and scaling solutions for distributed environments. Such developments can further empower marketers with the tools to navigate the evolving complexities of social network influence maximization.

In conclusion, this paper contributes significantly to the discourse on effective marketing strategies in digital social networks, offering a tangible approach to overcoming the challenges associated with incomplete influence data. Through its robust exploration-exploitation mechanisms and computational optimizations, OIM presents a compelling solution framework that is both theoretically sound and practically relevant.