Combinatorial Multi-Armed Bandit Problems with Submodular Rewards: Applications and Recent Advances

In social networks, influence maximization is a crucial problem where we aim to identify the most influential individuals or nodes that can help spread information or ideas to others. This problem has been studied extensively in recent years, and various algorithms have been proposed to solve it. However, most of these algorithms are designed for offline scenarios, where all the data is available at once, and they are not suitable for online scenarios where new data keeps arriving continuously.
In this article, we address the problem of online influence maximization under linear threshold models. Linear threshold models are widely used to represent how people’s opinions or behaviors are influenced by their peers. We propose a novel algorithm that can handle online data streams and adaptively select the most influential nodes based on their past behavior and the new incoming data. Our algorithm is designed to maximize the overall influence of the selected nodes in the network while ensuring that the constraint on the cardinality of the selected set is satisfied.
We evaluate our algorithm through extensive simulations and compare it with existing algorithms under different scenarios. Our results show that our proposed approach consistently outperforms other algorithms, especially when the number of influential nodes is large. We also demonstrate the practicality of our algorithm by applying it to a real-world social network dataset.
In essence, our work provides a new and efficient way to identify influential individuals in online social networks, which has important implications for various applications such as marketing, public health, or political campaigns. By leveraging the latest advances in machine learning and data stream mining, we can now better understand how information spreads through social networks and how to maximize its influence.