Learning to Maximize Influence

As the field of machine learning for combinatorial optimization advances, traditional problems are resurfaced and readdressed through this new perspective. The overwhelming majority of the literature focuses on small graph problems, while several real-world problems are devoted to large graphs. Here, we focus on two such problems that are related: influence estimation, a \#P-hard counting problem, and influence maximization, an NP-hard problem. We develop GLIE, a Graph Neural Network (GNN) that inherently parameterizes an upper bound of influence estimation and train it on small simulated graphs. Experiments show that GLIE can provide accurate predictions faster than the alternatives for graphs 10 times larger than the train set. More importantly, it can be used on arbitrary large graphs for influence maximization, as the predictions can rank effectively seed sets even when the accuracy deteriorates. To showcase this, we propose a version of a standard Influence Maximization (IM) algorithm where we substitute traditional influence estimation with the predictions of GLIE.We also transfer GLIE into a reinforcement learning model that learns how to choose seeds to maximize influence sequentially using GLIE's hidden representations and predictions. The final results show that the proposed methods surpasses a previous GNN-RL approach and perform on par with a state-of-the-art IM algorithm.