  The goal of influence maximization (IM) is to select a small set of seed
nodes which maximizes the spread of influence on a network. In this work, we
propose BOPIM, a Bayesian Optimization (BO) algorithm for IM on temporal
networks. The IM task is well-suited for a BO solution due to its expensive and
complicated objective function. We propose a simple surrogate function to model
the objective function and leverage Gaussian Process regression with shrinkage
priors to fit the model. A major difficulty in combinatorial BO is constructing
an appropriate covariance matrix. We overcome this challenge with a kernel
function based on the amount of overlap in seed set neighbors, thus tailoring
the solution to our IM application. This also allows us to use the Expected
Improvement acquisition function to choose the next point to evaluate. In
numerical experiments on real-world networks, we prove that BOPIM outperforms
competing methods and yields comparable influence spreads to a gold-standard
greedy algorithm while being as much as five times faster. We also demonstrate
the proposed method's ability to quantify uncertainty in optimal seed sets. To
our knowledge, this is the first attempt to look at uncertainty in the seed
sets for IM.
