  We consider the learning of multi-agent Hawkes processes, a model containing
multiple Hawkes processes with shared endogenous impact functions and different
exogenous intensities. In the framework of stochastic maximum likelihood
estimation, we explore the associated risk bound. Further, we consider the
superposition of Hawkes processes within the model, and demonstrate that under
certain conditions such an operation is beneficial for tightening the risk
bound. Accordingly, we propose a stochastic optimization algorithm assisted
with a diversity-driven superposition strategy, achieving better learning
results with improved convergence properties. The effectiveness of the proposed
method is verified on synthetic data, and its potential to solve the cold-start
problem of sequential recommendation systems is demonstrated on real-world
data.
