  Predictive state representation~(PSR) uses a vector of action-observation
sequence to represent the system dynamics and subsequently predicts the
probability of future events. It is a concise knowledge representation that is
well studied in a single-agent planning problem domain. To the best of our
knowledge, there is no existing work on using PSR to solve multi-agent planning
problems. Learning a multi-agent PSR model is quite difficult especially with
the increasing number of agents, not to mention the complexity of a problem
domain. In this paper, we resort to tensor techniques to tackle the challenging
task of multi-agent PSR model development problems. By first focusing on a
two-agent setting, we construct the system dynamics matrix as a high order
tensor for a PSR model, learn the prediction parameters and deduce state
vectors directly through two different tensor decomposition methods
respectively, and derive the transition parameters via linear regression.
Subsequently, we generalize the PSR learning approaches in a multi-agent
setting. Experimental results show that our methods can effectively solve
multi-agent PSR modelling problems in multiple problem domains.
