  Markov Decision Process (MDP) is the underlying model for optimal planning
for decision-theoretic agents in stochastic environments. Although much
research focuses on solving MDP problems both in tabular form or using factored
representations, none focused on tensor decomposition methods. Solving MDPs
using tensor algebra offers the prospect of leveraging advances in tensor-based
computations to further increase solver efficiency. In this paper, we develop
an MDP solver for a multidimensional problem using a tensor decomposition
method to compress the transition models and optimize the value iteration and
policy iteration algorithms. We empirically evaluate our approach against
tabular methods and show our approach can compute much larger problems using
substantially less memory, opening up new possibilities for tensor-based
approaches in stochastic planning
