CP-MDP: A CANDECOMP-PARAFAC Decomposition Approach to Solve a Markov Decision Process Multidimensional Problem
This addresses the memory efficiency challenge in stochastic planning for decision-theoretic agents, though it is incremental as it applies an existing tensor method to MDPs.
The paper tackled the problem of solving Markov Decision Processes (MDPs) for multidimensional problems by using a tensor decomposition method to compress transition models and optimize algorithms, showing that it can compute much larger problems with substantially less memory compared to tabular methods.
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