Learning Good State and Action Representations for Markov Decision Process via Tensor Decomposition

The transition kernel of a continuous-state-action Markov decision process (MDP) admits a natural tensor structure. This paper proposes a tensor-inspired unsupervised learning method to identify meaningful low-dimensional state and action representations from empirical trajectories. The method exploits the MDP's tensor structure by kernelization, importance sampling and low-Tucker-rank approximation. This method can be further used to cluster states and actions respectively and find the best discrete MDP abstraction. We provide sharp statistical error bounds for tensor concentration and the preservation of …

abstraction approximation cluster continuous decision diffusion embedding error exploits good identify importance kernel low markov natural paper preservation process sampling state statistical tensor transition tucker unsupervised unsupervised learning