On compressibility and acceleration of orthogonal nmf for pomdp compression

State space compression is one of the recently proposed approaches for improving POMDP's tractability. Despite its initial success, it still carries two intrinsic limitations. First, not all POMDP problems can be compressed equally well. Also, the cost of computing the compressed space itself may become significant as the size of the problem is scaled up. In this paper, we address the two issues with respect to an orthogonal non-negative matrix factorization recently proposed for POMDP compression. In particular, we first propose an eigenvalue analysis to evaluate the compressibility of a POMDP and determine an effective range for the dimension reduction. Also, we incorporate the interior-point gradient acceleration into the orthogonal NMF and derive an accelerated version to minimize the compression overhead. The validity of the eigenvalue analysis has been evaluated empirically. Also, the proposed accelerated orthogonal NMF has been demonstrated to be effective in speeding up the policy computation for a set of robot navigation related problems.