Direct methods have made remarkable progress in the computational efficiency of factorization algorithms during the last three decades. The advances in graph theoretic algorithms have not received enough attention from the iterative methods community. For example, we demonstrate how symbolic factorization algorithms from direct methods can accelerate the computation of a factored approximate in...

Graphplan has attracted considerable interest because of its extremely high performance, but the algorithm’s inability to handle action representations more expressive than STRIPS is a major limitation. In particular, extending Graphplan to handle conditional effects is a surprisingly subtle enterprise. In this paper, we describe the space of possible alternatives, and then concentrate on one p...

Graphplan has attracted considerable interest because of its extremely high performance, but the algorithm's inability to handle action representations more expressive than STRIPS is a major limitation. In particular, extending Graphplan to handle conditional e ects is a surprisingly subtle enterprise. In this paper, we describe the space of possible alternatives, and then concentrate on one pa...

We consider ordering techniques to improve the performance of factored sparse approximate inverse preconditioners, concentrating on the AINV technique of M. Benzi and M. Tůma. Several practical existing unweighted orderings are considered along with a new algorithm, minimum inverse penalty (MIP), that we propose. We show how good orderings such as these can improve the speed of preconditioner c...

We investigate the use of sparse approximate inverse techniques (SAI) in a grid based multilevel ILU preconditioner (GILUM) to design a robust parallelizable precon-ditioner for solving general sparse matrix. Taking the advantages of grid based mul-tilevel methods, the resulting preconditioner outperforms sparse approximate inverse in robustness and eeciency. Conversely, taking the advantages o...

One of the central challenges in reinforcement learning is to balance the exploration/exploitation tradeoff while scaling up to large problems. Although model-based reinforcement learning has been less prominent than value-based methods in addressing these challenges, recent progress has generated renewed interest in pursuing modelbased approaches: Theoretical work on the exploration/exploitati...

We introduce a new preconditioner for elliptic PDE’s on unstructured meshes. Using a wavelet-inspired basis we compress the inverse of the matrix, allowing an effective sparse approximate inverse by solving the sparsity vs. accuracy conflict. The key issue in this compression is to use second-generation wavelets which can be adapted to the unstructured mesh, the true boundary conditions, and ev...

In this paper we propose a novel algorithm, factored value iteration (FVI), for the approximate solution of factored Markov decision processes (fMDPs). The traditional approximate value iteration algorithm is modified in two ways. For one, the least-squares projection operator is modified so that it does not increase max-norm, and thus preserves convergence. The other modification is that we un...