Learning the Markov Decision Process in the Sparse Gaussian Elimination
This work addresses performance issues in sparse solvers for computational mathematics, but it appears incremental as it applies existing Q-Learning techniques to a new domain.
The authors tackled the problem of handling NP-hard combinatorial optimization in sparse Gaussian elimination by proposing a learning-based approach using Q-Learning algorithms for modules like minimum degree ordering, task scheduling, and adaptive pivoting. They recast the sparse solver into a Q-Learning framework, with numerical experiments verifying performance improvements.
We propose a learning-based approach for the sparse Gaussian Elimination. There are many hard combinatorial optimization problems in modern sparse solver. These NP-hard problems could be handled in the framework of Markov Decision Process, especially the Q-Learning technique. We proposed some Q-Learning algorithms for the main modules of sparse solver: minimum degree ordering, task scheduling and adaptive pivoting. Finally, we recast the sparse solver into the framework of Q-Learning. Our study is the first step to connect these two classical mathematical models: Gaussian Elimination and Markov Decision Process. Our learning-based algorithm could help improve the performance of sparse solver, which has been verified in some numerical experiments.