On Using Reinforcement Learning to Solve Sparse Linear Systems

Abstract

Abstract. This paper describes how reinforcement learning can be used to select from a wide variety of preconditioned solvers for sparse linear systems. This approach provides a simple way to consider complex metrics of goodness, and makes it easy to evaluate a wide range of preconditioned solvers. A basic implementation recommends solvers that, when they converge, generally do so with no more than a 17% overhead in time over the best solver possible within the test framework. Potential refinements of, and extensions to, the system are discussed.

Algorithm Selection for Combinatorial Search Problems: A Survey

“…Armstrong et al (2006) use an agent-based model that rewards good actions and punishes bad actions based on computation time. Kuefler and Chen (2008) follow a very similar approach that also takes success or failure into account. Carchrae andBeck (2004, 2005) monitor the solution quality during search.…”

Machine-Learned Preconditioners for Linear Solvers in Geophysical Fluid Flows

“…There have been some advances to apply machine-learning methods within the context of linear solvers. So far, work has focused on using machine learning to either select the best solver-preconditioner setup from a set of preconditioners and/or linear solvers for a given linear problem (Holloway & Chen, 2007;Kuefler & Chen, 2008;Xu & Zhang, 2005;George et al, 2008;Yamada et al, 2018;Huang et al, 2016;Peairs & Chen, 2011), to help improve efficiency for Block-Jacobi type preconditioners (Götz & Anzt, 2018), to reduce the time-to-solution by interspersing linear solver iterations with neural-network based correction steps (Rizzuti et al, 2019), or to replace the linear solver entirely (Tompson et al, 2017;Yang, Yang, & Xiao, 2016;Ladický et al, 2015). This paper will try a fundamentally new approach by using supervised machine learning to derive the preconditioner directly.…”

Solver Recommendation For Transport Problems in Slabs Using Machine Learning

“…The accuracy of the chosen transport model and the efficiency of the corresponding solver/preconditioner pair depend on these physical properties. Numerous studies have been carried out in the computer science and mathematics communities addressing the use of machine learning algorithms for choosing optimal solvers for linear systems [1,2,3,4,5]. None of these works, however, specifically target particle transport problems, and the authors are unaware of any such study addressing transport solvers.…”