{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/learning-the-markov-decision-process-in-the","title":"Learning the Markov Decision Process in the Sparse Gaussian Elimination","arxiv_id":"2109.14929","date":"2021-09-30","proceeding":null,"authors":["Yingshi Chen"],"abstract":"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.","url_abs":"https://arxiv.org/abs/2109.14929v1","url_pdf":"https://arxiv.org/pdf/2109.14929v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"learning-the-markov-decision-process-in-the","repo_url":"https://github.com/closest-git/gss","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"combinatorial-optimization","task_name":"Combinatorial Optimization"},{"task_slug":"q-learning","task_name":"Q-Learning"},{"task_slug":"scheduling","task_name":"Scheduling"}],"methods":[{"method_slug":"q-learning","method_name":"Q-Learning"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}