Online Autotuning of Algebraic Multigrid via Contextual Bandits and Reinforcement Learning
Abstract
Algebraic multigrid (AMG) methods are widely used for solving large sparse linear systems, but their efficiency depends strongly on interacting setup and solve parameters. Effective parameter choices typically depend on the problem. We develop a phase-aware online autotuning method for hypre's BoomerAMG to reduce cumulative time-to-solution over sequences of related linear systems. A LinUCB-based contextual bandit selects mixed-type parameters for AMG hierarchy construction using a shared cost model over PDE descriptors and configuration encodings. A recursive LSTDQ controller uses residual and timing observations to estimate the AMG solve time within each attempt and adapt relaxation weights between multigrid cycles. Both learners update from ongoing solves without offline pretraining. Across grids of sizes 403, 603, and 803, the joint autotuning method reduces total runtime, including recurring learner computation, by 36.1-43.3% for diffusion problems and 19.8-31.0% for diffusion-advection problems over sequences of 5000 linear systems, relative to the reference BoomerAMG default configuration. On a variable-flow diffusion-advection benchmark comprising 30,000 systems on a 603 grid, 2 systems fail to converge with joint autotuning, compared with 1677 for the reference configuration, under their respective attempt budgets.
Related
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BibTeX
@misc{he2026online,
title = {{Online Autotuning of Algebraic Multigrid via Contextual Bandits and Reinforcement Learning}},
author = {Xudong He and Ruiyu Wang and Yilang Ding and Rui Peng Li and Yuanzhe Xi},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01193},
eprint = {2611.01193},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01193},
}
RIS
TY - UNPB
TI - Online Autotuning of Algebraic Multigrid via Contextual Bandits and Reinforcement Learning
AU - Xudong He
AU - Ruiyu Wang
AU - Yilang Ding
AU - Rui Peng Li
AU - Yuanzhe Xi
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01193
UR - https://arxiv.org/abs/2611.01193
AB - Algebraic multigrid (AMG) methods are widely used for solving large sparse linear systems, but their efficiency depends strongly on interacting setup and solve parameters. Effective parameter choices typically depend on the problem. We develop a phase-aware online autotuning method for hypre's BoomerAMG to reduce cumulative time-to-solution over sequences of related linear systems. A LinUCB-based contextual bandit selects mixed-type parameters for AMG hierarchy construction using a shared cost model over PDE descriptors and configuration encodings. A recursive LSTDQ controller uses residual and timing observations to estimate the AMG solve time within each attempt and adapt relaxation weights between multigrid cycles. Both learners update from ongoing solves without offline pretraining. Across grids of sizes 40^3, 60^3, and 80^3, the joint autotuning method reduces total runtime, including recurring learner computation, by 36.1-43.3% for diffusion problems and 19.8-31.0% for diffusion-advection problems over sequences of 5000 linear systems, relative to the reference BoomerAMG default configuration. On a variable-flow diffusion-advection benchmark comprising 30,000 systems on a 60^3 grid, 2 systems fail to converge with joint autotuning, compared with 1677 for the reference configuration, under their respective attempt budgets.
ER -