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Life sciences · Preprint
arXiv · September 8, 2026
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This is an open-source Python package (rlaopt) that implements GPU-accelerated solvers for large-scale optimization using randomized linear algebra, with preliminary computational experiments on ridge regression, multinomial logistic regression, and elastic net. The work demonstrates technical feasibility and reports GPU speedups in controlled benchmarks, but has not undergone peer review and does not address clinical or scientific discovery outcomes.
Preprint. Intervention: rlaopt package: GPU-accelerated solvers using randomized linear algebra (NystromPCG, NysADMM, SAPPHIRE) with modeling language interface..
Package provides GPU-enabled solvers for positive-definite linear systems and convex empirical risk minimization Implements randomized preconditioning methods (NystromPCG, NysADMM, SAPPHIRE) with differentiation support Experiments on ridge regression, bounded multinomial logistic regression, and bounded elastic net show when randomized preconditioning improves performance and demonstrate speedups from GPU execution
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This is a software package paper introducing a computational tool with experimental validation on benchmark problems; it demonstrates feasibility and performance but lacks clinical application, peer review, or rigorous comparative validation against established baselines.
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This paper introduces rlaopt, a PyTorch-based package for large-scale optimization and scientific computing using randomized numerical linear algebra (RandNLA). Despite substantial progress in RandNLA-based algorithms, few implementations combine GPU acceleration with a simple interface for specifying optimization problems. rlaopt addresses this gap by providing GPU-enabled solvers for positive-definite linear systems and convex empirical risk minimization with constraints and regularizers. These solvers use RandNLA to accelerate conjugate gradient (NystromPCG), operator splitting (NysADMM), and stochastic gradient methods (SAPPHIRE). Moreover, rlaopt includes a modeling language that lets users specify problems using natural mathematical syntax. rlaopt automatically checks compatibility with the selected solver and performs the required problem decomposition. The solvers also support differentiation through their iterations, enabling applications such as hyperparameter tuning. Experiments on ridge regression, bounded multinomial logistic regression, and bounded elastic net identify when randomized preconditioning improves performance and demonstrate substantial speedups from GPU execution. The package is open-source under an Apache license, with source code at https://github.com/udellgroup/rlaopt and version 0.1.0 available on PyPI.
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