Researchers Develop Generalization Guarantees for Hyperparameter Tuning in GPU-Accelerated Linear Programming Solver
Researchers have developed generalization guarantees for hyperparameter tuning in cuPDLP, a state-of-the-art GPU-accelerated first-order linear programming solver. The work analyzes the underlying PDHG algorithm and PDLP's additional techniques—such as preconditioning, adaptive step sizes, and adaptive restarts—to establish polynomial sample complexity bounds for learning hyperparameters. The results provide a principled, data-driven foundation for parameter selection in large-scale optimization solvers, addressing a key practical bottleneck in their deployment.
A new preprint posted to arXiv presents theoretical generalization guarantees for hyperparameter tuning within cuPDLP, a first-order linear programming solver optimized for modern GPU hardware. The authors first characterize the behavior of PDHG (primal-dual hybrid gradient), the core algorithm underlying PDLP, as a function of step size and primal weight, yielding linear sample complexity guarantees for those parameters. They then extend the analysis to the full PDLP solver, which incorporates several additional techniques including preconditioning, adaptive step sizes, solution averaging, adaptive restarts, and smoothed primal weight updates. By capturing how the solution trajectory depends on hyperparameters and applying recent advances in data-driven algorithm design, the authors obtain polynomial sample complexity guarantees for the broader set of PDLP hyperparameters. Proof-of-concept experiments accompany the theory, demonstrating that data-driven parameter tuning meaningfully improves solver performance. The work highlights the applicability of the data-driven algorithm design framework to complex, solver-grade optimization implementations.
What's missing
The paper is a preprint and has not yet undergone peer review. The computational overhead of the proposed data-driven tuning procedure relative to baseline solver runs is not characterized in the abstract.
What different sources said
- arXiv cs.LGCenter
Parameter Tuning with Generalization Guarantees for GPU-Accelerated Linear Programming
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