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arXiv · 2605.18004

RL4RLA: Teaching ML to Discover Randomized Linear Algebra Algorithms Through Curriculum Design and Graph-Based Search

Jinglong Xiong·Xiaotian Liu·Ruoxin Wang·Zihang Liu·Yefan Zhou·Yujun Yan·Yaoqing Yang
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Abstract

Randomized linear algebra (RLA) algorithms are a modern class of numerical linear algebra techniques that play an essential role in scientific computing and machine learning, with broad and growing adoption. However, their discovery remains mostly a manual process that requires deep expert knowledge and inspiration. While Reinforcement Learning (RL) offers a pathway to automation, standard approaches struggle with sparse reward landscapes and vast search spaces inherent to high-performing RLA algorithms. In this paper, we present RL4RLA, a general RL framework that automates the discovery of interpretable, symbolic RLA algorithms. Unlike black-box approaches, our method builds explicit algorithms from basic linear algebra primitives, ensuring verifiable and implementable representations. To enable efficient discovery, we introduce: (1) a numerical curriculum that progressively increments problem difficulty to encode inductive bias specific to the RLA domain; (2) Monte Carlo Graph Search, which optimizes exploration by identifying and merging equivalent partial algorithms. We demonstrate that RL4RLA rediscovers state-of-the-art methods, including sketch-and-precondition solvers, Randomized Kaczmarz, and Newton Sketch, and can be targeted to produce algorithms optimized for specific trade-offs between accuracy, speed, and stability. Code is available at https://github.com/Tim-Xiong/RL4RLA.

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Jinglong Xiong, Xiaotian Liu, Ruoxin Wang, Zihang Liu, Yefan Zhou, Yujun Yan, Yaoqing Yang. 2026-05-18. RL4RLA: Teaching ML to Discover Randomized Linear Algebra Algorithms Through Curriculum Design and Graph-Based Search. https://arxiv.org/abs/2605.18004

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