mlsanityData to 14 Oct 2026

Mixed-Precision Conjugate Gradient Solvers with RL-Driven Precision Tuning

arXiv 2504.14268 ↗First posted 19 Apr 2025cs.LGcited by 0

On the map: Deep reinforcement learning methods → RL theory and sample complexity

Abstract (arXiv)

This paper presents a novel reinforcement learning (RL) framework for dynamically optimizing numerical precision in the preconditioned conjugate gradient (CG) method. By modeling precision selection as a Markov Decision Process (MDP), we employ Q-learning to adaptively assign precision levels to key operations, striking an optimal balance between computational efficiency and numerical accuracy, while ensuring stability through double-precision scalar computations and residual computing. In practice, the algorithm is trained on a set of data and subsequently performs inference for precision selection on out-of-sample data, without requiring re-analysis or retraining for new datasets. This enables the method to adapt seamlessly to new problem instances without the computational overhead of recalibration. Our results demonstrate the effectiveness of RL in enhancing solver's performance, marking the first application of RL to mixed-precision numerical methods. The findings highlight the approach's practical advantages, robustness, and scalability, providing valuable insights into its integration with iterative solvers and paving the way for AI-driven advancements in scientific computing.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods. Builds on 5 of its 34 references that are in the map. First posted on arXiv 19 Apr 2025.

Builds on

5 of 34 references.

References · 5

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
  2. 2016Optimization Methods for Large-Scale Machine Learningcited by 1,150
  3. 2018NVIDIA Tensor Core Programmability, Performance & Precisioncited by 79
  4. 2023Data Quality-aware Mixed-precision Quantization via Hybrid Reinforcement Learningcited by 17
  5. 2017Krylov Subspace Recycling for Fast Iterative Least-Squares in Machine Learningcited by 2

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  5. 2025RL-PINNs: Reinforcement Learning-Driven Adaptive Sampling for Efficient Training of PINNs
  6. 2023Cal-QL: Calibrated Offline RL Pre-Training for Efficient Online Fine-Tuning
  7. 2026Accelerating Reinforcement Learning via MPC Solver-Gradient Guidance for Weights-varying MPC
  8. 2024A Differential and Pointwise Control Approach to Reinforcement Learning