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

arXiv: https://arxiv.org/abs/2504.14268 · HTML: https://mlsanity.com/paper/2504.14268/

## 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.

## Placed in

- Deep reinforcement learning methods / [RL theory and sample complexity](https://mlsanity.com/deeprl/rl-theory-and-sample-complexity/)

## Builds on (most cited first, 5 of 5)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [NVIDIA Tensor Core Programmability, Performance & Precision](https://mlsanity.com/paper/1803.04014/) (2018)
- [Data Quality-aware Mixed-precision Quantization via Hybrid Reinforcement Learning](https://mlsanity.com/paper/2302.04453/) (2023)
- [Krylov Subspace Recycling for Fast Iterative Least-Squares in Machine Learning](https://mlsanity.com/paper/1706.00241/) (2017)

## 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.