Mixed-Precision Conjugate Gradient Solvers with RL-Driven Precision Tuning
This work addresses the challenge of improving performance in iterative solvers for scientific computing, representing an incremental advancement by applying RL to mixed-precision methods.
This paper tackles the problem of optimizing numerical precision in preconditioned conjugate gradient solvers by introducing a reinforcement learning framework that dynamically assigns precision levels, achieving a balance between computational efficiency and numerical accuracy without requiring retraining for new datasets.
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.