Precision Autotuning for Linear Solvers via Contextual Bandit-Based RL

Abstract: We propose a reinforcement learning (RL) framework for adaptive precision tuning of linear solvers, and can be extended to general algorithms. The framework is formulated as a contextual bandit problem and solved using incremental action-value estimation with a discretized state space to select optimal precision configurations for computational steps, balancing precision and computational efficiency. To verify its effectiveness, we apply the framework to iterative refinement for solving linear systems $Ax = b$. In this application, our approach dynamically chooses precisions based on calculated features from the system. In detail, a Q-table maps discretized features (e.g., approximate condition number and matrix norm)to actions (chosen precision configurations for specific steps), optimized via an epsilon-greedy strategy to maximize a multi-objective reward balancing accuracy and computational cost. Empirical results demonstrate effective precision selection, reducing computational cost while maintaining accuracy comparable to double-precision baselines. The framework generalizes to diverse out-of-sample data and offers insight into utilizing RL precision selection for other numerical algorithms, advancing mixed-precision numerical methods in scientific computing. To the best of our knowledge, this is the first work on precision autotuning with RL and verified on unseen datasets.