Accelerating Matrix Diagonalization through Decision Transformers with Epsilon-Greedy Optimization
This work addresses computational efficiency in matrix operations for numerical computing, though it is incremental in applying existing ML techniques to a new domain.
The paper tackled matrix diagonalization by framing it as a sequential decision problem using Decision Transformers with epsilon-greedy optimization, achieving significant speedups over the traditional max-element Jacobi method.
This paper introduces a novel framework for matrix diagonalization, recasting it as a sequential decision-making problem and applying the power of Decision Transformers (DTs). Our approach determines optimal pivot selection during diagonalization with the Jacobi algorithm, leading to significant speedups compared to the traditional max-element Jacobi method. To bolster robustness, we integrate an epsilon-greedy strategy, enabling success in scenarios where deterministic approaches fail. This work demonstrates the effectiveness of DTs in complex computational tasks and highlights the potential of reimagining mathematical operations through a machine learning lens. Furthermore, we establish the generalizability of our method by using transfer learning to diagonalize matrices of smaller sizes than those trained.