Accelerating Matrix Diagonalization through Decision Transformers with Epsilon-Greedy Optimization

TL;DR

This paper presents a machine learning-based framework using Decision Transformers and epsilon-greedy strategies to accelerate matrix diagonalization, achieving faster performance and robustness over traditional methods.

Contribution

It introduces a novel approach that formulates matrix diagonalization as a decision-making process and applies DTs with epsilon-greedy optimization for improved speed and robustness.

Findings

Significant speedups over traditional Jacobi method

Enhanced robustness with epsilon-greedy strategy

Successful transfer learning for smaller matrices

Abstract

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.