Solving the k-sparse Eigenvalue Problem with Reinforcement Learning

09/09/2020
by   Li Zhou, et al.
0

We examine the possibility of using a reinforcement learning (RL) algorithm to solve large-scale eigenvalue problems in which the desired the eigenvector can be approximated by a sparse vector with at most k nonzero elements, where k is relatively small compare to the dimension of the matrix to be partially diagonalized. This type of problem arises in applications in which the desired eigenvector exhibits localization properties and in large-scale eigenvalue computations in which the amount of computational resource is limited. When the positions of these nonzero elements can be determined, we can obtain the k-sparse approximation to the original problem by computing eigenvalues of a k× k submatrix extracted from k rows and columns of the original matrix. We review a previously developed greedy algorithm for incrementally probing the positions of the nonzero elements in a k-sparse approximate eigenvector and show that the greedy algorithm can be improved by using an RL method to refine the selection of k rows and columns of the original matrix. We describe how to represent states, actions, rewards and policies in an RL algorithm designed to solve the k-sparse eigenvalue problem and demonstrate the effectiveness of the RL algorithm on two examples originating from quantum many-body physics.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 19

06/02/2017

An improved Krylov eigenvalue strategy using the FEAST algorithm with inexact system solves

The FEAST eigenvalue algorithm is a subspace iteration algorithm that us...
10/28/2020

Quantum algorithms for the polynomial eigenvalue problems

Polynomial eigenvalue problems (PEPs) arise in a variety of science and ...
03/24/2020

An Inverse-free Truncated Rayleigh-Ritz Method for Sparse Generalized Eigenvalue Problem

This paper considers the sparse generalized eigenvalue problem (SGEP), w...
12/19/2020

Quantum reinforcement learning in continuous action space

Quantum mechanics has the potential to speed up machine learning algorit...
11/15/2021

AutoGMap: Learning to Map Large-scale Sparse Graphs on Memristive Crossbars

The sparse representation of graphs has shown its great potential for ac...
02/21/2022

Isogeometric Analysis of Bound States of a Quantum Three-Body Problem in 1D

In this paper, we initiate the study of isogeometric analysis (IGA) of a...
03/23/2020

Geometric Sparsification of Closeness Relations: Eigenvalue Clustering for Computing Matrix Functions

We show how to efficiently solve a clustering problem that arises in a m...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.