Efficient randomized algorithms for PageRank problem

TL;DR

This paper compares existing PageRank algorithms, introduces a Markov Chain Monte Carlo approach with new estimations, and proposes a novel matrix game reduction solved via randomized mirror descent, enhancing computational efficiency.

Contribution

It presents a new randomized algorithm for PageRank based on matrix game reduction and applies non-standard randomization techniques, advancing existing methods.

Findings

New estimation for Markov Chain Monte Carlo method

Reduction of PageRank to matrix game solved with randomized mirror descent

Utilization of non-standard randomization techniques in KL-projection

Abstract

In the paper we compare well known numerical methods of finding PageRank vector. We propose Markov Chain Monte Carlo method and obtain a new estimation for this method. We also propose a new method for PageRank problem based on the reduction of this problem to the matrix game. We solve this (sparse) matrix game with randomized mirror descent. It should be mentioned that we used non-standard randomization (in KL-projection) goes back to Grigoriadis-Khachiayn (1995).