Computing Stationary Distribution via Dirichlet-Energy Minimization by Coordinate Descent
Konstantin Avrachenkov, Lorenzo Gregoris, Nelly Litvak
TL;DR
This paper introduces an optimization framework for the RLGL algorithm to compute stationary distributions of large Markov chains, providing theoretical insights and practical improvements.
Contribution
It reformulates RLGL as an energy minimization problem, proving exponential convergence and proposing scheduling strategies for faster computation.
Findings
Exponential convergence for certain Markov chains
Practical scheduling strategies improve convergence speed
Clarifies the behavior of RLGL through optimization perspective
Abstract
We present an optimization-based formulation of the Red Light Green Light (RLGL) algorithm for computing stationary distributions of large Markov chains. This perspective clarifies the algorithm's behavior, establishes exponential convergence for a class of chains, and suggests practical scheduling strategies to accelerate convergence.
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Taxonomy
TopicsMarkov Chains and Monte Carlo Methods · Bayesian Modeling and Causal Inference · Gaussian Processes and Bayesian Inference