Two-time scale Controlled Markov Chains: A decomposition and parallel processing approach

doi:10.1109/TAC.2007.910692

Return

Two-time scale Controlled Markov Chains: A decomposition and parallel processing approach

2007-12-01

PRE

Alain Haurie *

Francesco Moresino

DOI：10.1109/TAC.2007.910692

Original

Original request for help

Save

Abstract

En 中文

This correspondence deals with a class of ergodic control problems for systems described by Markov chains with strong and weak inter actions. These systems are composed of a set of m subchains that are weakly coupled. Using results already available in the literature one formulates a limit control problem the solution of which can be obtained via an associated nondifferentiable convex programming (NDCP) problem. The technique used to solve the NDCP problem is the Analytic Center Cutting Plane Method (ACCPM) which implements a dialogue between, on one hand, a master program computing the analytical center of a localization set containing the solution and, on the other hand, an oracle proposing cutting planes that reduce the size of the localization set at each main iteration. The interesting aspect of this implementation comes from two characteristics: (i) the oracle proposes cutting planes by solving reduced sized Markov Decision Problems (MDP) via a linear program (LP) or a policy iteration method; (ii) several cutting planes can be proposed simultaneously through a parallel implementation on m processors. The correspondence concentrates on these two aspects and shows, on a large scale MDP obtained from the numerical approximation a la Kushner-Dupuis of a singularly perturbed hybrid stochastic control problem, the important computational speed-up obtained.

Keywords:

decomposition technique

interior point method

singular perturbations

two-timescale Markov chain

AI Summary

Key information extracted from the uploaded paper, including a brief overview, abstract, background, key highlights, visual analysis, and future outlook.