Skip to main content
Log in

Constrained Markov decision processes with total cost criteria: Lagrangian approach and dual linear program

  • Published:
Mathematical Methods of Operations Research Aims and scope Submit manuscript

Abstract.

The aim of this paper is to investigate the Lagrangian approach and a related Linear Programming (LP) that appear in constrained Markov decision processes (CMDPs) with a countable state space and total expected cost criteria (of which the expected discounted cost is a special case). We consider transient MDPs and MDPs with uniform Lyapunov functions, and obtain for these an LP which is the dual of another one that has been shown to provide the optimal values and stationary policies [3, 4]. We show that there is no duality gap between these LPs under appropriate conditions. In obtaining the Linear Program for the general transient case, we establish, in particular, a calculation approach for the value function of the CMDP based on finite state approximation. Unlike previous approaches for state approximations for CMDPs (most of which were derived for the contracting framework), we do not need here any Slater type condition. We finally present another type of LP that allows the computation of optimal mixed stationary-deterministic policies.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Author information

Authors and Affiliations

Authors

Additional information

Received June 1995/Revised version September 1997

Rights and permissions

Reprints and permissions

About this article

Cite this article

Altman, E. Constrained Markov decision processes with total cost criteria: Lagrangian approach and dual linear program. Mathematical Methods of OR 48, 387–417 (1998). https://doi.org/10.1007/s001860050035

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s001860050035

Navigation