Continuity of optimal values and solutions for control of Markov chains with constraints

Continuity of optimal values and solutions for control of Markov chains with constraints

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Article ID: iaor20012035
Country: United States
Volume: 38
Issue: 4
Start Page Number: 1204
End Page Number: 1222
Publication Date: Apr 2000
Journal: SIAM Journal on Control and Optimization
Authors: , , ,
Keywords: markov processes
Abstract:

We consider in this paper constrained Markov decision processes. This type of control model has many applications in telecommunications and other fields. We address the issue of the convergence of the value and optimal policies of the problem with discounted costs, to the ones for the problem with expected average cost. We consider the general multichain ergodic structure. We present two stability results in this paper. We establish the continuity of optimal values and solutions of as well as some type of robustness of some suboptimal solutions in the discount factor. Our proof relies on same general theory on continuity of values and solutions in convex optimization that relies on well-known notions of Γ-convergence.

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