Fixed point theorems for discounted finite markov decision processes

✍ Scribed by Ulrich Dieter Holzbaur

• Publisher: Elsevier Science
• Year: 1986
• Tongue: English
• Weight: 141 KB
• Volume: 116
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1016/s0022-247x(86)80021-x

✦ Synopsis

We establish the existence of a solution to the optimality equation for discounted finite Markov decision processes by means of Birkhoffs fixed point theorem. The proof yields the well-known linear programming formulation for the optimal value function while its dual characterizes the optimal value function as the maximum over all value functions.