Abstract
We consider a discounted Markovian Decision Process (MDP) with finite state and action space. For a fixed discount factor we derive a bound for the number of steps, taken by Howard's policy improvement algorithm (PIA) to determine an optimal policy for the MDP, that is essentially polynomial in the number of states and actions of the MDP. The main tools are the contraction properties of the PIA and a lower bound for the difference of the value functions of a MDP with rational data. Wir betrachten einen Markoffschen Entscheidungsprozeβ mit endlichem Zustands- und Aktionenraum. Bei festgehaltenem Diskontierungsfaktor bestimmen wir eine Grenze fur die Anzahl der Schritte in Howards Politikverbesserungsverfahren, die im wesentlichen polynomial in der Anzahl der Zustande und Aktionen ist. Die Haupthilfsmittel sind dabei die Kontraktionseigenschaft des Algorithmus und eine untere
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