Infinite-Horizon Discounted Markov Decision …

Infinite-Horizon Discounted Markov Decision processes Dan Zhang Leeds School of Business University of Colorado at Boulder Dan Zhang, Spring 2012 Infinite Horizon Discounted MDP 1. Outline The expected total Discounted reward Policy evaluation Optimality equations Value iteration Policy iteration Linear Programming Dan Zhang, Spring 2012 Infinite Horizon Discounted MDP 2. Expected Total Reward Criterion Let = (d1 , d2 , .. ) HR. Starting at a state s, using policy leads to a sequence of state-action pairs {Xt , Yt }. The sequence of rewards is given by {Rt rt (Xt , Yt ) : t = 1, 2, .. }. Let [0, 1) be the discount factor The expected total rewards from policy starting in state s is given by " N #. X. v (s) lim E s t 1 r (Xt , Yt ) . N . t=1. The limit above exists when r ( ) is bounded; , sups S,a As |r (s, a)| = M <.]

In nite-Horizon Discounted Markov Decision Processes Dan Zhang Leeds School of Business University of Colorado at Boulder Dan Zhang, Spring 2012 In nite Horizon Discounted MDP 1

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  Processes, Decision, Horizons, Discounted, Markov, Horizon discounted markov decision, Horizon discounted markov decision processes

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