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* In problem 1 and 2, we consider a two-state Markov decision process (S, A, P, R, X) where S = {1,2} is a state space, A = {a¹, a²} is an action space, P is a transition probability matrix such that P(1|1,a¹) = 0.9, P(2|1, a¹) = 0.1, P(1|2, a¹) = 0, P(2|2, a¹) = 1, R is the reward such that P(1|1, a²) = P(2|1, a²) = 0.5, P(1|2, a²) = 0.2, P(2|2, a²) = 0.8, R(1, a¹) = 1, R(1, a²) = 3, R(2, a¹) = − 1, R(2, a²) = 0 and λ = [0, 1) is a discounted factor. 2. Assume the discounted factor X = 0.9. Find all optimal Markovian deterministic stationary policies.

* In problem 1 and 2, we consider a two-state Markov decision process (S, A, P, R, X) where S = {1,2} is a state space, A = {a¹, a²} is an action space, P is a transition probability matrix such that P(1|1,a¹) = 0.9, P(2|1, a¹) = 0.1, P(1|2, a¹) = 0, P(2|2, a¹) = 1, R is the reward such that P(1|1, a²) = P(2|1, a²) = 0.5, P(1|2, a²) = 0.2, P(2|2, a²) = 0.8, R(1, a¹) = 1, R(1, a²) = 3, R(2, a¹) = − 1, R(2, a²) = 0 and λ = [0, 1) is a discounted factor. 2. Assume the discounted factor X = 0.9. Find all optimal Markovian deterministic stationary policies.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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* In problem 1 and 2, we consider a two-state Markov decision process (S, A, P, R, X) where S = state space, A = {a¹, a²} is an action space, P is a transition probability matrix such that P(1|1, a¹) = 0.9, P(2|1, a¹) = 0.1, P(1|2, a¹) = 0, P(2|2, a¹) = 1, R is the reward such that P(1|1, a²) = P(2|1, a²) = 0.5, P(1|2, a²) = 0.2, P(2|2, a²) = 0.8, R(1, a¹) = 1, R(1, a²) = 3, R(2, a¹) = −1, R(2, a²) = 0 {1,2} is a and X = [0, 1) is a discounted factor. 2. Assume the discounted factor X = 0.9. Find all optimal Markovian deterministic stationary policies.
Transcribed Image Text:* In problem 1 and 2, we consider a two-state Markov decision process (S, A, P, R, X) where S = state space, A = {a¹, a²} is an action space, P is a transition probability matrix such that P(1|1, a¹) = 0.9, P(2|1, a¹) = 0.1, P(1|2, a¹) = 0, P(2|2, a¹) = 1, R is the reward such that P(1|1, a²) = P(2|1, a²) = 0.5, P(1|2, a²) = 0.2, P(2|2, a²) = 0.8, R(1, a¹) = 1, R(1, a²) = 3, R(2, a¹) = −1, R(2, a²) = 0 {1,2} is a and X = [0, 1) is a discounted factor. 2. Assume the discounted factor X = 0.9. Find all optimal Markovian deterministic stationary policies.
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