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Summary: ISyE 6664 Exam # 2
Fall 2005
Name
Please be neat and show all your work so that I can give you partial credit.
GOOD LUCK AND HAVE A GOOD BREAK.
Question 1
Question 2
Question 3
Total
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1. (30) Consider a model with S = {s1, s2, s3}, As1 = {a1,1, a1,2} and As2 =
{a2,1}, and As3 = {a3,1}; r1(s1, a1,1) = r1(s1, a1,2) = 0, r1(s2, a2,1) = 3, and
r1(s3, a3,1) = 4 and p1(s1|s1, a1,1) = p1(s2|s1, a1,1) = 1/2, p1(s1|s1, a1,2) = 2/3,
p1(s3|s1, a1,2) = 1/3, p1(s1|s2, a2,1) = 1, and p1(s1|s3, a3,1) = 1.
a. (15) Is this model unichain? Justify your answer.
b. (15) Using this example show that the policy iteration may fail to find a
bias optimal policy (i.e. a maximal gain policy which has greater bias than any
other maximal gain policy).
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2. (40) A decision maker observes a discrete time system which moves between
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