Artificial Intelligence Homework 02 Solution

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Description

Recall from lecture1 that Sam is either t or un t

  • = f t, un tg

and has to decide whether to exercise or relax

  • = fexercise, relaxg

on the basis of the following (probability, reward)-matrices (p(s; a; s0); r(s; a; s0))

for row s, column s0 in table with corner a

exercise

t

un t

relax

t

un t

t

.99, 8

.01, 8

t

.7, 10

.3, 10

un t

.2, 0

.8, 0

un t

0, 5

1, 5

The -discounted value of (s; a) is

lim

qn(s; a)

n!1

where

q0(s; a) := p(s; a; t)r(s; a; t) + p(s; a; un t)r(s; a; un t)

Vn(s) := max(qn(s; exercise); qn(s; relax))

qn+1(s; a) := q0(s; a) + p(s; a; t)Vn( t) + p(s; a; un t)Vn(un t) :

In particular, = 0:9 leads to the following qn(s; a) for n = 0; 1; 2

exercise

relax

t

8, 16.955, 23.812

10, 17.65, 23.685

relax, relax, exercise

un t

0, 5.4, 10.017

5, 9.5, 13.55

relax, relax, relax

Your task is to write a program that given

a positive integer n, a -setting G (0 < G < 1), and a state s

returns the values

qn(s; exercise) and qn(s; relax)

for = G. You may use any of the following programming languages

Prolog, Java, Python

but be prepared to demonstrate your program on Tue, March 6 (noon-1, LG 12, O’Reilly) or Wed, March 7 (10-11, LB04; on your machine).


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