Homework Due March 3, before 3:30 pm

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HomeworkDue March 3, before 330 pm

• Based on readings in the syllabus
• All questions carry equal points

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Problem 1Learn more about DCSP Representation
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Sensor DCSP

• Each sensor has three 120 degree sectors,
  numbered 0, 1 or 2 as shown on the previous slide
• Each sensor is controlled by one agent
• The agent decides which of the sensors sectors
  to activate or to go into rotate mode
• Rotate mode causes the sensor to repeatedly scan
  the three sectors
• At any point in time, a sensor must have either
  one sector active or be in rotate mode, NOT BOTH
• Tracking a target requires at least three sectors
  to be active from three different sensors (more
  than three does not hurt the tracking of the
  target)
• A sensor cannot contribute to tracking by going
  into rotate mode
• DONT WORRY ABOUT WEIRD GEOMETRY ON THE NEXT
  PROBLEM or STRANGE BOUNDARY CONDITIONS

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Question 1

• (a) Represent the problem1 as DCSP
• Sensor agents as variables
• Values 3 sectors, rotate-mode
• What are the binary constraints?
• (b) What is a solution if Target1 is seen
• by Agent As sector 0 in Problem1?
• Represent as assignment of DCSP values for
  variables
• How many sensors allocated to Target1?

A
B
E
Target2
Target1
G
C
D
Problem 1 Parts a, b
Addition For Part c,d
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Question 1

• (c) If Additions extra sensors and target are
  also present
• Solve the DCSP again (Using the same
  representation you used in Part a, but with
• Sensors E and G added in)
• Report on the results
• Should the problem be solvable in principle?
• (d) Represent the problem in part c as
• a DCOP rather than a DCSP
• Report on the possible optima
• solutions to this DCOP
• Is there any difference from the results
• Obtained via DCSP?

A
B
E
Target2
Target1
G
C
D
Problem 1 Parts a, b
Addition For Part c,d
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Problem 2 RMTDP
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The numbers above each node are referring to
RMTDP evaluations of nodes just one level above
the leaf nodes.
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Node expanded

• As explained in class, numbers such as 3420 are
  obtained by taking the sum of the max of each
  component
• 3420 came about from 84330036
• For how these numbers (84, 3300, 36) are computed
  please refer to the paper

3420
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Question 2

• Which nodes can be pruned and why? Please
  explain.
• (Hint At least one node could be pruned).

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Problem 3 SharedPlans

• One criticism of SharedPlans that Prof. Grosz
  agrees with is that it does not take into account
  uncertainties in the environment.
• Suppose you were to redesign axiom A7 relating to
  intends.that in the sharedplans theory, to enable
  reasoning about uncertainties as well as cost
  (not just cost as presently done)
• Please write down your new Axiom, A7-new.

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Problem 4 Game theory

• Prof. Embat has suggested the following theorem
• Theorem 1 Suppose (P1, P2) in a stochastic
  game are in Nash equilibrium, then for all other
  policies P1
• v1(s, P1, P2) v2(s, P1, P2) gt
• v1(s, P1, P2) v2(s, P1, P2)
• (a) Prove or disprove Prof. Embats theorem.
• (b) If you disprove the theorem, please explain
  if there are special classes of stochastic games
  where the theorem holds OR
• If you prove the theorem, please give an
  example illustrating the concept of the theorem.