robot 1 Constructing a decision network for the mail delivery 2 - PDF document

CS 486/686 Lecture 13 Evaluating a Decision Network What are the random variables? • If the robot goes on the long route, no accident occurs. Based on the problem description, let’s assume that • A is only afgected by S and not afgected by P. the long route, an accident won’t occur. • S afgects A. If the robot chooses the short route, an accident may occur. If the robot chooses How do the random variables and the decision variables relate to one another? • S: whether the robot chooses the short route. • P: whether the robot puts on pad. What are the decision variables (actions)? • A: whether an accident occurs or not. robot 1 Constructing a decision network for the mail delivery 2 What should the robot do? mail quickly with little/no damage. Unfortunately, the pads add weight and slow the robot down. The robot would like to pick up the pads. This won’t change the probability of an accident, but it will make it less severe if it happens. long route is slower, but on the short route the robot might slip and fall. The robot can put on The robot must choose its route to pickup the mail. There is a short route and a long route. The The Mail Delivery Robot 1 • If the robot goes on the short route, an accident occurs with a fjxed probability q .

CS 486/686 Lecture 13 Evaluating a Decision Network Pads Utility Accident Short Pads Let’s add arcs to the utility node. Which variables directly infmuence the robot’s happiness? Utility 2 Short Accident The decision network so far Here is the defjnition of the robot’s utility function. Let’s make sense of it. P ( A |¬ S ) = 0 The conditional distribution of A given S is P ( A | S ) = q P ( A |¬ S ) = 0 P ( A | S ) = q Answer: All of PS , S and A directly infmuence the robot’s happiness. P ( A |¬ S ) = 0 P ( A | S ) = q

CS 486/686 Lecture 13 Evaluating a Decision Network wearing pads because it’s faster. • When an accident does not happen, the robot prefers the short route over the long one. • When an accident occurs, the robot must have taken the short route. Thus, there is no utility for • When the robot took the short route and an accident occurrs, the robot prefers wearing pads than not wearing pads because pads reduce the severity of damage. 3 How does the robot’s utility/happiness depend on the random variables and the decision variables? State U ( w i ) ¬ P, ¬ S, ¬ A w 0 slow, no weight 6 ¬ P, ¬ S, A w 1 impossible ¬ P, S, ¬ A w 2 quick, no weight 10 ¬ P, S, A w 3 severe damage 0 P, ¬ S, ¬ A w 4 slow, extra weight 4 P, ¬ S, A w 5 impossible P, S, ¬ A w 6 quick, extra weight 8 P, S, A w 7 moderate damage 2 • When an accident does not happen ( w 0 , w 2 , w 4 , w 6 ), the robot prefers not wearing pads than U ( ¬ P ∧ ¬ S ∧ ¬ A ) > U ( P ∧ ¬ S ∧ ¬ A ) U ( ¬ P ∧ S ∧ ¬ A ) > U ( P ∧ S ∧ ¬ A ) U ( P ∧ S ∧ ¬ A ) > U ( P ∧ ¬ S ∧ ¬ A ) U ( ¬ P ∧ S ∧ ¬ A ) > U ( ¬ P ∧ ¬ S ∧ ¬ A ) ¬ P ∧ ¬ S ∧ A and P ∧ ¬ S ∧ A . U ( P ∧ S ∧ A ) > U ( ¬ P ∧ S ∧ A )

CS 486/686 Lecture 13 Evaluating a Decision Network State Accident Short Pads 4 Utility Our fjnal decision network: U ( w i ) ¬ P, ¬ S, ¬ A 6 w 0 slow, no weight ¬ P, ¬ S, A w 1 impossible ¬ P, S, ¬ A 10 w 2 quick, no weight ¬ P, S, A w 3 severe damage 0 P, ¬ S, ¬ A 4 w 4 slow, extra weight P ( A |¬ S ) = 0 P, ¬ S, A w 5 impossible P ( A | S ) = q P, S, ¬ A 8 w 6 quick, extra weight P, S, A w 7 moderate damage 2

CS 486/686 Lecture 13 Evaluating a Decision Network 5 What should the robot do? EU ( ¬ P, ¬ S ) = P ( w 0 |¬ P ∧ ¬ S ) ∗ U ( w 0 ) + P ( w 1 |¬ P ∧ ¬ S ) ∗ U ( w 1 ) = P ( ¬ P ∧ ¬ S ∧ ¬ A |¬ P ∧ ¬ S ) ∗ U ( w 0 ) + P ( ¬ P ∧ ¬ S ∧ A |¬ P ∧ ¬ S ) ∗ U ( w 1 ) = P ( ¬ A |¬ P ∧ ¬ S ) ∗ U ( w 0 ) + P ( A |¬ P ∧ ¬ S ) ∗ U ( w 1 ) = P ( ¬ A |¬ S ) ∗ U ( w 0 ) + P ( A |¬ S ) ∗ U ( w 1 ) =(1)(6) + (0)( − ) =6 EU ( ¬ P, S ) = P ( w 2 |¬ P ∧ S ) ∗ U ( w 2 ) + P ( w 3 |¬ P ∧ S ) ∗ U ( w 3 ) = P ( ¬ P ∧ S ∧ ¬ A |¬ P ∧ S ) ∗ U ( w 2 ) + P ( ¬ P ∧ S ∧ A |¬ P ∧ S ) ∗ U ( w 3 ) = P ( ¬ A |¬ P ∧ S ) ∗ U ( w 2 ) + P ( A |¬ P ∧ S ) ∗ U ( w 3 ) = P ( ¬ A | S ) ∗ U ( w 2 ) + P ( A | S ) ∗ U ( w 3 ) =(1 − q )(10) + ( q )(0) =10 − 10 q

CS 486/686 Lecture 13 Evaluating a Decision Network 6 EU ( P, ¬ S ) = P ( w 4 | P ∧ ¬ S ) ∗ U ( w 4 ) + P ( w 5 | P ∧ ¬ S ) ∗ U ( w 5 ) = P ( P ∧ ¬ S ∧ ¬ A | P ∧ ¬ S ) ∗ U ( w 4 ) + P ( P ∧ ¬ S ∧ A | P ∧ ¬ S ) ∗ U ( w 5 ) = P ( ¬ A | P ∧ ¬ S ) ∗ U ( w 4 ) + P ( A | P ∧ ¬ S ) ∗ U ( w 5 ) = P ( ¬ A |¬ S ) ∗ U ( w 4 ) + P ( A |¬ S ) ∗ U ( w 5 ) =(1)(4) + (0)( − ) =4 EU ( P, S ) = P ( w 6 | P ∧ S ) ∗ U ( w 6 ) + P ( w 7 | P ∧ S ) ∗ U ( w 7 ) = P ( P ∧ S ∧ ¬ A | P ∧ S ) ∗ U ( w 6 ) + P ( P ∧ S ∧ A | P ∧ S ) ∗ U ( w 7 ) = P ( ¬ A | P ∧ S ) ∗ U ( w 6 ) + P ( A | P ∧ S ) ∗ U ( w 7 ) = P ( ¬ A | S ) ∗ U ( w 6 ) + P ( A | S ) ∗ U ( w 7 ) =(1 − q )(8) + ( q )(2) =8 − 6 q 10 8 no pad, long, 6 6 pad, long, 4 4 2 pad, short, 8 − 6 q 0 no pad, short, 10 − 10 q 0 0 . 2 0 . 4 0 . 6 0 . 8 1

CS 486/686 Lecture 13 Evaluating a Decision Network 7 What should the robot do? • If q ≤ 2 / 5 , then wear no pad and go the short route. • If q > 2 / 5 , then wear no pad and go the long route.