final-vpi

CS 188 Spring 2023 Final Review: VPI Q1. Vehicle Perception Indication A vehicle is trying to identify the situation of the world around it using a set of sensors located around the vehicle. Each sensor reading (SRead) is based off of an object’s location (LOC) and an object’s movement (MOVE). The sensor reading will then produce various values for its predicted location (SLoc) and predicted movement (SMove). The user will receive these readings, as well as the the image (IMAGE) as feedback. (a) The vehicle takes an action, and we assign some utility to the action based on the object’s location and movement. Possible actions are MOVE TOWARDS, MOVE AWAY, and STOP. Suppose the decision network faced by the vehicle is the following. (i) Based on the diagram above, which of the following could possibly be true? □ VPI (Image) = 0 □ VPI (SRead) < 0 □ VPI (SMove , SRead) > VPI (SRead) □ VPI (Feedback) = 0 *$ None of the above (ii) Based on the diagram above, which of the following must necessarily be true? □ VPI (Image) = 0 □ VPI (SRead) = 0 □ VPI (SMove , SRead) = VPI (SRead) □ VPI (Feedback) = 0 *$ None of the above 1

Let’s assume that your startup has less money, so we use a simpler sensor network. One possible sensor network can be represented as follows. You have distributions of P (LOC) , P (MOVE) , P ( SRead | LOC , MOVE) , P ( SLoc | SRead ) and utility values U ( a, l, m ). (b) Complete the equation for determining the expected utility for some ACTION a . EU ( a ) = (i) (ii) (iii) U ( a, l, m ) (i) *$ ∑ l P ( l ) *$ ∑ sloc P ( sloc | l ) *$ ∑ l ∑ sloc P ( sloc | l ) *$ 1 (ii) *$ ∑ m P ( m ) *$ ∑ m P ( sloc | m ) *$ ∑ l ∑ m ∑ sloc P ( sloc | l ) P ( sloc | m ) *$ 1 (iii) *$ ∗ ∑ l ∑ m ∑ sloc P ( sloc | l ) P ( sloc | m ) *$ + ∑ l ∑ m ∑ sloc P ( sloc | l ) P ( sloc | m ) *$ + ∑ l ∑ m ∑ sloc P ( sloc | l, m ) P ( l ) P ( m ) *$ ∗ 1 (c) Your colleague Bob invented a new sensor to observe values of SLoc . (i) Suppose that your company had no sensors till this point. Which of the following expression is equivalent to VPI( SLoc )? □ VPI( SLoc ) = ( ∑ sloc P ( sloc ) MEU( SLoc = sloc )) − max a EU( a ) □ VPI( SLoc ) = MEU( SLoc ) − MEU( ∅ ) □ VPI( SLoc ) = max sloc MEU( SLoc = sloc ) − MEU( ∅ ) *$ None of the above (ii) Gaagle, an established company, wants to sell your startup a device that gives you SRead . Given that you already have Bob’s device (that gives you SLoc ), what is the maximum amount of money you should pay for Gaagle’s device? Suppose you value $ 1 at 1 utility. □ VPI( SRead ) □ VPI( SRead ) − VPI( SLoc ) □ VPI( SRead, SLoc ) □ VPI( SRead, SLoc ) − VPI( SLoc ) *$ None of the above 2