CECS 451

Assignment 10

Total: 22 Points

General Instruction

• I recommend you can write your answer using LATEX.

• Submit uncompressed file(s) in the Dropbox folder via BeachBoard (Not email or in

class).

1. Consider the 101 × 3 world shown in Figure 1. In the start state the agent has a choice

of two deterministic actions, Up or Down, but in the other states the agent has one

deterministic action, Right. Assuming a discounted reward function.

(a) (4 points) Compute the utility of each action as a function of γ.

(b) (4 points) Draw the utility of each action for the range 0 ≤ γ ≤ 1 using Matlab of

your familiar numerical analysis software.

(c) (2 points) For γ =

1

2

, which action is recommend? Why?

Figure 1: 101 × 3 world

2. Consider the following data set comprised of three binary input attributes (A1, A2, and

A3) and one binary output:

(a) (2 points) Compute Gain(A1).

(b) (2 points) Compute Gain(A2).

(c) (2 points) Compute Gain(A3).

Figure 2: Example data set

3. (6 points) Consider the XOR function of three binary input attributes (A1, A2, and A3),

which produces the value 1 if and only if an odd number of the three input attributes

has value 1. Draw a minimal-sized decision tree for the three-input XOR function.

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