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) Compute the utility of each action as a function of γ.
(b) Draw the utility of each action for the range 0 ≤ γ ≤ 1 using Matlab of your familiar numerical analysis software.
(c) For , 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) Compute Gain(A1).
(b) Compute Gain(A2). (c) Compute Gain(A3).
Figure 2: Example data set
3. 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.
