CS 484 - Artificial Intelligence
Fall 2007
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Homework 6
1) Consider the deterministic grid world shown below with the absorbing goal-state G. Here the immediate rewards are 10 for the labeled transistions and 0 for all unlabeled transitions. (a) Using a random policy (equal probabilities for each action), what are the values of the states after appling the Bellman equation 2 times to each state. Use lambda = 0.8 as the discount value. (b) What are the values of the states using the optimal policy after two iterations with the same discount value?
2) Consider two perceptrons defined by the threshold expression w0 + w1x1 + w2x2 > 0. Perceptron A has weight values
w0 = 1, w1 = 2, w2 = 1
and perceptron B has the weight values
w0 = 0, w1 = 2, w2 = 1
True or False? Perceptron A is more_general_than perceptron B. (Recall more_general_than was defined in lecture 9 and has to do with the number of positive instances.) Explain.
3) Consider a two-layer feedforward ANN with two inputs a and b, one hidden unit c, and one output unit d. This network has five weights (wca, wcb, wc0, wdc, wd0) where wx0 represents the threshold weight for unit x. Initialize these weights to the values (.1, .1, .1, .1, .1), then give their values after each of the first two training iterations of the BACKPROPAGATION algorithm. Assume the learning rate a = .3, and momentum beta = 0.9, incremental weight updates, and the following training examples