HW2.pdf - Homework 2 ELEN E6885 Reinforcement Learning Problem 1(n-Step Return 15 Credits The expected value of all n-step returns is guaranteed to

HW2.pdf - Homework 2 ELEN E6885 Reinforcement Learning...

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Homework 2 ELEN E6885: Reinforcement Learning November 15, 2018 Problem 1 ( n -Step Return, 15 Credits ) The expected value of all n -step returns is guaranteed to improve in a certain way over the current value function as an approximation to the true value function. Prove the following error reduction property of n-step returns max s E π n R ( n ) t s t = s o - V π ( s ) γ n max s V ( s ) - V π ( s ) , where R ( n ) t is n -step return at time t . Problem 2 ( Value-Based RL, 20 Credits ) Consider the small corridor gridworld shown in Fig. 1 below. S and G represents the start and goal (terminal) states, respectively. In each of the two non-terminal states there are only two actions, right and left . These actions have their usual consequences in the start state (left causes no movement in the first state), but in the second state they are reversed, so that right moves to the left and left moves to the right. The reward is - 1 per step as usual. We approximate the action-value function using two features x 1 ( s, a ) = 1 ( a = right ) and x 2 ( s, a ) = 1 ( a = left
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