Consider the $101 \times 3$ world shown in
Figure grid-mdp-figure(b). 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, for what values of the discount $\gamma$ should the agent
choose Up and for which Down? Compute the
utility of each action as a function of $\gamma$. (Note that this simple
example actually reflects many real-world situations in which one must
weigh the value of an immediate action versus the potential continual
long-term consequences, such as choosing to dump pollutants into a
lake.)
Consider the $101 \times 3$ world shown in Figure grid-mdp-figure(b). 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, for what values of the discount $\gamma$ should the agent choose Up and for which Down? Compute the utility of each action as a function of $\gamma$. (Note that this simple example actually reflects many real-world situations in which one must weigh the value of an immediate action versus the potential continual long-term consequences, such as choosing to dump pollutants into a lake.)