Homework 1 - Problem 3: agents
For example, "psl" (this is not your student id number)
(a) [2 points]
Given a utility function $U$, an agent that achieves the maximum value of $U$ is rational with respect to $U$. Suppose that an agent maximizes a different utility function $U'$ which is guaranteed to be at least as large as $U$. Is this agent rational with respect to $U$? Please prove or give a counterexample.
(b) [1 point]
Suppose I flip a fair coin. You guess either heads or tails and get 1 point if you're correct and 0 points otherwise. If your utility function is the number of points, construct a rational agent. There are many possibilities here, so just choose any one.
(c) [2 points]
Suppose I flip a biased coin with some probability of heads $p$ (this is the real environment), but you don't know the probability. If you guess the outcome of one flip correctly, you gain 1 point and 0 otherwise. So you build a model where the probability of heads is $q$. For which values of $p$ and $q$ is the rational agent based on the model rational in the real-world?
(d) [1 point]
Imagine constructing a very simple
agent to navigate a maze with code that looks like this:
// If there is a wall in front of the robot, turn right in-place.
// Else, move forward
If the agent reaches the goal, it gains 10 points. In which of the following starting locations is the agent
variable represents the state of the block in front of the robot (whether or not its a wall).
* Turning occurs in-place.
* The agent begins facing West in locations A and B, and North in C.
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