This test is open book, open notes. Do **not**
discuss this test with anyone except the professor
until the designated time is up (Friday at 5:00). For
the purposes of planning, it might help to know that I
will be out of town all day on Friday. Assume that
your score is now a 0 and that the only way to get points
is to demonstrate your knowledge. Show your work!

**1.**
You are going to design a game playing system and have
decided to use reinforcement learning to train it. For
training purposes you have several options with regard
to an opponent. One option is an opponent that plays
randomly. A second option is an opponent that uses
a fixed strategy (i.e. doesn't learn during training).
There are several fixed strategies to choose from,
corresponding to opponents that play at very high levels,
average levels, and poor levels of play. Discuss how your
choice of opponent is likely to impact the following:

a) Convergence speed. Defined as the number of training epochs required for the agent's average performance to reach some given level of performance against its training opponent.

b) Exploration. Defined as the percentage of possible states that the agent visits before convergence.

c) Performance against a new opponent with unknown capabilities.

d) Performance against the best possible opponent.

**2.**A "perfectly imperfect" heuristic is one that is admissible,
but the inverse of the perfect heuristic. A perfect heuristic
would optimally rank the nodes on the open list and
always choose the best one. A "perfectly imperfect" heuristic,
on the other hand, will order the nodes in exactly the opposite
fashion. Assume that all paths lead to a solution, but
no two paths have the same solution depth. Describe the
performance of A* with the given heuristic.

**3.**A **beam** search is a kind of breadth-first
search where the number of nodes expanded at each level is
limited to some user-defined number **n**. The nodes are
chosen according to the h() function. What would be the relative
advantage of beam search versus depth-first and breadth-first
search? Analyze beam search in terms of time and space
complexity, as well as the guarantees it makes with regard
to finding a solution if one exists, and finding optimal
solutions.

**4.** We have defined four different binary logical
connectives.

a) Are there any others that might be useful?

b) How many binary connectives can there possibly be?

c) Why are some of them not very useful?

**5.** Write down George W. Bush's complete knowledge
base. Show formally that Alec Baldwin will move to Canada
if Bush wins the election.

**6.**

**7.**