NAME:
SID#:
Login:
Sec:
1
CS 188
Introduction to
Spring 2006
Artifcial Intelligence
Practice Final Sol’ns
1. (20 points.)
True/False
Each problem is worth 2 points. Incorrect answers are worth 0 points. Skipped questions are worth 1 point.
(a)
True/False
: All MDPs can be solved using expectimax search.
False.
MDPs with self loops lead to inFnite expectimax trees. Unlike search problems, this issue cannot
be addressed with a graphsearch variant.
(b)
True/False
: There is some single Bayes’ net structure over three variables which can represent any prob
ability distribution over those variables.
True.
A fully connected Bayes’ net can represent any joint distribution.
(c)
True/False
: Any rational agent’s preferences over outcomes can be summarized by a single real valued
utility function over those outcomes.
True.
Any set of preferences which conform to the six constraints on rational preferences (orderability,
transitivity, continuity, substitutability, monotonicity, decomposability) can be summarized by a single,
realvalued function.
(d)
True/False
: Temporal di±erence learning of optimal utility values (U) requires knowledge of the transition
probability tables (T).
Mostly True.
Temporal di±erence learning is a modelless learning technique that requires only example
state sequences to learn the utilities for a Fxed policy. However, to derive the best policy from those
utilities, which would be required to Fnd the optimal utility values, we would need to compute
π
(
s
) = arg max
a
±
s
±
T
(
s,a,s
±
)
U
(
s
±
)
which of course includes a transition probability. The solution reads “mostly” true because the optimal
utility values could be found without the transition probabilities if the agent were also supplied with the
optimal policy. In practice, we could also estimate the transition probabilities from the training data
(using maximumlikelihood estimates, for example), so they need not necessarily be known in advance.
NOTE:
This solution was updated since the review session.
(e)
True/False
: Pruning nodes from a decision tree may have no e±ect on the resulting classiFer.
True.
Trivially, a decision tree may have branches that are unreachable. ²urthermore, splits in the
decision tree may also reFne
P
(
class
), but have no e±ect in practice because of rounding. Imagine a leaf
has 10 true, 3 false, and splits to 5/2 and 5/1 – you’ll still guess true on each branch, but the split is
reFning the conditional probabilities.
NOTE:
This solution was updated since the review session.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document2
2. (20 points.)
Search
Consider the following search problem formulation:
States
: 16 integer coordinates, (
x,y
)
∈
[1
,
4]
×
[1
,
4]
Initial state
: (1
,
1)
Successor function
: The successor function generates 2 states with diFerent
y
coordinates
Goal test
: (4
,
4) is the only goal state
Step cost
: The cost of going from one state to another is the Euclidean distance between the points
We can specify a state space by drawing a graph with directed edges from each state to its successors:
1
2
3
4
1
2
3
4
x
y
Uninformed Search
Consider the performance of D±S, B±S, and UCS on the state space above. Order
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '10
 AliceOh
 Artificial Intelligence, Conditional Probability, Manhattan, Rclean, Rwait

Click to edit the document details