Section 1 Computational models of human behavior

brewerobstructionAI and Robotics

Nov 7, 2013 (3 years and 10 months ago)

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Syllabus of

Artificial Intelligence

课程编号:
210014

中文名:人工智能

Category

Optional


P
rerequisite
: Object Oriented Programming, Data Structure

Credit

3


Hours


54
hours

Course Staff: Han Wei

Textbook

Artificial Intelligence: A Modern Approach (First Edition
)


Course Description


T
he course

is a graduate
-
level introduction to artificial intelligence. Topics include:
representation and inference in first
-
order logic; modern deterministic an
d decision
-
theoretic
planning techniques; basic supervised learning methods; and Bayesian network inference
and learning

.

I
t
features

interactive demonstrations

which are intended to stimulate interest and to help
students gain intuition about how artificial intelligence methods work under a variety of
circumstances. An intensified version of the course offers student
s the opportunity to
complete two

kind of abilities

which focus on the application and science aspects of artificial
intelligence.


L
earning objectives

This course introduces students to the basic knowledge representation, problem solving, and
learning me
thods of

artificial intelligence. Upon completion of

artificial intelligence
, students
should be able to: develop intelligent systems by assembling solutions to concrete
computational problems, understand the role of knowledge representation, problem solvi
ng,
and learning in intelligent
-
system engineering, and appreciate the role of problem solving,
vision, and language in understanding human intelligence from a computational perspective.


C
hapter 1

What is Artificial Intelligence (AI)?

(3 hours)

S
ection

1
Computational models of human behavior

Programs that behave (externally) like humans



Computational models of human “thought”

Programs that operate (internally) the way humans do



Computational systems that behave intelligently

What does it mean to behave

intelligently?



Computational systems that behave rationally

More on this later
AI applications
• Monitor trades, detect fraud, schedule shuttle loading, etc.

S
ection 2
Agents



The Agent and the Environment



World Model



Rationality



T
hinking and learning

S
e
ction 3
Classes of Environments



Accessible (vs. Inaccessible)

Can you see the state of the world directly?



Deterministic (vs. Non
-
Deterministic)

Does an action map one state into a single other state?



Static (vs. Dynamic)

Can the world change while yo
u are thinking?



Discrete (vs. Continuous)

Are the percepts and actions discrete (like integers) or continuous (like reals)?

S
ection 4
E
xample:
Backgammon
-
Playing Agent


Homework:

You’re a taxi driver. Your taxi can hold 4 passengers. Passengers pay a

fl
at fee for a ride to the
airport, so goal is to pick up 4 passengers and take them

to the airport in the smallest number of
miles. Your world can be modeled as

a graph of locations with distances between them. Some, but
not all, of the

locations have passe
ngers that you can pick up.

a. Describe the state space of this search problem.

b. What would be a good cost function for this search problem?

c. Now, consider a case where passengers have to pay according to how far

away they are from
the airport when the
y’re picked up (note: they don’t

pay according to how long a ride they take in
your taxi, but according to

the length of the shortest path from their pickup
-
point to the airport).

Describe the state space of this search problem.

d. What would be a good cos
t function for this version of the problem? You

still have a desire to
save gas.

e. Is uniform cost search guaranteed to find the optimal solution in either or

both versions of the
problem? Why or why not?


Chapter 2.


Problem Solving and Search
(6 hours)

S
ection 1
Problem Solving



Agent knows world dynamics



World state is finite, small enough to enumerate



World is deterministic



Utility for a sequence of states is a sum over path



Agent knows current state

We are going to relax the assumption that the ag
ent knows the world dynamics at the very end of
this course, when we talk about learning.

S
ection 2
Example: Route Planning in a Map



A map is a graph where nodes are cities and links are roads. straction of the real world.



Map gives world dynamics: startin
g at city X on the map and taking some road gets to you to
city Y.



If I give you a map that has dots on it, standing for the towns that somebody thought were big
enough to merit a dot, somebody decided that was a good level of abstraction to think about
dr
iving around this place.



World (set of cities) is finite and enumerable.



World is deterministic: taking a given road from a given city leads to only one possible
destination.



Utility for a sequence of states is usually either total distance traveled on t
he path or total
time for the path. • We assume current state is known

S
ection 3
Depth
-
First Search

S
ection 4
Breadth
-
First Search

S
ection 5
Uniform Cost Search

S
ection 6
Example: Traveling Salesman

Homework:

Consider a world with objects A, B, and C. We
’ll look at a logical languge

with constant symbols X, Y , and Z, function symbols f and g, and predicate

symbols p, q, and r. Consider the following interpretation:

• I(X) = A, I(Y ) = A, I(Z) = B

• I(f) = {hA,Bi, hB,Ci, hC,Ci}

• I(p) = {A,B}

I(q) = {C}



I(r) = {hB,Ai, hC,Bi, hC,Ci}

For each of the following sentences, say whether it is true or false in the given

interpretation I:

a. q(f(Z))

b. r(X, Y )

c. w.f (w) = Y

d.w.r(f(w),w)

e.u, v.r(u, v) ! (w.r(u,w) ! v = w)

f. u, v.r(u, v) ! (w.r(w, v) ! u = w)



Chapter 3.



Logic
( 3 hours)

S
ection 1
What is a logic



A formal language



Syntax


what expressions are legal



Semantics


what legal expressions mean



Proof system


a way of manipulating syntactic expressions to get other syntactic expressions
(which w
ill tell us something new)



Why proofs? of inferences an agent might want to make:



Multiple percepts => conclusions about the world



Current state & operator => properties of next state Two kinds Another use of logic would be
that you know something about

the current state of the world and you know something about
the operator that you're considering doing. You wonder what will happen if you take that
action. You have a formal description of what that action does in the world. You might want
to take those
things together and infer something about the next state of the world. So these
are two kinds of inferences that an agent might want to do. We could come up with a lot of
other ones, but those are two good examples to keep in mind.

S
ection 2
Propositional
Logic Syntax

S
ection 3
Semantics

S
ection 4
Terminology

S
ection 5
Models and Entailment

H
omework:

Write the following sentences in first
-
order logic, using S(x) for slow, S(x,y)

to mean that x is slower than y, H(x) for horse, B(x) for brown, and W(x,r)

fo
r horse x winning race r.

1. All brown horses are slow.

2. All slow horses are brown.

3. All slow things are brown horses.

4. Some slow horses are brown.

5. The slowest horse is brown.

6. There is a winner in every race.

Tasks



You are to try two algorithm
s (explained in the next section) on the SAT problem.
Input to the algorithms should be given as a CNF sentence. Output should be the
satisfying assignment, if one is found; if none is found, output an empty assignment.
An assignment is a mapping from prop
ositional variables to boolean values.

1.

(Optional) Brute Force
: You may want to try implementing a brute force
(exhaustive search through the solution space) algorithm before DPLL and
WalkSAT. This is just so you have something that works and can check you
r
answers from the other two algorithms. You do not need to write up anything
for this.

2.

DPLL
: Implement the DPLL algorithm.

3.

WalkSAT
: Implement the WalkSAT algorithm.



Run your algorithms on the test cases below.



Using the random CNF generator given in t
he PL.jar code, run your algorithms on
random CNF sentences of varying length and measure the speed of the two
algorithms.

For this assignment, we present the following SAT instances in text files. Your code should be
able to solve these in reasonable tim
e.

Chapter 4.



Satisfiability and Validity

(3 hours)

Section 1

Satisfiability and Validity

Satisfiable sentence: there exists a truth value assignment for the variables that makes the sentence
true (truth value =
t
).



Algorithm
.
Try all the possible assign
ments to see if one works.



Valid sentence: all truth value assignments for the variables make the sentence true.



Algorithm? • Try all possible assignments and check that they all work. Are there better
algorithms than these?

Section

2
Conjunctive Normal
Form



Converting to CNF



CNF Conversion Example



Simplifying CNF

S
ection 3
Algorithms for Satisfiability



Many problems can be expressed as a list of constraints. Answer is assignment to variables
that satisfy all the constraints.



Examples: • Scheduling people

to work in shifts at a hospital


Some people don’t work at
night


No one can work more than x hours a week


Some pairs of people can’t be on the
same shift


Is there assignment of people to shifts that satisfy all constraints? • Finding bugs
in progra
ms [Daniel Jackson, MIT]


Write logical specification of, e.g. air traffic controller


Write assertion “two airplanes on same runway at same time”


Can these be satisfied
simultaneously?

S
ection 4
Assign and Simplify Example

S
ection 5
Recitation Problem
s

S
ection 6
Natural Deduction

Homework:

1.For each pair of literals below, specify a most general unifier, or indicate

that they are not unifiable.

a. r(f(x), y) and r(z, g(w))

b. r(f(x), x) and r(y, g(y))

c. r(a,C, a) and r(f(x), x, y)

2. Convert each sen
tence below to clausal form.

a. y.x.r(x, y) _ s(x, y)

b. y.( x.r(x, y)) ! p(y)

c. y.x.(r(x, y) ! p(x))


Chapter 5.



First
-
Order Logic
(3 hours)

S
ection 1
First
-
Order Logic



Propositional logic only deals with “facts”, statements that may or may not be true

of the
world, e.g. “It is raining”. , one cannot have variables that stand for books or tables.



In first
-
order logic variables refer to things in the world and, furthermore, you can quantify
over them


to talk about all of them or some of them without h
aving to name them explicitly.



FOL motivation



FOL syntax



FOL Interpretations



Basic FOL Semantics



Semantics of Quantifiers

S
ection 2
FOL

domain and

Example

S
ection 3
writing

FOL


Chapter
6
.



Resolution Theorem Proving: Propositional Logic


(3 hours)

Sectio
n 1
Resolution Theorem Proving: Propositional Logic



Propositional resolution



Propositional theorem proving



Unification

S
ection 2
Proof Strategies

and examples

S
ection 3
Recitation Problems

S
ection 4
First
-
Order Resolution

S
ection 5
Unification

and
Unifi
cation Algorithm

S
ection 6
Unify
-
var subroutine

Chapter
7
.



Resolution Theorem Proving: First Order Logic


(3 hours)

Section 1
Resolution Theorem Proving: First Order Logic



Resolution with variables



Clausal form

S
ection 2
Resolution
-

Converting to Clausa
l Form



Input are sentences in conjunctive normal form with no apparent quantifiers (implicit
universal quantifiers). How do we go from the full range of sentences in FOL, with the full
range of quantifiers, to sentences that enable us to use resolution as
our single inference rule?



We will convert the input sentences into a new normal form called clausal form.

S
ection 3 example

A Silly Recitation Problem

Symbolize the following argument, and then derive the conclusion from the premises using
resolution ref
utation. • Nobody who really appreciates Beethoven fails to keep silence while the
Moonlight sonata is being played. • Guinea pigs are hopelessly ignorant of music. • No one who is
hopelessly ignorant of music ever keeps silence while the moonlight sonata
is being played. •
Therefore, guinea pigs never really appreciate Beethoven.


Chapter
8
.

Planning


(3 hours)

Section 1
Planning

introduction



Planning vs problem solving



Situation calculus



Plan
-
space planning

In the first section of the class, we talked a
bout problem solving, and search in general, then we
did logical representations. The motivation that I gave for doing the problem solving stuff was
that you might have an agent that is trying to figure out what to do in the world, and problem
solving woul
d be a way to do that.

And then we motivated logic by trying to do problem solving in a little bit more general way, but
then we kind of really digressed off into the logic stuff, and so now what I want to do is go back
to a section on planning, which wil
l be the next four lectures.

Now that we know something about search and something about logic, we can talk about how an
agent really could figure out how to behave in the world. This will all be in the deterministic case.
We're still going to assume that

when you take an action in the world, there's only a single possible
outcome. After this, we'll back off on that assumption and spend most of the rest of the term
thinking about what happens when the deterministic assumption goes away.

S
ection 2
Planning
as
problem solving

S
ection 3 Planning as logic

S
ection 4
Planning in Situation Calculus

S
ection 5
Special Properties of Planning



Reducing specific planning problem to general problem of theorem proving is not efficient.



We will be build a more specialized

approach that exploits special properties of planning
problems.



Connect action descriptions and state descriptions [focus searching]



Add actions to a plan in any order



Sub
-
problem independence • Restrict language for describing goals, states and action
s

S
ection 6
Planning Algorithms

S
ection 7
Plan
-
Space Search


Chapter
9
.

Partial
-
Order Planning Algorithms
(3 hours)


section 1
Partial
-
Order Planning Algorithms



Choose Operator



Resolve Threats

S
ection 2
Subgoal Dependence

S
ection 3
Sussman Anomaly

Consider

a world with a push
-
button light switch. Pushing the button

changes the state of the light from on to off, or from off to on.

a. Describe this domain in situation calculus.

b. Describe this domain using one or more
strips
operators.


Chapter 1
0
.

Graph Pla
n
(3 hours)


i
n this section, we moved to highly restricted operator representations, and then the partial
orderplanner, which seemed like a good idea because it would let you do non
-
linear planning; to
put in planned steps in whatever order you wanted to
and hook

them up. And there's something
attractive about the partial
-

order planners.

They seem almost like you might imagine that a person
would go about

planning, right? You put these steps in and then try to fix up the problems, and

it seems kind of app
ealing and intuitive, and so, attractive to people, but they're

really awfully
slow. The structure of the search space is kind of hard to

understand. It's not at all clear how to
apply the things that we learned, say, in

the SAT stuff to partial order plan
ning. It's not clear how
to prune the state

space, how to recognize failures early, all those kinds of things.

Section 1 Mutually Exclusive Actions

Section 2 Solution Extraction

Section 3
Birthday Dinner Example


H
omework:

Draw the graphplan graph for a d
epth
-
two plan given the following operator

descriptions. Starting state is: not have
-
keys, not open, not painted. Goal state

is: open, painted. Show all mutexes.

• Get Keys: (Pre: ) (Eff: have
-
keys)

• Open Door: (Pre: not open) (Eff: open)

• Paint Door: (P
re: not open) (Eff: painted)


Chapter 1
1
.

Planning

Miscellany
(3 hours)


S
ection 1

SAT PLAN

One approach: Extract SAT problem from planninggraph

• Another approach: Make a sentence for depth n,

that has a satisfying assignment iff a plan exists at

depth n

• Variables:


Every proposition at every even depth index:

clean0, garb2


Every action at every odd depth index: cook1

S
ection 2
Constructing SATPLAN sentence

S
ection 3
Planning Assumptions

Section

4
Conditional Planning Example

S
ection 5
Partial Order Con
ditional Plan


S
ection 6
Replanning

• One place where replanning can help is to fill in the steps

in a very high
-
level plan

• Another is to overcome execution errors


Chapter 1
2
.

Probability
(3 hours)

S
ection 1
Foundations of Probability



Logic represents
uncertainty by disjunction



But, cannot tell us how likely the differentconditions are



Probability theory provides a quantitative way of

encoding likelihood

Section 2 Random Variables

Section 3 Joint Distribution

Section 4 Bayes’ Rule

Section 5 Independence

of variables

H
omework:

We would like to compute Pr(a, b|c, d) but we only have available to us

the following quantities: Pr(a), Pr(b), Pr(c), Pr(a|d), Pr(b|d), Pr(c|d), Pr(d|a),

Pr(a, b), Pr(c, d), Pr(a|c, d), Pr(b|c, d), Pr(c|a, b), Pr(d|a, b).

For each
of the assumptions below, give a set of terms that is sufficient to

compute the desired probability, or “none” if it can’t be determined from the

given quantities.

a. A and B are conditionally independent given C and D

b. C and D are conditionally independ
ent given A and B

c. A and B are independent

d. A, B, and C are all conditionally independent given D


Chapter 1
3
.

Bayesian Networks
(6 hours)

section

1
Bayesian Networks



Holmes and Watson in LA



Where do Bayesian Networks Come From?




Learning With Hidden V
ariables



Backward Serial Connection



Diverging Connection



D
-
separation

Section

2
Bayesian (Belief) Networks



Chain Rule



Icy Roads with Numbers



Probability that Watson Crashes

S
ection 3
Inference in Bayesian Networks



Exact inference



Approximate inference



Usin
g the joint distribution

S
ection 4
Variable Elimination Algorithm



Properties of Variable Elimination

S
ection 5
Sampling

H
omework:


1

Following is a list of conditional independence statements. For each statement,name all of the graph
structures, G1


G4,
or “none” that imply it.

a. A is conditionally independent of B given C

b. A is conditionally independent of B given D

c. B is conditionally independent of D given A

d. B is conditionally independent of D given C

e. B is independent of C

f. B is conditiona
lly independent of C given A



2.
In this network, what is the size of the biggest factor that gets generated if

a.
we do variable elimination with elimination order A,B,C,D,E, F, G?

b. Give an elimination order that has a smaller largest factor.


3.
Given
the following data set, what is the maximum likelihood estimate for

Pr(
A
|
B
)?


What result do you get with the Bayesian correction?


Chapter
14
.

Markov Decision Processes
(6 hours)

Markov Decision Processes



• Framework



• Markov chains



•MDPs



• Value iterati
on



• Extensions

Markov Chain



Finding the Best Policy



Computing V*



Big state spaces



Partial Observability


H
omework:


What are the values of the states in the following MDP, assuming

=0
.
9? In order to keep the diagram
for being too complicated, we’ve draw
n the

transition probabilities for action 1 in one figure and the
transition probabilities

for action 2 in another. The rewards for the states are the same in both cases.


Chapter
15
.

Reinforcement Learning

3⁨潵牳


When we talked about MDPs, we assumed t
hat we knew the agent’s reward

function, R, and a model of how the world works, expressed as the transition

probability distribution. In reinforcement learning, we would like an agent to

learn to behave well in an MDP world, but without knowing anything ab
out R

or P when it starts out.


S
ection 1 what will you do without



One option:

estimate R (reward function) and P (transition

function) from data



solve for optimal policy given estimated R and P



Another option:



estimate a value function directly

section

2
Bandit Problems



Bandit Strategies



Q Function

Section

3
Q Learning



Convergence




E
xamples


H
omework:

The Prisoner’s Dilemma is a well
-
known problem in game theory. Two thieves(partners in crime)
are arrested and held in custody separately. The police offe
r

each the same deal. Inform on your
partner and we will reduce your sentence.

The following outcomes and costs are possible:

1. If both you and your partner stay quiet, you will both be convicted of

misdemeanor offenses
(lesser charges). The cost of this
is 10.

2. If you turn state’s evidence (cooperate with the police), you will be convicted

of a misdemeanor
and fined. The cost of this is 50.

If you do not cooperate, but your partner does, you will be convicted of a

felony (a major crime).
The cost of thi
s is 100.

The dilemma is that the best course of action is for both of you to stay

quiet, but since there is no
honor among thieves, you do not trust one another.

Then you both will turn state’s evidence in order to avoid being convicted of

the major crime

(which happens if your partner turns state’s evidence and you

do not).

Consider this twist. Before you are hauled away, you and your partner swear

to keep quiet. You
believe that there is a 60% chance that he will keep his word.

Draw a decision tree that
represents
your decision (to keep quiet or to cooperate)

and the possible outcomes. What decision has the
highest expected value? If x

represents the probability that your partner will keep quiet, for what
value of x

is the value of keeping quiet equal to
the value of cooperating?


执笔人:

韩伟


200
6


5



审定人:

程国达

200
6

6



(
系、部
)
负责人:韩忠愿

200
6

7