Belief-optimal Reasoning for Cyber

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Transcript Belief-optimal Reasoning for Cyber

CS B551: Elements of Artificial
Intelligence
Instructor: Kris Hauser
http://cs.indiana.edu/~hauserk
1
Recap
http://cs.indiana.edu/classes/b551
 Brief history and philosophy of AI
 What is intelligence? Can a machine
act/think intelligently?

• Turing machine, Chinese room
2
Agenda
Agent Frameworks
 Problem Solving and the Heuristic
Search Hypothesis

3
Agent Frameworks
4
Definition of Agent

Anything that:
• Perceives its environment
• Acts upon its environment

A.k.a. controller,
robot
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Definition of “Environment”
The real world, or a virtual world
 Rules of math/formal logic
 Rules of a game
 …
 Specific to the problem domain

6
Agent
Percepts
Sensors
Actions
Actuators
Environment
?
7
Agent
Percepts
Sensors
Actions
Actuators
Environment
?
Sense – Plan – Act
8
“Good” Behavior
Performance measure (aka reward,
merit, cost, loss, error)
 Part of the problem domain

9
Exercise

Formulate the problem domains for:
• Tic-tac-toe
• A web server
• An insect
• A student in B551
• A doctor diagnosing
a patient
• IU’s basketball team
• The U.S.A.
What is/are the:
• Environment
• Percepts
• Actions
• Performance measure
How might a “goodbehaving” agent process
information?
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Types of agents
Simple reflex (aka reactive, rulebased)
 Model-based
 Goal-based
 Utility-based (aka decision-theoretic,
game-theoretic)
 Learning (aka adaptive)

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Simple Reflex
Percept
Interpreter
State
Rules
Action
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Simpl(est) Reflex
State
Observable
Environment
Interpreter
State
Rules
Action
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Simpl(est) Reflex
State
Observable
Environment
Rules
Action
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Rule-based Reflex Agent
A
B
if DIRTY = TRUE then SUCK
else if LOCATION = A then RIGHT
else if LOCATION = B then LEFT
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Model-Based Reflex
Percept
Interpreter
State
Rules
Action
Action
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Model-Based Reflex
Percept
Model
State
Rules
Action
Action
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Model-Based Reflex
Percept
Model
State
State
estimation
Rules
Action
Action
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Model-Based Agent
State:
LOCATION
HOW-DIRTY(A)
Rules:
if LOCATION = A then
if HAS-SEEN(B) = FALSE then RIGHT
HOW-DIRTY(B)
else if HOW-DIRTY(A) > HOW-DIRTY(B) then SUCK
HAS-SEEN(A)
HAS-SEEN(B)
A
else RIGHT
…
B
Model:
HOW-DIRTY(LOCATION) = X
HAS-SEEN(LOCATION) = TRUE
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Model-Based Reflex Agents
Controllers in cars, airplanes,
factories
 Robot obstacle avoidance, visual
servoing

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Goal-Based, Utility-Based
Percept
Model
State
Rules
Action
Action
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Goal- or Utility-Based
Percept
Model
State
Decision Mechanism
Action
Action
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Goal- or Utility-Based
State
Decision Mechanism
Action Generator
Percept Model
Model
Simulated State
Performance tester
Best Action
Action
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Goal-Based Agent
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Big Open Questions:
Goal-Based Agent = Reflex Agent?
Physical Environment
“Mental Environment”
Percept
Model
Mental Model
State
Mental State
DM Rules
Action
Action
Mental Action
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Big Open Questions:
Goal-Based Agent = Reflex Agent?
Physical Environment
“Mental Environment”
Percept
Model
Mental Model
State
Mental State
DM Rules
Action
Action
Mental Action
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With Learning
Percept
Model/Learning
State/Model/DM specs
Decision Mechanism
Action
Action
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Big Open Questions: Learning Agents
The modeling, learning, and decision
mechanisms of artificial agents are
tailored for specific tasks
 Are there general mechanisms for
learning?
 If not, what are the limitations of the
human brain?

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Types of Environments
Observable / non-observable
 Deterministic / nondeterministic
 Episodic / non-episodic
 Single-agent / Multi-agent

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Observable Environments
Percept
Model
State
Decision Mechanism
Action
Action
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Observable Environments
State
Model
State
Decision Mechanism
Action
Action
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Observable Environments
State
Decision Mechanism
Action
Action
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Nondeterministic Environments
Percept
Model
State
Decision Mechanism
Action
Action
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Nondeterministic Environments
Percept
Model
Set of States
Decision Mechanism
Action
Action
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Agents in the bigger picture


Binds disparate fields
(Econ, Cog Sci, OR,
Control theory)
Framework for technical
components of AI
• Components are useful and
rich topics themselves
• Rest of class primarily
studies components

Casting problems in the
framework sometimes
brings insights
Agent
Robotics
Reasoning
Search
Perception
Learning
Knowledge Constraint
rep.
satisfaction
Planning
Natural
language
...
Expert
Systems
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Problem Solving and the
Heuristic Search Hypothesis
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Example: 8-Puzzle
8
2
3
4
5
1
1
2
3
7
4
5
6
6
7
8
Initial state
Goal state
State: Any arrangement of 8 numbered tiles and an empty tile on a 3x3 board
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Successor Function: 8-Puzzle
2
3
4
5
1
6
8
2
7
8
6
3
8
2
3
4
7
3
4
5
1
6
5
1
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SUCC(state)  subset of states
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The successor function is knowledge
about the 8-puzzle game, but it does
not tell us which outcome to use, nor to
which state of the board to apply it.
5
2
7
4
1
6
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Across history, puzzles and games
requiring the exploration of alternatives
have been considered a challenge for
human intelligence:
 Chess originated in Persia and India
about 4000 years ago
 Checkers appear in 3600-year-old
Egyptian paintings
 Go originated in China over 3000 years
ago
So, it’s not surprising that AI uses games
to design and test algorithms
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Exploring Alternatives
Problems that seem to require
intelligence require exploring
multiple alternatives
 Search: a systematic way of
exploring alternatives

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Defining a Search Problem
S
 State space S
 Successor function:
x  S  SUCC(x)  2S
 Initial state s0
 Goal test:
xS  GOAL?(x) =T or F
 Arc cost
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Problem Solving Agent
Algorithm
1. I  sense/read initial state
2. GOAL?  select/read goal test
3. SUCC  select/read successor
function
4. solution  search(I, GOAL?, SUCC)
5. perform(solution)
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State Graph



Each state is
represented by a
distinct node
An arc (or edge)
connects a node s
to a node s’ if
s’  SUCC(s)
The state graph may
contain more than one
connected component
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Solution to the Search Problem




A solution is a path
connecting the initial
node to a goal node
(any one)
The cost of a path is
the sum of the arc
costs along this path
An optimal solution is
a solution path of
minimum cost
There might be
no solution !
G
I
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Pathless Problems




Sometimes the path
doesn’t matter
A solution is any goal
node
Arcs represent
potential state
transformations
E.g. 8-queens,
Simplex for LPs, Map
coloring
G
I
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8-Queens Problem

State repr. 1
• Any nonconflicting
placement of
0-8 queens

State repr. 2
• Any placement
of 8 queens
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Intractability



It may not be
feasible to
construct the
state graph
completely
n-puzzle:
(n+1)! states
k-queens:
kk states
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Heuristic Search Hypothesis
(Newell and Simon, 1976)
“The solutions to problems are represented as symbol
structures. A physical symbol system exercises its intelligence
in problem solving by search - that is, by generating and
progressively modifying symbol structures until it produces a
solution structure.”


Intelligent systems must use heuristic
search to find solutions efficiently
Heuristic: knowledge that is not presented
immediately by the problem specification
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Example

I’ve thought of a number between 1
and 100. Guess it.
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Example

I’ve picked a password between 3
and 8 alphanumeric characters that
I’ll never forget. Guess it.
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Discussion

Debated whether all intelligence is
modifying symbol structures…
• e.g., Elephants don’t play chess, Brooks ’91

But for those tasks that do require
modifying symbol structures,
hypothesis seems true
• Perhaps circular logic?
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Topics of Next 3-4 Classes

Blind Search
• Little or no knowledge about how to
search

Heuristic Search
• How to use heuristic knowledge

Local Search
• With knowledge about goal distribution
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Recap
Agent: a sense-plan-act framework
for studying intelligent behavior
 “Intelligence” lies in sophisticated
components

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Recap

General problem solving framework
• State space
• Successor function
• Goal test
• => State graph

Search is a methodical way of
exploring alternatives
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Homework
Register!
 Readings: R&N Ch. 3.1-3.3

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What is a State?

A compact representation of
elements of the world relevant to
the problem at hand
• Sometimes very clear (logic, games)
• Sometimes not (brains, robotics, econ)
History is a general-purpose state
representation: [p1,a1,p2,a2,…]
 State should capture how history
affects the future

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