Act like people Think rationally

KIK614303

Artificial Intelligence

What is AI?

The science of making machines that:

Think like people

Act like people

Think rationally

Act rationally

Purposes of AI

• To build models of (or

replicate) human cognition

• Psychology, neuroscience, cognitive science: the brain is tricky

• To build useful intelligent artifacts

• Engineering

• To create and understand intelligence as a general property of systems

• Rationality within

computational limitations

Rationality

• Maximally achieving pre-defined goals

• Goals are expressed in terms of the utility of outcomes • Being rational means maximizing your expected utility

History of AI

1940-1950: Early days

1943: McCulloch & Pitts: Boolean circuit model of brain

1950: Turing's “Computing Machinery and Intelligence”

1950—70: Excitement: Look, Ma, no hands!

1950s: Early AI programs, including Samuel's checkers program, Newell & Simon's Logic Theorist, Gelernter's Geometry Engine

1956: Dartmouth meeting: “Artificial Intelligence” adopted

1965: Robinson's complete algorithm for logical reasoning 1966-9: Failure of naïve MT and learning methods

1970—90: Knowledge-based approaches

1969—79: Early development of knowledge-based systems 1980—88: Expert systems industry booms

1988—93: Expert systems industry busts: “AI Winter” 1990—: Statistical approaches

Resurgence of probability, focus on uncertainty General increase in technical depth

Agents and learning systems… “AI Spring”?

Intelligent Agent

• An agent is an entity that

perceives and acts.

• A rational agent selects

actions that maximize its (expected) utility.

• Characteristics of the

percepts, environment, and

action space dictate

Intelligent Agents

• What is an agent?

• What makes an agent rational?

Key points:

• Performance measure

• Actions

• Percept sequence

Agents and Environments

• An agent is anything that can

perceive its environment through

sensors and act upon that

environment through actuators

• Human agent: eyes, ears, and other organs for sensors; hands, legs,

mouth, and other body parts for actuators

• Robotic agent: camera and

microphone for sensors; various motors for actuators

Agent

?

Sensors

Actuators

Environment

Percepts

Environments

•

To design an agent we must specify its

task environment.

•

PEAS description of the task environment:

•

P

erformance

•

E

nvironment

•

A

ctuators

Environment Types

• Fully observable (vs. partially observable): An agent's sensors give it access to the complete state of the environment at each point in time.

• Deterministic (vs. stochastic): The next state of the

environment is completely determined by the current state and the action executed by the agent. (If the environment is

deterministic except for the actions of other agents, then the environment is strategic)

• Episodic (vs. sequential): The agent's experience is divided into atomic "episodes" (each episode consists of the agent

Environment Types

•

Static

(vs. dynamic): The environment is unchanged

while an agent is deliberating. (The environment is

semidynamic

if the environment itself does not

change with the passage of time but the agent's

performance score does)

•

Discrete

(vs. continuous): A limited number of distinct,

clearly defined percepts and actions.

Reflex Agents

• Select action on the basis of only the current percept.

– E.g. the vacuum-agent

• Large reduction in possible percept/action

situations(next page). • Implemented through

condition-action rules

Goal-based Agents

• The agent needs a goal to know which situations are desirable.

– Things become difficult when long

sequences of actions are required to find the goal.

• Typically investigated in search and

planning research.

Learning Agents

• Learning element: introduce improvements in performance element.

– Critic provides feedback on agents

performance based on fixed performance standard.

• Performance element: selecting actions based on percepts.

– Corresponds to the previous agent programs

• Problem generator: suggests actions that will lead to new and informative experiences.

Problem Solving

• It is possible to convert difficult goals into one or more easier-to-achieve subgoals.

• Using the problem-reduction method, you generally recognize goals and convert them into

appropriate subgoals.

Problem Reduction Method

Example Problem

− 5𝑥4

1 − 𝑥2 5 ₂ 𝑑𝑥 I. _𝑥1𝑑𝑥 = ln 𝑥

II. 𝑥𝑛𝑑𝑥 = 𝑥𝑛+1 𝑛+1 III. cos 𝑥 𝑑𝑥 = sin 𝑥

1. −𝑓(𝑥)𝑑𝑥 = − 𝑓(𝑥)𝑑𝑥 2. 𝑐𝑓(𝑥)𝑑𝑥 = 𝑐 𝑓(𝑥)𝑑𝑥 3. 𝑓_𝑖(𝑥) 𝑑𝑥 = 𝑓_𝑖(𝑥)𝑑𝑥 4. 𝑃𝑚(𝑥)

𝑄𝑛_(𝑥) 𝑑𝑥 =

𝑃𝑚 𝑥 𝑑𝑥

𝑄𝑛 𝑥 𝑑𝑥 (m≥n)

A. f(sinx, cosx, tanx, cotx, secx, cscx)

≈ g1(sinx, cosx) ≈ g2(tanx, cscx) ≈

g₃(cotx, secx)

B. 𝑓(𝑡𝑎𝑛𝑥)𝑑𝑥 = 𝑓(𝑦) 1+𝑦2𝑑𝑦

C. 1-x2 _{... x=siny [sin}2_y+cos2_y=1]

D. 1+x2 _{... x=tany [sec}2_y-tan2_y=1]

Depth-First Search

S a b d p a c e p h f r q

q c _G a q e p h f r q

q c _G a S G d b p _q c e h a f r q p h f d b a c e r Strategy: expand a deepest node first

Implementation:

Search Algorithm Properties

• Complete: Guaranteed to find a solution if one exists? • Optimal: Guaranteed to find the least cost path?

• Time complexity? • Space complexity?

• Cartoon of search tree:

• b is the branching factor

• m is the maximum depth

• solutions at various depths

• Number of nodes in entire tree?

• 1 + b + b2 + …. _bm _{= O(b}m₎

… b

1 node b nodes

b2 _nodes

bm _nodes

Depth-First Search (DFS) Properties

… b

1 node b nodes

b2 _nodes

bm _nodes

m tiers

• What nodes DFS expand?

• Some left prefix of the tree.

• Could process the whole tree!

• If m is finite, takes time O(bm₎

• How much space does the fringe

take?

• Only has siblings on path to root, so O(bm)

• Is it complete?

• m could be infinite, so only if we prevent cycles (more later)

• Is it optimal?

• No, it finds the “leftmost”

Breadth-First Search

S a b d p a c e p h f r q

q c _G a q e p h f r q

q c _G a S G d b p _q c e h a f r Search Tiers Strategy: expand a shallowest node first

Implementation:

Breadth-First Search (BFS) Properties

• What nodes does BFS expand?

• Processes all nodes above shallowest solution

• Let depth of shallowest solution be s

• Search takes time O(bs₎

• How much space does the fringe

take?

• Has roughly the last tier, so O(bs₎

• Is it complete?

• s must be finite if a solution exists, so yes!

• Is it optimal?

• Only if costs are all 1 (more on costs later)

… b

1 node b nodes

b2 _nodes

bm _nodes

s tiers

Uniform Cost Search

S a b d p a c e p h f r q

q c _G a q e p h f r q

q c G

a Strategy: expand a

cheapest node first: Fringe is a priority queue (priority: cumulative cost) S G d b p _q c e h a f r

3 9 1

…

Uniform Cost Search (UCS) Properties

• What nodes does UCS expand?

• Processes all nodes with cost less than cheapest solution!

• If that solution costs C* _{and arcs cost at least}  _,

then the “effective depth” is roughly C*/

• Takes time O(bC*/_{) (exponential in effective}

depth)

• How much space does the fringe take?

• Has roughly the last tier, so O(bC*/₎

• Is it complete?

• Assuming best solution has a finite cost and minimum arc cost is positive, yes!

• Is it optimal?

• Yes! (Proof next lecture via A*)

b

C*/

“tiers” c  3

Route Finding Problem

Goal

Start

States

Actions

Flowchart of search algorithms

Initialize queue with the initial state

Is the queue empty?

Is this node a goal?

Remove the first node from the queue

No

Generate children and add them into the queue according to some strategy

No

Yes

Return fail

Yes

Searching with a Search Tree

• Search:

• Expand out potential plans (tree nodes)

• Maintain a frontier of partial plans under consideration

Heuristic Search

Def.:

A search heuristic h(n) is an estimate of the cost of the optimal (cheapest) path from node n to a goal node.

Estimate: h(n1)

Estimate: h(n2)

Estimate: h(n3)

n3

n2 n1

• h can be extended to paths: h(<n₀,…,n_k>)=h(n_k)

A

*

search

•

Idea: avoid expanding paths that are already

expensive

•

The evaluation function

f

(

n

) is the estimated total

cost of the path through node

n

to the goal:

•

f

(

n

)

= g

(

n

)

+ h

(

n

)

• g(n): cost so far to reach n (path cost)

Properties of A*

• Complete?

• Yes – unless there are infinitely many nodes with f(n) ≤ C*

• Optimal?

• Yes

• Time?

• Number of nodes for which f(n) ≤ C*

(exponential)

• Space?

• Exponential

… b …

b

Route Finding

374

253 366

329

A* search example

34

Start: Arad

A* search example

35

Start: Arad

A* search example

36

Start: Arad

A* search example

37

Start: Arad

A* search example

38

Start: Arad

A* search example

39

Start: Arad

A* search example

40

Start: Arad

Remarks : Problem solving by search

Toy Problem

• Toy problems

• Vacuum world

• The N-Queen

• Rubik's cube

• The 8-Puzzle

Real World Problem

• Touring problems

• Route Finding

• Travelling salesperson

• VLSI Layout

• Robot navigation