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Lecture 26 of 42. Conditional, Continuous, and Multi-Agent Planning Discussion: Probability Refresher. Wednesday. 24 October 2007 William H. Hsu Department of Computing and Information Sciences, KSU KSOL course page: http://snipurl.com/v9v3

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Lecture 26 of 42

Conditional, Continuous, and Multi-Agent Planning

Discussion: Probability Refresher

Wednesday. 24 October 2007

William H. Hsu

Department of Computing and Information Sciences, KSU

KSOL course page: http://snipurl.com/v9v3

Course web site: http://www.kddresearch.org/Courses/Fall-2007/CIS730

Section 12.5 – 12.8, Russell & Norvig 2nd edition

CIS 530 / 730: Artificial Intelligence

Lecture Outline

• Today’s Reading: Sections 12.1 – 12.4, R&N 2e
• Friday’s Reading: Sections 12.5 – 12.8, R&N 2e
• Today: Practical Planning, concluded
• Conditional Planning
• Replanning
• Monitoring and Execution
• Continual Planning
• Hierarchical Planning Revisited
• Examples: Korf
• Real-World Example
• Friday and Next Week: Reasoning under Uncertainty
• Basics of reasoning under uncertainty
• Probability review
• BNJ interface (http://bnj.sourceforge.net)

CIS 530 / 730: Artificial Intelligence

• Bounded Indeterminacy (12.3)
• Four Techniques for Dealing with Nondeterministic Domains
• 1. Sensorless/Conformant Planning: “Be Prepared” (12.3)
• Idea: be able to respond to any situation (universal planning)
• Coercion
• 2. Conditional / Contingency Planning: “Plan B” (12.4)
• Idea: be able to respond to many typical alternative situations
• Actions for sensing (“reviewing the situation”)
• 3. Execution Monitoring / Replanning: “Show Must Go On” (12.5)
• Idea: be able to resume momentarily failed plans
• Plan revision
• 4. Continuous Planning: “Always in Motion, The Future Is” (12.6)
• Formulate new goals

CIS 530 / 730: Artificial Intelligence

Hierarchical Abstraction Planning:Review

• Need for Abstraction
• Question: What is wrong with uniform granularity?
• Representational problems
• Inferential problems: inefficient plan synthesis
• Family of Solutions: Abstract Planning
• But what to abstract in “problem environment”, “representation”?
• Objects, obstacles (quantification: later)
• Assumptions (closed world)
• Other entities
• Operators
• Situations
• Hierarchical abstraction
• See: Sections 12.2 – 12.3 R&N, pp. 371 – 380
• Figure 12.1, 12.6 (examples), 12.2 (algorithm), 12.3-5 (properties)

CIS 530 / 730: Artificial Intelligence

Universal Quantifiers in Planning

• Quantification within Operators
• p. 383 R&N
• Examples
• Shakey’s World
• Blocks World
• Grocery shopping
• Others (from projects?)
• Exercise for Next Tuesday: Blocks World

CIS 530 / 730: Artificial Intelligence

Practical Planning

• The Real World
• What can go wrong with classical planning?
• What are possible solution approaches?
• Conditional Planning
• Monitoring and Replanning (Next Time)

CIS 530 / 730: Artificial Intelligence

Review:How Things Go Wrong in Planning

Adapted from slides by S. Russell, UC Berkeley

CIS 530 / 730: Artificial Intelligence

Review:Practical Planning Solutions

Adapted from slides by S. Russell, UC Berkeley

CIS 530 / 730: Artificial Intelligence

Conditional Planning

Adapted from slides by S. Russell, UC Berkeley

CIS 530 / 730: Artificial Intelligence

Monitoring and Replanning

CIS 530 / 730: Artificial Intelligence

Preconditions for Remaining Plan

Adapted from slides by S. Russell, UC Berkeley

CIS 530 / 730: Artificial Intelligence

Replanning

Adapted from slides by S. Russell, UC Berkeley

CIS 530 / 730: Artificial Intelligence

Making Decisions under Uncertainty

Adapted from slides by S. Russell, UC Berkeley

CIS 530 / 730: Artificial Intelligence

Sample Space (): Range of a Random Variable X

• Probability Measure Pr()
•  denotes a range of “events”; X: 
• ProbabilityPr, or P, is a measure over 2
• In a general sense, Pr(X = x  ) is a measure of belief in X = x
• P(X = x) = 0 or P(X = x) = 1: plain (akacategorical) beliefs (can’t be revised)
• All other beliefs are subject to revision
• Kolmogorov Axioms
• 1. x  . 0  P(X = x)  1
• 2. P() x  P(X = x) = 1
• 3.
• Joint Probability: P(X1X2)  Probability of the Joint Event X1X2
• Independence: P(X1X2) = P(X1)  P(X2)

Probability:Basic Definitions and Axioms

CIS 530 / 730: Artificial Intelligence

Product Rule (Alternative Statement of Bayes’s Theorem)

• Proof: requires axiomatic set theory, as does Bayes’s Theorem
• Sum Rule
• Sketch of proof (immediate from axiomatic set theory)
• Draw a Venn diagram of two sets denoting events A and B
• Let A B denote the event corresponding to A B…
• Theorem of Total Probability
• Suppose events A1, A2, …, An are mutually exclusive and exhaustive
• Mutually exclusive: i j Ai Aj =
• Exhaustive:  P(Ai) = 1
• Then
• Proof: follows from product rule and 3rd Kolmogorov axiom

Basic Formulas for Probabilities

A

B

CIS 530 / 730: Artificial Intelligence