Computing & Information SciencesKansas State University
Wednesday, 25 Oct 2006CIS 490 / 730: Artificial Intelligence
Lecture 26 of 42
Wednesday. 25 October 2006
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-2006/CIS730
Instructor home page: http://www.cis.ksu.edu/~bhsu
Reading for Next Class:
Section 12.5 – 12.8, Russell & Norvig 2nd edition
Conditional, Continuous, and Multi-Agent PlanningDiscussion: Agents Revisited
Computing & Information SciencesKansas State University
Wednesday, 25 Oct 2006CIS 490 / 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)
Computing & Information SciencesKansas State University
Wednesday, 25 Oct 2006CIS 490 / 730: Artificial Intelligence
Planning and Learning Roadmap
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) Lifetime planning (and learning!)
Formulate new goals
Computing & Information SciencesKansas State University
Wednesday, 25 Oct 2006CIS 490 / 730: Artificial Intelligence
Computing & Information SciencesKansas State University
Wednesday, 25 Oct 2006CIS 490 / 730: Artificial Intelligence
Computing & Information SciencesKansas State University
Wednesday, 25 Oct 2006CIS 490 / 730: Artificial Intelligence
Computing & Information SciencesKansas State University
Wednesday, 25 Oct 2006CIS 490 / 730: Artificial Intelligence
Computing & Information SciencesKansas State University
Wednesday, 25 Oct 2006CIS 490 / 730: Artificial Intelligence
Computing & Information SciencesKansas State University
Wednesday, 25 Oct 2006CIS 490 / 730: Artificial Intelligence
Hierarchical Abstraction Planning:Review
Adapted from Russell and Norvig
Need for Abstraction Question: What is wrong with uniform granularity?
Answers (among many)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 abstractionSee: Sections 12.2 – 12.3 R&N, pp. 371 – 380
Figure 12.1, 12.6 (examples), 12.2 (algorithm), 12.3-5 (properties)
Computing & Information SciencesKansas State University
Wednesday, 25 Oct 2006CIS 490 / 730: Artificial Intelligence
Universal Quantifiers in Planning
Quantification within Operators p. 383 R&N
ExamplesShakey’s World
Blocks World
Grocery shopping
Others (from projects?)
Exercise for Next Tuesday: Blocks World
Computing & Information SciencesKansas State University
Wednesday, 25 Oct 2006CIS 490 / 730: Artificial Intelligence
Practical Planning
Adapted from Russell and Norvig
The Real World What can go wrong with classical planning?
What are possible solution approaches?
Conditional Planning
Monitoring and Replanning (Next Time)
Computing & Information SciencesKansas State University
Wednesday, 25 Oct 2006CIS 490 / 730: Artificial Intelligence
Review:Clobbering and Promotion / Demotion in
Plans
Adapted from slides by S. Russell, UC Berkeley
Computing & Information SciencesKansas State University
Wednesday, 25 Oct 2006CIS 490 / 730: Artificial Intelligence
Review:How Things Go Wrong in Planning
Adapted from slides by S. Russell, UC Berkeley
Computing & Information SciencesKansas State University
Wednesday, 25 Oct 2006CIS 490 / 730: Artificial Intelligence
Review:Practical Planning Solutions
Adapted from slides by S. Russell, UC Berkeley
Computing & Information SciencesKansas State University
Wednesday, 25 Oct 2006CIS 490 / 730: Artificial Intelligence
Adapted from slides by S. Russell, UC Berkeley
Conditional Planning
Computing & Information SciencesKansas State University
Wednesday, 25 Oct 2006CIS 490 / 730: Artificial Intelligence
Monitoring and ReplanningMonitoring and Replanning
Computing & Information SciencesKansas State University
Wednesday, 25 Oct 2006CIS 490 / 730: Artificial Intelligence
Adapted from slides by S. Russell, UC Berkeley
Preconditions for Remaining Plan
Computing & Information SciencesKansas State University
Wednesday, 25 Oct 2006CIS 490 / 730: Artificial Intelligence
Adapted from slides by S. Russell, UC Berkeley
Replanning
Computing & Information SciencesKansas State University
Wednesday, 25 Oct 2006CIS 490 / 730: Artificial Intelligence
Making Decisions under Uncertainty
Adapted from slides by S. Russell, UC Berkeley
Computing & Information SciencesKansas State University
Wednesday, 25 Oct 2006CIS 490 / 730: Artificial Intelligence
Probability:Basic Definitions and Axioms
Sample Space (): Range of a Random Variable X
Probability Measure Pr() denotes a range of “events”; X: Probability Pr, or P, is a measure over 2
In a general sense, Pr(X = x ) is a measure of belief in X = xP(X = x) = 0 or P(X = x) = 1: plain (aka categorical) 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)
1ii
1ii
ji21
XPXP
.XXji,X,X
Computing & Information SciencesKansas State University
Wednesday, 25 Oct 2006CIS 490 / 730: Artificial Intelligence
Basic Formulas for Probabilities
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
BP
BAPB|AP
BAPBP APBAP
i
n
ii APA|BPBP
1
A B