Computing & Information Sciences Kansas 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: Course web site: Instructor home page: Reading for Next Class: Section 12.5 – 12.8, Russell & Norvig 2 nd edition Conditional, Continuous, and Multi-Agent Planning Discussion: Agents Revisited

Computing & Information Sciences Kansas 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 (

Computing & Information Sciences Kansas 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 Sciences Kansas State University Wednesday, 25 Oct 2006CIS 490 / 730: Artificial Intelligence

Computing & Information Sciences Kansas State University Wednesday, 25 Oct 2006CIS 490 / 730: Artificial Intelligence

Computing & Information Sciences Kansas State University Wednesday, 25 Oct 2006CIS 490 / 730: Artificial Intelligence

Computing & Information Sciences Kansas State University Wednesday, 25 Oct 2006CIS 490 / 730: Artificial Intelligence

Computing & Information Sciences Kansas State University Wednesday, 25 Oct 2006CIS 490 / 730: Artificial Intelligence

Computing & Information Sciences Kansas 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 abstraction  See: Sections 12.2 – 12.3 R&N, pp. 371 – 380  Figure 12.1, 12.6 (examples), 12.2 (algorithm), (properties)

Computing & Information Sciences Kansas State University Wednesday, 25 Oct 2006CIS 490 / 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

Computing & Information Sciences Kansas 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 Sciences Kansas 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 Sciences Kansas 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 Sciences Kansas State University Wednesday, 25 Oct 2006CIS 490 / 730: Artificial Intelligence Review: Practical Planning Solutions Adapted from slides by S. Russell, UC Berkeley

Computing & Information Sciences Kansas State University Wednesday, 25 Oct 2006CIS 490 / 730: Artificial Intelligence Adapted from slides by S. Russell, UC Berkeley Conditional Planning

Computing & Information Sciences Kansas State University Wednesday, 25 Oct 2006CIS 490 / 730: Artificial Intelligence Monitoring and Replanning

Computing & Information Sciences Kansas State University Wednesday, 25 Oct 2006CIS 490 / 730: Artificial Intelligence Adapted from slides by S. Russell, UC Berkeley Preconditions for Remaining Plan

Computing & Information Sciences Kansas State University Wednesday, 25 Oct 2006CIS 490 / 730: Artificial Intelligence Adapted from slides by S. Russell, UC Berkeley Replanning

Computing & Information Sciences Kansas State University Wednesday, 25 Oct 2006CIS 490 / 730: Artificial Intelligence Making Decisions under Uncertainty Adapted from slides by S. Russell, UC Berkeley

Computing & Information Sciences Kansas 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 = x  P(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(X 1  X 2 )  Probability of the Joint Event X 1  X 2 Independence: P(X 1  X 2 ) = P(X 1 )  P(X 2 )

Computing & Information Sciences Kansas 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 A 1, A 2, …, A n are mutually exclusive and exhaustive  Mutually exclusive: i  j  A i  A j =   Exhaustive:  P(A i ) = 1  Then  Proof: follows from product rule and 3 rd Kolmogorov axiom A B