computing & information sciences kansas state university wednesday, 15 oct 2008cis 530 / 730:...

Computing & Information SciencesKansas State University

Wednesday, 15 Oct 2008CIS 530 / 730: Artificial Intelligence

Lecture 20 of 42

Wednesday, 15 October 2008

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-2008/CIS730

Instructor home page: http://www.cis.ksu.edu/~bhsu

Reading for Next Class:

Section 12.1 – 12.4, Russell & Norvig 2nd edition

HTN Planning and Robust PlanningDiscussion: CSP & Game Trees Review



Constraint satisfaction problems (CSPs):Review

Constraint satisfaction problems (CSPs):Review

Standard search problem: state is a "black box“ – any data structure that supports successor function, heuristic

function, and goal test CSP:

state is defined by variables Xi with values from domain Di

goal test is a set of constraints specifying allowable combinations of values for subsets of variables

Simple example of a formal representation language

Allows useful general-purpose algorithms with more power than standard search algorithms

© 2004 S. J. RussellFrom: http://aima.eecs.berkeley.edu/slides-ppt/ Reused with permission.



Constraint graph:Review

Constraint graph:Review

Binary CSP: each constraint relates two variables Constraint graph: nodes are variables, arcs are constraints




Standard search formulation:Review

Standard search formulation:Review

Let's start with the straightforward approach, then fix it

States are defined by the values assigned so far

Initial state: the empty assignment { } Successor function: assign a value to an unassigned variable that does not conflict with

current assignment fail if no legal assignments

Goal test: the current assignment is complete

1. This is the same for all CSPs2. Every solution appears at depth n with n variables

use depth-first search3. Path is irrelevant, so can also use complete-state formulation4. b = (n - l )d at depth l, hence n! · dn leaves

5.




Arc consistency algorithm AC-3:Review

Arc consistency algorithm AC-3:Review

Time complexity: O(n2d3)




Local search for CSPsLocal search for CSPs

Hill-climbing, simulated annealing typically work with "complete" states, i.e., all variables assigned

To apply to CSPs: allow states with unsatisfied constraints operators reassign variable values

Variable selection: randomly select any conflicted variable

Value selection by min-conflicts heuristic: choose value that violates the fewest constraints i.e., hill-climb with h(n) = total number of violated constraints




Alpha-Beta (-) Pruning:Modified Minimax Algorithm

Adapted from slides by S. RussellUC Berkeley



Expectiminimax [1]



Expectiminimax [2]



Expectiminimax [3]



Expectiminimax [4]



Lecture Outline

Today’s Reading: Sections 11.4 – 11.7, 12.1 – 12.4, R&N 2e

Today and Wednesday: Practical Planning Conditional Planning

Replanning

Monitoring and Execution

Continual Planning

Wednesday: Hierarchical Planning Revisited Examples: Korf

Real-World Example

Friday: Robust Planning, Uncertainty, Planning-Like Problems Planning-like problems: design; scheduling; tutoring, critiquing

Why probability?

Planning and reaction

Planning under Uncertainty



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



Review: Clobbering andPromotion / Demotion

Adapted from slides by S. Russell, UC Berkeley



Review:POP Example – Sussman Anomaly




Hierarchical Abstraction Planning

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)



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



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)



Review:How Things Go Wrong in Planning



Review:Practical Planning Solutions




Conditional Planning




Monitoring and ReplanningMonitoring and Replanning




Preconditions for Remaining Plan




Replanning




Summary Points

Previously: Logical Representations and Theorem Proving Propositional, predicate, and first-order logical languages

Proof procedures: forward and backward chaining, resolution refutation

Today: Introduction to Classical Planning Search vs. planning

STRIPS axiomsOperator representation

Components: preconditions, postconditions (ADD, DELETE lists)

Friday: Robust Planning, Uncertainty, Planning-Like Problems Planning-like problems: design; scheduling; tutoring, critiquing

Why probability?

Planning and reaction

Planning under Uncertainty



Terminology

Classical Planning Planning versus search

Problematic approaches to planningForward chaining

Situation calculus

Representation Initial state

Goal state / test

Operators

Efficient Representations STRIPS axioms

Components: preconditions, postconditions (ADD, DELETE lists)

Clobbering / threatening

Reactive plans and policies

Markov decision processes

computing & information sciences kansas state university wednesday, 15 oct 2008cis 530 / 730:...

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