AI Planning Coordinates - gki.informatik.uni-freiburg.de
Transcript of AI Planning Coordinates - gki.informatik.uni-freiburg.de
AI Planning
Coordinates
Introduction
Principles of AI Planning
Dr. Jussi Rintanen
Albert-Ludwigs-Universität Freiburg
Summer term 2005
AI Planning
CoordinatesLectures
Exercises
Introduction
Course: Principles of AI Planning
Lecturer
Dr Jussi Rintanen ([email protected])
Lecture
Monday 2-4pm, Wednesday 2-3pm in SR 101-01-009/13No lecture on May 16 & 18 (Pentecost)www.informatik.uni-freiburg.de/~ki/teaching/ss05/aip/
Text
Complete lecture notes are available on the web page asthe course proceeds.
AI Planning
CoordinatesLectures
Exercises
Introduction
Exercises and Examination
Exercises
assistant: Marco Ragni ([email protected])Wednesday 3pm after lecture (not on May 18: Pentecost)Assignments are given out on Wednesday, returned onMonday.
Examination
Takes place either in July or in September (exact date to bedetermined).grade: 0.85× exam +0.15× exercises
AI Planning
Coordinates
IntroductionProblem classes
Nondeterminism
Observability
Objectives
vs. Game Theory
Summary
What is planning?
Intelligent decision making: What actions to take?
general-purpose problem representation
algorithms for solving any problem expressible in therepresentationapplication areas:
high-level planning for intelligent robotsautonomous systems: NASA Deep Space One, ...problem-solving (single-agent games like Rubik’s cube)
AI Planning
Coordinates
IntroductionProblem classes
Nondeterminism
Observability
Objectives
vs. Game Theory
Summary
Why is planning difficult?
Solutions to simplest planning problems are paths froman initial state to a goal state in the transition graph.Efficiently solvable e.g. by Dijkstra’s algorithm inO(n log n) time.Why don’t we solve all planning problems this way?
State spaces may be huge: 109, 1012, 1015, . . . states.Constructing the transition graph and using e.g.Dijkstra’s algorithm is not feasible!!
Planning algorithms try to avoid constructing the wholegraph.
Planning algorithms often are – but are not guaranteedto be – more efficient than the obvious solution methodof constructing the transition graph + running e.g.Dijkstra’s algorithm.
AI Planning
Coordinates
IntroductionProblem classes
Nondeterminism
Observability
Objectives
vs. Game Theory
Summary
Why is planning difficult?
Solutions to simplest planning problems are paths froman initial state to a goal state in the transition graph.Efficiently solvable e.g. by Dijkstra’s algorithm inO(n log n) time.Why don’t we solve all planning problems this way?
State spaces may be huge: 109, 1012, 1015, . . . states.Constructing the transition graph and using e.g.Dijkstra’s algorithm is not feasible!!
Planning algorithms try to avoid constructing the wholegraph.
Planning algorithms often are – but are not guaranteedto be – more efficient than the obvious solution methodof constructing the transition graph + running e.g.Dijkstra’s algorithm.
AI Planning
Coordinates
IntroductionProblem classes
Nondeterminism
Observability
Objectives
vs. Game Theory
Summary
Why is planning difficult?
Solutions to simplest planning problems are paths froman initial state to a goal state in the transition graph.Efficiently solvable e.g. by Dijkstra’s algorithm inO(n log n) time.Why don’t we solve all planning problems this way?
State spaces may be huge: 109, 1012, 1015, . . . states.Constructing the transition graph and using e.g.Dijkstra’s algorithm is not feasible!!
Planning algorithms try to avoid constructing the wholegraph.
Planning algorithms often are – but are not guaranteedto be – more efficient than the obvious solution methodof constructing the transition graph + running e.g.Dijkstra’s algorithm.
AI Planning
Coordinates
IntroductionProblem classes
Nondeterminism
Observability
Objectives
vs. Game Theory
Summary
Why is planning difficult?
Solutions to simplest planning problems are paths froman initial state to a goal state in the transition graph.Efficiently solvable e.g. by Dijkstra’s algorithm inO(n log n) time.Why don’t we solve all planning problems this way?
State spaces may be huge: 109, 1012, 1015, . . . states.Constructing the transition graph and using e.g.Dijkstra’s algorithm is not feasible!!
Planning algorithms try to avoid constructing the wholegraph.
Planning algorithms often are – but are not guaranteedto be – more efficient than the obvious solution methodof constructing the transition graph + running e.g.Dijkstra’s algorithm.
AI Planning
Coordinates
IntroductionProblem classes
Nondeterminism
Observability
Objectives
vs. Game Theory
Summary
Different classes of problems
actions deterministic nondeterministicprobabilities no yesobservability full partialhorizon finite infinite...
1 classical planning2 conditional planning with full/partial observability3 Markov decision processes (MDP)4 partially observable MDPs (POMDP)
AI Planning
Coordinates
IntroductionProblem classes
Nondeterminism
Observability
Objectives
vs. Game Theory
Summary
Different classes of problems
actions deterministic nondeterministicprobabilities no yesobservability full partialhorizon finite infinite...
1 classical planning2 conditional planning with full/partial observability3 Markov decision processes (MDP)4 partially observable MDPs (POMDP)
AI Planning
Coordinates
IntroductionProblem classes
Nondeterminism
Observability
Objectives
vs. Game Theory
Summary
Different classes of problems
actions deterministic nondeterministicprobabilities no yesobservability full partialhorizon finite infinite...
1 classical planning2 conditional planning with full/partial observability3 Markov decision processes (MDP)4 partially observable MDPs (POMDP)
AI Planning
Coordinates
IntroductionProblem classes
Nondeterminism
Observability
Objectives
vs. Game Theory
Summary
Different classes of problems
actions deterministic nondeterministicprobabilities no yesobservability full partialhorizon finite infinite...
1 classical planning2 conditional planning with full/partial observability3 Markov decision processes (MDP)4 partially observable MDPs (POMDP)
AI Planning
Coordinates
IntroductionProblem classes
Nondeterminism
Observability
Objectives
vs. Game Theory
Summary
Different classes of problems
actions deterministic nondeterministicprobabilities no yesobservability full partialhorizon finite infinite...
1 classical planning2 conditional planning with full/partial observability3 Markov decision processes (MDP)4 partially observable MDPs (POMDP)
AI Planning
Coordinates
IntroductionProblem classes
Nondeterminism
Observability
Objectives
vs. Game Theory
Summary
Different classes of problems
actions deterministic nondeterministicprobabilities no yesobservability full partialhorizon finite infinite...
1 classical planning2 conditional planning with full/partial observability3 Markov decision processes (MDP)4 partially observable MDPs (POMDP)
AI Planning
Coordinates
IntroductionProblem classes
Nondeterminism
Observability
Objectives
vs. Game Theory
Summary
Properties of the world: nondeterminism
Deterministic world/actionsAction and current state uniquely determine the successorstate.
Nondeterministic world/actionsFor an action and a current state there may be severalsuccessor states.
Analogy: deterministic versus nondeterministic automata
AI Planning
Coordinates
IntroductionProblem classes
Nondeterminism
Observability
Objectives
vs. Game Theory
Summary
NondeterminismExample
Moving objects with an unreliable robotic hand: move thegreen block onto the blue block.
p = 0.9
p = 0.1
AI Planning
Coordinates
IntroductionProblem classes
Nondeterminism
Observability
Objectives
vs. Game Theory
Summary
Properties of the world: observability
Full observability
Observations/sensing allow to determine the current stateof the world uniquely.
Partial observability
Observations/sensing allow to determine the current stateof the world only partially: we only know that the currentstate is one of several of possible ones.Consequence: It is necessary to represent the knowledgean agent has.
AI Planning
Coordinates
IntroductionProblem classes
Nondeterminism
Observability
Objectives
vs. Game Theory
Summary
What difference does observability make?
Camera A Camera B
Goal
AI Planning
Coordinates
IntroductionProblem classes
Nondeterminism
Observability
Objectives
vs. Game Theory
Summary
Different objectives
1 Reach a goal state.Example: Earn 500 euro.
2 Stay in goal states indefinitely (infinite horizon).Example: Never allow the bank account balance to benegative.
3 Maximize the probability of reaching a goal state.Example: To be able to finance buying a house by 2015study hard and save money.
4 Collect the maximal expected rewards / minimalexpected costs (infinite horizon).Example: Maximize your future income.
5 ...
AI Planning
Coordinates
IntroductionProblem classes
Nondeterminism
Observability
Objectives
vs. Game Theory
Summary
Different objectives
1 Reach a goal state.Example: Earn 500 euro.
2 Stay in goal states indefinitely (infinite horizon).Example: Never allow the bank account balance to benegative.
3 Maximize the probability of reaching a goal state.Example: To be able to finance buying a house by 2015study hard and save money.
4 Collect the maximal expected rewards / minimalexpected costs (infinite horizon).Example: Maximize your future income.
5 ...
AI Planning
Coordinates
IntroductionProblem classes
Nondeterminism
Observability
Objectives
vs. Game Theory
Summary
Different objectives
1 Reach a goal state.Example: Earn 500 euro.
2 Stay in goal states indefinitely (infinite horizon).Example: Never allow the bank account balance to benegative.
3 Maximize the probability of reaching a goal state.Example: To be able to finance buying a house by 2015study hard and save money.
4 Collect the maximal expected rewards / minimalexpected costs (infinite horizon).Example: Maximize your future income.
5 ...
AI Planning
Coordinates
IntroductionProblem classes
Nondeterminism
Observability
Objectives
vs. Game Theory
Summary
Different objectives
1 Reach a goal state.Example: Earn 500 euro.
2 Stay in goal states indefinitely (infinite horizon).Example: Never allow the bank account balance to benegative.
3 Maximize the probability of reaching a goal state.Example: To be able to finance buying a house by 2015study hard and save money.
4 Collect the maximal expected rewards / minimalexpected costs (infinite horizon).Example: Maximize your future income.
5 ...
AI Planning
Coordinates
IntroductionProblem classes
Nondeterminism
Observability
Objectives
vs. Game Theory
Summary
Different objectives
1 Reach a goal state.Example: Earn 500 euro.
2 Stay in goal states indefinitely (infinite horizon).Example: Never allow the bank account balance to benegative.
3 Maximize the probability of reaching a goal state.Example: To be able to finance buying a house by 2015study hard and save money.
4 Collect the maximal expected rewards / minimalexpected costs (infinite horizon).Example: Maximize your future income.
5 ...
AI Planning
Coordinates
IntroductionProblem classes
Nondeterminism
Observability
Objectives
vs. Game Theory
Summary
Relation to games and game theory
Game theory addresses decision making in multi-agentsetting: “Assuming that the other agents are intelligent,what do I have to do to achieve my goals?”
Game theory is related to multi-agent planning.
In this course we concentrate on single-agent planning.In certain special cases our techniques are applicableto multi-agent planning:
Finding a winning strategy of a game (example: chess).In this case it is not necessary to distinguish betweenan intelligent opponent and a randomly behavingopponent.
Game theory in general is about optimal strategieswhich do not necessarily guarantee winning. Forexample card games like poker do not have a winningstrategy.
AI Planning
Coordinates
IntroductionProblem classes
Nondeterminism
Observability
Objectives
vs. Game Theory
Summary
Relation to games and game theory
Game theory addresses decision making in multi-agentsetting: “Assuming that the other agents are intelligent,what do I have to do to achieve my goals?”
Game theory is related to multi-agent planning.
In this course we concentrate on single-agent planning.In certain special cases our techniques are applicableto multi-agent planning:
Finding a winning strategy of a game (example: chess).In this case it is not necessary to distinguish betweenan intelligent opponent and a randomly behavingopponent.
Game theory in general is about optimal strategieswhich do not necessarily guarantee winning. Forexample card games like poker do not have a winningstrategy.
AI Planning
Coordinates
IntroductionProblem classes
Nondeterminism
Observability
Objectives
vs. Game Theory
Summary
Relation to games and game theory
Game theory addresses decision making in multi-agentsetting: “Assuming that the other agents are intelligent,what do I have to do to achieve my goals?”
Game theory is related to multi-agent planning.
In this course we concentrate on single-agent planning.In certain special cases our techniques are applicableto multi-agent planning:
Finding a winning strategy of a game (example: chess).In this case it is not necessary to distinguish betweenan intelligent opponent and a randomly behavingopponent.
Game theory in general is about optimal strategieswhich do not necessarily guarantee winning. Forexample card games like poker do not have a winningstrategy.
AI Planning
Coordinates
IntroductionProblem classes
Nondeterminism
Observability
Objectives
vs. Game Theory
Summary
Prerequisites of the course
1 basics of AI (you have attended an introductory courseon AI)
2 basics of propositional logic
AI Planning
Coordinates
IntroductionProblem classes
Nondeterminism
Observability
Objectives
vs. Game Theory
Summary
What do you learn in this course?
1 Classification of different problems to different classes1 Classification according to observability,
nondeterminism, goal objectives, ...2 complexity
2 Techniques for solving different problem classes1 algorithms based on heuristic search2 algorithms based on satisfiability testing (SAT)3 algorithms based on exhaustive search with logic-based
data structures
Many of these techniques are applicable to problemsoutside AI as well.