Principles of AI Planning
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1 Principles of Dr. Jussi Rintanen Albert-Ludwigs-Universität Freiburg Summer term 2005
2 Course: Principles of Lecturer Dr Jussi Rintanen Lecture Monday 2-4pm, Wednesday 2-3pm in SR /13 No lecture on May 16 & 18 (Pentecost) Lectures Exercises Text Complete lecture notes are available on the web page as the course proceeds.
3 Exercises and Examination Exercises assistant: Marco Ragni Wednesday 3pm after lecture (not on May 18: Pentecost) Assignments are given out on Wednesday, returned on Monday. Lectures Exercises Examination Takes place either in July or in September (exact date to be determined). grade: 0.85 exam exercises
4 What is planning? Intelligent decision making: What actions to take? general-purpose problem representation algorithms for solving any problem expressible in the representation application areas: high-level planning for intelligent robots autonomous systems: NASA Deep Space One,... problem-solving (single-agent games like Rubik s cube)
5 Why is planning difficult? Solutions to simplest planning problems are paths from an initial state to a goal state in the transition graph. Efficiently solvable e.g. by Dijkstra s algorithm in O(n log n) time. Why don t we solve all planning problems this way? State spaces may be huge: 10 9, 10 12, 10 15,... states. Constructing the transition graph and using e.g. Dijkstra s algorithm is not feasible!! Planning algorithms try to avoid constructing the whole graph. Planning algorithms often are but are not guaranteed to be more efficient than the obvious solution method of constructing the transition graph + running e.g. Dijkstra s algorithm.
6 Why is planning difficult? Solutions to simplest planning problems are paths from an initial state to a goal state in the transition graph. Efficiently solvable e.g. by Dijkstra s algorithm in O(n log n) time. Why don t we solve all planning problems this way? State spaces may be huge: 10 9, 10 12, 10 15,... states. Constructing the transition graph and using e.g. Dijkstra s algorithm is not feasible!! Planning algorithms try to avoid constructing the whole graph. Planning algorithms often are but are not guaranteed to be more efficient than the obvious solution method of constructing the transition graph + running e.g. Dijkstra s algorithm.
7 Why is planning difficult? Solutions to simplest planning problems are paths from an initial state to a goal state in the transition graph. Efficiently solvable e.g. by Dijkstra s algorithm in O(n log n) time. Why don t we solve all planning problems this way? State spaces may be huge: 10 9, 10 12, 10 15,... states. Constructing the transition graph and using e.g. Dijkstra s algorithm is not feasible!! Planning algorithms try to avoid constructing the whole graph. Planning algorithms often are but are not guaranteed to be more efficient than the obvious solution method of constructing the transition graph + running e.g. Dijkstra s algorithm.
8 Why is planning difficult? Solutions to simplest planning problems are paths from an initial state to a goal state in the transition graph. Efficiently solvable e.g. by Dijkstra s algorithm in O(n log n) time. Why don t we solve all planning problems this way? State spaces may be huge: 10 9, 10 12, 10 15,... states. Constructing the transition graph and using e.g. Dijkstra s algorithm is not feasible!! Planning algorithms try to avoid constructing the whole graph. Planning algorithms often are but are not guaranteed to be more efficient than the obvious solution method of constructing the transition graph + running e.g. Dijkstra s algorithm.
9 Different classes of problems actions deterministic nondeterministic probabilities no yes observability full partial horizon finite infinite. 1 classical planning 2 conditional planning with full/partial observability 3 Markov decision processes (MDP) 4 partially observable MDPs (POMDP)
10 Different classes of problems actions deterministic nondeterministic probabilities no yes observability full partial horizon finite infinite. 1 classical planning 2 conditional planning with full/partial observability 3 Markov decision processes (MDP) 4 partially observable MDPs (POMDP)
11 Different classes of problems actions deterministic nondeterministic probabilities no yes observability full partial horizon finite infinite. 1 classical planning 2 conditional planning with full/partial observability 3 Markov decision processes (MDP) 4 partially observable MDPs (POMDP)
12 Different classes of problems actions deterministic nondeterministic probabilities no yes observability full partial horizon finite infinite. 1 classical planning 2 conditional planning with full/partial observability 3 Markov decision processes (MDP) 4 partially observable MDPs (POMDP)
13 Different classes of problems actions deterministic nondeterministic probabilities no yes observability full partial horizon finite infinite. 1 classical planning 2 conditional planning with full/partial observability 3 Markov decision processes (MDP) 4 partially observable MDPs (POMDP)
14 Different classes of problems actions deterministic nondeterministic probabilities no yes observability full partial horizon finite infinite. 1 classical planning 2 conditional planning with full/partial observability 3 Markov decision processes (MDP) 4 partially observable MDPs (POMDP)
15 Properties of the world: nondeterminism Deterministic world/actions Action and current state uniquely determine the successor state. Nondeterministic world/actions For an action and a current state there may be several successor states. Analogy: deterministic versus nondeterministic automata
16 Example Moving objects with an unreliable robotic hand: move the green block onto the blue block. p = 0.1 p = 0.9
17 Properties of the world: observability Full observability Observations/sensing allow to determine the current state of the world uniquely. Partial observability Observations/sensing allow to determine the current state of the world only partially: we only know that the current state is one of several of possible ones. Consequence: It is necessary to represent the knowledge an agent has.
18 What difference does observability make? Camera A Camera B Goal
19 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 be negative. 3 Maximize the probability of reaching a goal state. Example: To be able to finance buying a house by 2015 study hard and save money. 4 Collect the maximal expected rewards / minimal expected costs (infinite horizon). Example: Maximize your future income. 5...
20 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 be negative. 3 Maximize the probability of reaching a goal state. Example: To be able to finance buying a house by 2015 study hard and save money. 4 Collect the maximal expected rewards / minimal expected costs (infinite horizon). Example: Maximize your future income. 5...
21 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 be negative. 3 Maximize the probability of reaching a goal state. Example: To be able to finance buying a house by 2015 study hard and save money. 4 Collect the maximal expected rewards / minimal expected costs (infinite horizon). Example: Maximize your future income. 5...
22 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 be negative. 3 Maximize the probability of reaching a goal state. Example: To be able to finance buying a house by 2015 study hard and save money. 4 Collect the maximal expected rewards / minimal expected costs (infinite horizon). Example: Maximize your future income. 5...
23 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 be negative. 3 Maximize the probability of reaching a goal state. Example: To be able to finance buying a house by 2015 study hard and save money. 4 Collect the maximal expected rewards / minimal expected costs (infinite horizon). Example: Maximize your future income. 5...
24 Relation to games and game theory Game theory addresses decision making in multi-agent setting: 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 applicable to multi-agent planning: Finding a winning strategy of a game (example: chess). In this case it is not necessary to distinguish between an intelligent opponent and a randomly behaving opponent. Game theory in general is about optimal strategies which do not necessarily guarantee winning. For example card games like poker do not have a winning strategy.
25 Relation to games and game theory Game theory addresses decision making in multi-agent setting: 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 applicable to multi-agent planning: Finding a winning strategy of a game (example: chess). In this case it is not necessary to distinguish between an intelligent opponent and a randomly behaving opponent. Game theory in general is about optimal strategies which do not necessarily guarantee winning. For example card games like poker do not have a winning strategy.
26 Relation to games and game theory Game theory addresses decision making in multi-agent setting: 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 applicable to multi-agent planning: Finding a winning strategy of a game (example: chess). In this case it is not necessary to distinguish between an intelligent opponent and a randomly behaving opponent. Game theory in general is about optimal strategies which do not necessarily guarantee winning. For example card games like poker do not have a winning strategy.
27 Prerequisites of the course 1 basics of AI (you have attended an introductory course on AI) 2 basics of propositional logic
28 What do you learn in this course? 1 Classification of different problems to different classes 1 Classification according to observability, nondeterminism, goal objectives,... 2 complexity 2 Techniques for solving different problem classes 1 algorithms based on heuristic search 2 algorithms based on satisfiability testing (SAT) 3 algorithms based on exhaustive search with logic-based data structures Many of these techniques are applicable to problems outside AI as well.
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