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Peter Norvig on Planning - Dictionary of Arguments

Norvig I 156
Planning/artificial intelligence/Norvig/Russell: The unpredictability and partial observability of real environments were recognized early on in robotics projects that used planning techniques, including Shakey (Fikes et al., 1972)(1) and (Michie, 1974)(2). The problems received more attention after the publication of McDermott’s (1978a) influential article, Planning and Acting(3). >Belief states/Norvig.
Norvig I 366
Problems: [a sinple] problem-solving agent (…) can find sequences of actions that result in a goal state. But it deals with atomic representations of states and thus needs good domain-specific heuristics to perform well. [A] hybrid propositional logical agent (…) can find plans without domain-specific heuristics because it uses domain-independent heuristics based on the logical structure of the problem. But it relies on ground (variable-free) propositional inference, which means that it may be swamped when there are many actions and states.
Norvig I 367
planning researchers have settled on a factored representation - one in which a state of the world is represented by a collection of variables. We use a language called PDDL, the Planning Domain Definition Language, that allows us to express all 4Tn2 actions with one action schema. Each state is represented as a conjunction of fluents that are ground, functionless atoms. Database semantics is used: the closed-world assumption means that any fluents that are not mentioned are false, and the unique names assumption means that [x] 1 and [x] 2 are distinct. Actions are described by a set of action schemas that implicitly define the ACTIONS(s) and RESULT(s, a) functions needed to do a problem-solving search. >Frame Problem.
Classical planning concentrates on problems where most actions leave most things unchanged.
Actions: A set of ground (variable-free) actions can be represented by a single action schema.
The schema is a lifted representation—it lifts the level of reasoning from propositional logic to a restricted subset of first-order logic.
Action schema: The schema consists of the action name, a list of all the variables used in the schema, a precondition and an effect.
Norvig I 367
Forward/backward (progression/regression) state-space search: Cf. >Forward chaining, >backward chaining.
Norvig I 376
Heuristics for planning: a heuristic function h(s) estimates the distance from a state s to the goal and that if we can derive an admissible heuristic for this distance - one that does not overestimate - then we can use A∗ search to find optimal solutions.
Representation: Planning uses a factored representation for states and action schemas. That makes it possible to define good domain-independent heuristics and for programs to automatically apply a good domain-independent heuristic for a given problem. Think of a search problem as a graph where the nodes are states and the edges are actions. The problem is to find a path connecting the initial state to a goal state. There are two ways we can relax this problem to make it easier: by adding more edges to the graph, making it strictly easier to find a path, or by grouping multiple nodes together, forming an abstraction of the state space that has fewer states, and thus is easier to search.
Norvig I 377
State abstraction: Many planning problems have 10100 states or more, and relaxing the actions does nothing to reduce the number of states. Therefore, we now look at relaxations that decrease the number of states by forming a state abstraction - a many-to-one mapping from states in the ground representation of the problem to the abstract representation. The easiest form of state abstraction is to ignore some fluents.
Norvig I 378
Heuristics: A key idea in defining heuristics is decomposition: dividing a problem into parts, solving each part independently, and then combining the parts. The subgoal independence assumption is that the cost of solving a conjunction of subgoals is approximated by the sum of the costs of solving each subgoal independently.
Norvig I 390
Planning as constraint satisfaction: >Constraint satisfaction problems.

Norvig I 393
History of AI planning: AI planning arose from investigations into state-space search, theorem proving, and control theory and from the practical needs of robotics, scheduling, and other domains.
STRIPS (Fikes and Nilsson, 1971)(4), the first major planning system, illustrates the interaction of these influences.
General problem solver/GPS: the General Problem Solver (Newell and Simon, 1961)(5), [was] a state-space search system that used means–ends analysis. The control structure of STRIPS was modeled on that of GPS.
Norvig I 394
Language: The Problem Domain Description Language, or PDDL (Ghallab et al., 1998)(6), was introduced as a computer-parsable, standardized syntax for representing planning problems and has been used as the standard language for the International Planning Competition since 1998. There have been several extensions; the most recent version, PDDL 3.0, includes plan constraints and preferences (Gerevini and Long, 2005)(7).
Subproblems: Problem decomposition was achieved by computing a subplan for each subgoal and then stringing the subplans together in some order. This approach, called linear planning by Sacerdoti (1975)(8), was soon discovered to be incomplete. It cannot solve some very simple problems (…).A complete planner must allow for interleaving of actions from different subplans within a single sequence. The notion of serializable subgoals (Korf, 1987)(9) corresponds exactly to the set of problems for which oninterleaved planners are complete. One solution to the interleaving problem was goal-regression planning, a technique in which steps in a totally ordered plan are reordered so as to avoid conflict between subgoals. This was introduced by Waldinger (1975)(10) and also used by Warren’s (1974)(11) WARPLAN.
Partial ordering: The ideas underlying partial-order planning include the detection of conflicts (Tate, 1975a)(12) and the protection of achieved conditions from interference (Sussman, 1975)(13). The construction of partially ordered plans (then called task networks) was pioneered by the NOAH planner (Sacerdoti, 1975(8), 1977(14)) and by Tate’s (1975b(15), 1977(16)) NONLIN system. Partial-order planning dominated the next 20 years of research (…).
State-space planning: The resurgence of interest in state-space planning was pioneered by Drew McDermott’s UNPOP program (1996)(17), which was the first to suggest the ignore-delete-list heuristic (…).Bonet and Geffner’s Heuristic Search Planner (HSP) and its later derivatives (Bonet and Geffner, 1999(18); Haslum et al., 2005(19); Haslum, 2006(20)) were the first to make
Norvig I 395
state-space search practical for large planning problems. The most successful state-space searcher to date is FF (Hoffmann, 2001(21); Hoffmann and Nebel, 2001(22); Hoffmann, 2005(23)), winner of the AIPS 2000 planning competition. (Richter and Westphal, 2008)(24), a planner based on FASTDOWNWARD with improved heuristics, won the 2008 competition. >Environment/world/planning/Norvig. See also McDermot (1885(25).



1. Fikes, R. E., Hart, P. E., and Nilsson, N. J. (1972). Learning and executing generalized robot plans. AIJ,3(4), 251-288
2. Michie, D. (1974). Machine intelligence at Edinburgh. In On Intelligence, pp. 143–155. Edinburgh
University Press.
3. McDermott, D. (1978a). Planning and acting. Cognitive Science, 2(2), 71-109.
4. Fikes, R. E. and Nilsson, N. J. (1993). STRIPS, a retrospective. AIJ, 59(1–2), 227-232.
5. Newell, A. and Simon, H. A. (1961). GPS, a program that simulates human thought. In Billing, H.
(Ed.), Lernende Automaten, pp. 109-124. R. Oldenbourg.
6. Ghallab, M., Howe, A., Knoblock, C. A., and Mc-Dermott, D. (1998). PDDL—The planning domain definition language. Tech. rep. DCS TR-1165, Yale Center for Computational Vision and Control
7. Gerevini, A. and Long, D. (2005). Plan constraints and preferences in PDDL3. Tech. rep., Dept. of Electronics for Automation, University of Brescia, Italy
8. Sacerdoti, E. D. (1975). The nonlinear nature of plans. In IJCAI-75, pp. 206-214.
9. Korf, R. E. (1987). Planning as search: A quantitative approach. AIJ, 33(1), 65-88
10. Waldinger, R. (1975). Achieving several goals simultaneously. In Elcock, E. W. and Michie, D.
(Eds.), Machine Intelligence 8, pp. 94-138. Ellis Horwood
11. Warren, D. H. D. (1974). WARPLAN: A System for Generating Plans. Department of Computational
Logic Memo 76, University of Edinburgh
12. Tate, A. (1975a). Interacting goals and their use. In IJCAI-75, pp. 215-218.
13. Sussman, G. J. (1975). A Computer Model of Skill Acquisition. Elsevier/North-Holland.
14. Sacerdoti, E. D. (1977). A Structure for Plans and Behavior. Elsevier/North-Holland.
15. Tate, A. (1975b). Using Goal Structure to Direct Search in a Problem Solver. Ph.D. thesis, University of Edinburgh.
16. Tate, A. (1977). Generating project networks. In IJCAI-77, pp. 888-893.
17. McDermott, D. (1996). A heuristic estimator for means-ends analysis in planning. In ICAPS-96, pp.
142-149.
18. Bonet, B. and Geffner, H. (1999). Planning as heuristic search: New results. In ECP-99, pp. 360-372.
19. Haslum, P., Bonet, B., and Geffner, H. (2005). New admissible heuristics for domain-independent planning. In AAAI-05.
20. Haslum, P. (2006). Improving heuristics through relaxed search – An analysis of TP4 and HSP*a in the
2004 planning competition. JAIR, 25, 233-267.
21. Hoffmann, J. (2001). FF: The fast-forward planning system. AIMag, 22(3), 57-62.
22. Hoffmann, J. and Nebel, B. (2001). The FF planning system: Fast plan generation through heuristic search. JAIR, 14, 253-302.
23. Hoffmann, J. (2005). Where “ignoring delete lists” works: Local search topology in planning benchmarks. JAIR, 24, 685-758
24. Richter, S. and Westphal, M. (2008). The LAMA planner. In Proc. International Planning Competition at ICAPS.
25. McDermott, D. (1985). Reasoning about plans. In Hobbs, J. and Moore, R. (Eds.), Formal theories of the commonsense world. Intellect Books.


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Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. Translations: Dictionary of Arguments
The note [Author1]Vs[Author2] or [Author]Vs[term] is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.

Norvig I
Peter Norvig
Stuart J. Russell
Artificial Intelligence: A Modern Approach Upper Saddle River, NJ 2010


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