Planning with Incomplete, Unbounded Information

1. Planning with Incomplete, Unbounded Information May 20, 2003 Tal Shaked

2. Types of Incomplete Information • Finite set of states (objects, relations) • Uncertain of current state • Realistic? • Infinite set of states • Many objects and relations (most unknown) • Too large to reason about directly

3. Example Domains • Unix/Internet • Puccini and Rodney • Web • Web services • DAML-S (DAML+OIL)

4. Topics • Problems with existing planners • Puccini, PKS • What is difficult • LCW review • Ideas to improve planners • How PKS works

5. PKS (2002) Petrick and Bacchus Contingent plans Puccini (1998) Etzioni, Golden, Weld Internet softbot Two Recent Planners

6. Puccini • Partial-order-planner • Expressive • SADL • Interleaves Planning with Execution • Not clear how • Slow • Required domain-specific knowledge

7. PKS • Contingent, forward-chaining planner • Not Expressive • Slow • Constructs a complete, correct plan • Separates plan-time and execution-time effects • No universal quantification or LCW • No search control

8. Some Problems • Slow • How do we solve these planning problems? • What heuristics can we add? • Execution model • Are contingent plans practical? • When should actions be executed? • How can we find structure?

9. Extending Planning Graph • LCW • Unlimited sensing, run-time objects/relations • Contingent plans • Interleaved planning and execution • What is different? • Mutexes? • Scalability?

10. LCW Review • Why is LCW useful? • How does it work? • Avoid repeated sensing • Universal quantification • Inference • Compression • Lazy evaluation

11. Querying Ground Conjunction

12. Querying LCW How is inference done? If we know all files in jokes/, then we know if the file giggy is in jokes/ If we know all files in jokes/, and know all dirty jokes, then we know if giggy is dirty and in jokes/

13. Updating LCW • Information Gain: A formula that is originally U, becomes T or F • Generally cannot lose LCW • Information Loss: A formula initially T or F, becomes U • Generally, all LCW “relevant” to that literal are lost • Know the size of all files in root/. Execute compress root/passwords.txt

14. Sensing Actions • Bounded sensing • Set of possible observations • Unbounded sensing • Generic types and relations • Consider potential bindings at next level

15. Finding a Plan • Search for plans in the graph • Consider one branch at a time • Heuristics • Reachability • Amount of sensing to reach a literal • Depth in planning graph • Control execution • Agent-centered search?

16. Scalability • Mutexes • Same as normal Graphplan • LCW? • Generic types and relations? • Quick growth due to sensing • Limit to relevant actions • Learn relevance probabilities

17. Book Trading Example Start: ((own my_book) (book_subject my_book chess)) Goal: ((own ?book) (book_subject ?book go)) Predicates: (own ?book) (book_subject ?book ?subject) (at_store ?book ?book_store) action: trade(?book1 ?book2 ?book_store) precond: ((own ?book1) (at_store ?book2 ?book_store)) effect: ((own ?book2) (not (own?book1))) action: search(?book_store ?subject) precond: () effect: (forall (!book) (when (at_store !book ?book_store) (at_store !book ?book_store) (book_subject !book ?subject))) (LCW((at_store #book ?book_store) (book_subject #book ?subject))

18. Sample Graph

19. Using the Graph • Similar Graphplan search • LPG-like search (local search on graph) • Propagating sensing action links • Executing to reach ‘better’ states • Forward/backward chaining heuristics?

20. Other Problems • Agent wants to find a *.pdf file • Try ls • hope some file exists, possibly a *.pdf file • latex(paper.tex), dvipdf(paper.dvi) • check for read/write permissions • How can the agent learn? • Can this be represented in a planning graph?

21. Knowledge-Based Approach • Only represent what agent knows • Actions manipulate knowledge • Advantages • Compact Representation • Introducing new objects • Disadvantages? • Unable to distinguish between possible worlds

22. Modal Logic of Knowledge • Fancy way of just adding K •  is true at a particular world w iff it is true by standard rules • K() is true at w iff  is true at every possible world •  can be true, yet the agent may not know

23. Knowledge Representation • Databases store agent’s knowledge • Can be converted to modal logic formulas • Preconditions as knowledge • Effects as database modifications • Goals as knowledge

24. Databases • Kf – stores facts like STRIPs • Kw – agent either knows or negation • know(this) Kw  K(know(this)) v K(¬know(this)) • With variables, can model universal effects • At run time, generates LCW • Construct conditional branches

25. Databases (continued) • Kv – function values agent will know • Plan time just know value will exist • Execution time will know actual value • Kx – “exclusive or” knowledge • Exactly one proposition in a set is true

26. Knowledge State • Databases are conjunctions of formulas • Limits what the agent can know • Cannot represent some sets of worlds • w1: P(a), ¬P(b); w2: ¬P(a), P(b) • {w1,w2}  K(P(a) v P(b)) • If a directory contains the file a.out, then it also contains core

27. Querying Databases • K() – is  known to be true • K(¬) – is  known to be false • Kw() – is  knowneither true or false • Kv(t) – is t known to have fixed value • Negation of the above • What about LCW?

28. Planning Problem • {I, G, A, U} • I = initial state • G = goal conditions (primitive queries) • A = set of actions • U = domain specific update rules (optional)

29. Planning Algorithm PlanPKS if(goalsSatisfied) return plan else choose some action, apply it, PlanPKS or choose some ground instance  in Kw PlanPKS with  added to Kf PlanPKS with ¬ added to Kf return merged, contingent plan When does this search terminate? What are some problems and limitations?

30. Example Initial State: Kf = {(=(pwd) root), (indir papers root), (indir planner root), (dir root), (dir papers), (dir planner), (file paper_tex)} Kx = {((indir paper_tex planner) | (indir paper_tex papers))} Goal: K(indir paper_tex (pwd))

31. Directory Structure Contingent Plan Start: (pwd) = root Goal: Know paper_tex is in the current directory (pwd) Exclusive Or: paper_tex is in either papers or planner Is this plan optimal? What are problems with this representation of plans?

32. Expressiveness of Goals • Conditions that hold in final state • No universal quantification • What about SADL? • Initially? • Restore? • Hands-off?

33. Reasoning about Conditional Plans • Conditional plan is a tree • Nodes are knowledge states • Edges are actions • Each leave corresponds to one branch • Each branch one linear sequences of worlds • Reason about each linear sequence • How?

34. Example Initial State: bottle of liquid, a healthy lawn Goal: know whether liquid is poisonous

36. Inference Procedure • Consider two consecutive states, s1and s2, in a linearization and the related action, a •  newly known ins2 and a does not change , then  s1 •  newly known ins1 and a does not change , then  s2 •  newly known ins1 and a has conditional effect  , then  s2 • More inferences using similar ideas… • When can we apply these inferences? • At what points in conditional plans? • What about initially, restore, hands-off?

37. Flaws • Experiments misleading • Unclear about LCW • Not clear what is new and important • More discussion about incompleteness

38. Future Work • Heuristic search • Dealing with scalability issues • Contingent planning with universal quantification • Further implementation and testing • Parallel plans • Probabilistic knowledge