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

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 What is different? Mutexes? Scalability? –LCW –Unlimited sensing, run-time objects/relations –Contingent plans –Interleaved planning and execution

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 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)) Start: ((own my_book) (book_subject my_book chess)) Goal: ((own ?book) (book_subject ?book go))

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

25. Databases (continued) K v – function values agent will know –Plan time just know value will exist –Execution time will know actual value K x – “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 –w 1 : P(a), ¬P(b); w 2 : ¬P(a), P(b) –{w 1, w 2 }  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 K w (  ) – is  known either true or false K v (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 K w PlanPKS with  added to K f PlanPKS with ¬  added to K f return merged, contingent plan When does this search terminate? What are some problems and limitations?

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

31. Directory Structure Start: (pwd) = root Goal: Know paper_tex is in the current directory (pwd) Exclusive Or: paper_tex is in either papers or planner Contingent Plan 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, s 1 and s 2, in a linearization and the related action, a –  newly known in s 2 and a does not change , then  s 1 –  newly known in s 1 and a does not change , then  s 2 –  newly known in s 1 and a has conditional effect  , then   s 2 –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