1. Learning Declarative Control Rules for Constraint-Based Planning Yi-Cheng Huang Bart Selman Cornell University Henry Kautz University of Washington

2. Outline Overview of Planning Motivation Learning Framework Experimental Results Conclusion

3. Overview of Planning Planning - Find a sequence of actions that transform an initial state to a goal state State = complete truth assignment to a set of variables (fluents) Action = a partial function State State –specified by three sets of variables: precondition, add list, delete list

4. An Example a Goal Initial b BOSSFONYC b Initial a

5. A Sample Action ( UnloadAirplane (?pln ?pkg ?airport ) : preconditions (in ?pkg ?pln) (at ?pln ?airport) :effects (not (in ?pkg ?pln)) (at ?pkg ?airport) )

6. 1. LoadAirplane P pkg-a at BOS 2. FlyAirplane P from SFO to NYC 3. LoadAirplane P pkg-b at NYC 4. FlyAirplane P from NYC to SFO 5. UnloadAirplane P pkg-a at SFO 5. UnloadAirplane P pkg-b at SFO PLAN a Goal Initial b BOSSFONYC Initial ab

7. Planning Domain-independent planning: PSPACE- complete (Chapman 1987; Bylander 1991; Backstrom 1993) General focus on planning: avoid search as much as possible. TLPlan: use control knowledge to guild a forward-chaining planner (Bacchus & Kabanza 2000). Same level of control can be effectively used in Blackbox - a Constraint-Based Planner (Huang, Selman, & Kautz 1999).

8. A Control Rule Example aa Do NOT unload an object from an airplane if the airport is not in the object’s goal city GoalInitial a BOSSFONYC

9. Motivation Control Rules used in TLPlan and Blackbox are hand-coded. Can we acquire domain knowledge automatically? Idea: Learn control rules on a sequence of small problems solved by planner.

10. Plan Justification / Type Inference Blackbox Planner Problem ILP Learning Module / Verification Learning Framework Control Rules

11. Target Concepts for Actions Action Select Rule: indicate conditions under which the action can be performed immediately. –Ex. Unload a package at its goal location. Action Reject Rule: indicate conditions under which it must not be performed. –Ex. Do not load a package at its goal location.

12. Heuristics for Extracting Examples Basic Assumption: –Plan found by planner on simple problems are optimal or near-optimal. –Actions appear in an optimal plan must be selected. –Actions that do not appear must be rejected. Definition: –real action: action appears in the plan. –virtual action: action that its preconditions hold but does not appear in the plan.

13. Real & Virtual Actions for UnloadAirplane 1. LoadAirplane P pkg-a at BOS 2. UnloadAirplane P pkg-a at BOS 2. FlyAirplane P from BOSto NYC 3. UnloadAirplane P pkg-a at NYC 3. LoadAirplane P pkg-b at NYC 4. UnloadAirplane P pkg-a at NYC 4. UnloadAirplane P pkg-b at NYC 4. FlyAirplane P from NYC to SFO 5. UnloadAirplane P pkg-a at SFO 5. UnloadAirplane P pkg-b at SFO

14. Heuristics for Extracting Examples

15. ILP Rule Induction Based on Quinlan’s FOIL (Quinlan 1990; 1996). ( ) action literals Literal: –Xi = Xj –P(X1,…, Xn) –goal (P(X1,…, Xn)) –negation of the above

16. Reject Rule: UnloadAirplane UnloadAirplane (obj, plane, loc) goal(at (obj, loc2)) ^ (loc != loc2)

17. Learning Time

18. Empirical Results

19. Conclusion Our system is simple and modular; Learning time is short. Learned rules are useful on various domains. Learned rules are represented in logic form; Learned rules can be used to other planning systems.