General Purpose Case-Based Planning

General Purpose vs Domain Specific (Case-Based) Planning General purpose: symbolic descriptions of the problems and the domain. The (adaptation) generation rules are the same Domain Specific: The (adaptation) generation rules depend on the particular domain Advantage: - opportunity to have clear semantics Disadvantage: - symbolic description requirement Advantage: - can be very efficient Disadvantage: - lack of clear semantics - knowledge-engineering for adaptation (Case-Based) Planning: finding a sequence of actions to achieve a goal

Transformational adaptation: structural transformations are made to the plans Derivational transformation: Derivational vs Transformational Adaptation Case Replay: re-applying those decisions relative to the new problem Case: Plan step Case: sequence of planning decisions that led to the plan:

Domain Specific: Chef Cases contain cooking recipes (plans) and there are rules indicating how to transform pieces of the recipes Typical transformation rules will indicate alternative ingredients and what steps need to be added/changed to adapt the recipe (Hammond, 1986) Example: if using broccoli instead of beans the cooking time need to be adjusted. The cases contain domain-knowledge and transformational adaptation is performed

Generative Solution Adaptation If we have operators/rules with general knowledge about the domain why do we need adaptation? To find the solution faster To find solutions that are similar to the original case, why?  Solutions may be more acceptable to the user  Attempt to preserve quality

General-Purpose Planning: State & Goals Initial state: (on A Table) (on C A) (on B Table) (clear B) (clear C) Goals: (on C Table) (on B C) (on A B) (clear A) A C BC B A Initial stateGoals ( Ke Xu )

General-Purpose Planning: Operators ?y ?x No block on top of ?x transformation ?y ?x … … No block on top of ?y nor ?x Operator: (Unstack ?x) Preconditions: (on ?x ?y) (clear ?x) Effects: –Add: (on ?x table) (clear ?y) –Delete: (on ?x ?y) On table

Planning: Search Space A C B ABC AC B C B A B A C B A C BC A C A B A C B B C A AB C A B C A B C ( Michael Moll )

Planning: Formal Definition Planning problem: a tuple  =  P,O,I,G  P: a finite set of ground atoms  Let L = {all possible literals}, i.e., L = P  {  p : p  P} O: a finite set of operators of the form Pre  Post  Pre  L and Post  L are the preconditions and effects I  P is the initial state G  L is the goal move-C-from-A-to-Table Precondition: (and (on C A) (clear C)) Effect: (and (on C Table) (  (on C A)) (clear A))

Complexity of Plan Generation Plan Solution: Given a planning problem,  =  P,O,I,G  we will like to find the plan  that solves  For complexity analysis, need to encode plan solution as a decision problem  a problem that has a yes/no answer PLAN-EXISTENCE (  ):  Given a planning problem  =  P,O,I,G , does there exist a plan  that solves  ? Theorem. PLAN-EXISTENCE (  ) is NP-Complete

Complexity of Plan Adaptation Conservative plan-modification:  Given a planning problem  =  P,O,I,G , a plan  that solves , and another planning problem  ' =  P,O,I',G'  Find a plan  ' that solves  ' and reuses as much of  as possible consMODSAT ( , ,  ', k):  Given , , and  ' as above and given a k, is there a plan  ' that solves  ' and contains at least k steps of  ? Theorem. consMODSAT ( , ,  ', k) is P-SPACE

Complexity Issues: NP-Complete Problems are Not the Hardest PSPACE is the set of decision problems that can be solved by a Turing machine using a polynomial amount of memory, and unlimited time A problem P is in PSPACE-complete if:  P is in PSPACE,  every problem P’ in PSPACE can be reduced to P in polynomial time. PSPACE-complete problems are believed to be harder than NP-Complete ones

Complexity of Derivational Analogy Theorem. Derivational Analogy does not perform a conservative adaptation strategy Thus, worst-case analysis for P-SPACE result does not apply to it How do we proof that some property does not hold? Construct a counter-example

Counter-Example Case: New Problem: ` ` ` ` ` ` ??

Homework explain why planning is so hard. Use the search space. Propose a heuristic to guide search. Explain why your proposed heuristic will not work for every case. In slide 20, we define the decision problem consMODSAT for conservative plan-modification defined in the same slide. Define the following:  Plan-modification  The decision problem for plan modification: MODSAT (Hint: see the definition of plan solution and its decision problem PLAN-EXISTENCE in Slide 19) Due: Wednesday April 13