4/29: Conditional Planning  No Final. Instead we will have a last homework  Midterm to be returned Thursday; Homework reached Hanoi  Extra class on Thursday?

Conformant Heuristics

Sensing: General observations  Sensing can be thought in terms of  Speicific state variables whose values can be found  OR sensing actions that evaluate truth of some boolean formula over the state variables.  Sense(p) ; Sense(pV(q&r))  A general action may have both causative effects and sensing effects  Sensing effect changes the agent’s knowledge, and not the world  Causative effect changes the world (and may give certain knowledge to the agent)  A pure sensing action only has sensing effects; a pure causative action only has causative effects.  When applied to a belief state, the sensing effects of an action wind up reducing the cardinality of that belief state  basically by removing all states that are not consistent with the sensed effects  Sensing actions introduce branches into the plans  If you apply Sense-A? to a belief state B, you get a partition of B: B A and B ~A  You will have to make a plan for both the branches. And/Or search in the space of belief states

First we will see a model where observability is in terms of state variables Next we shall see a model where observability can be in terms of formulas [Bonet&Geffner]

Modeling observability in terms of observation actions that give values of single state variables If a state variable p Is in B, then there is some action A p that Can sense whether p is true or false

A Simple Progression Algorithm in the presence of pure sensing actions  Call the procedure Plan(B I,G,nil) where  Procedure Plan(B,G,P)  If G is satisfied in all states of B, then return P  Non-deterministically choose:  I. Non-deterministically choose a causative action a that is applicable in B.  Return Plan(a(B),G,P+a)  II. Non-deterministically choose a sensing action s that senses a formula f (could be a single state variable)  Let p’ = Plan(B f,G,nil); p’’=Plan(B ~f,G,nil)  /*B f is the set of states of B in which f is true */  Return P+(s?:p’;p’’) If we always pick I and never do II then we will produce conformant Plans (if we succeed).

Remarks on the progression with sensing actions  Progression is implicitly finding an AND subtree of an AND/OR Graph  If we look for AND subgraphs, we can represent looping plans.  The amount of sensing done in the eventual solution plan is controlled by how often we pick step I vs. step II (if we always pick I, we get conformant solutions).  Progression is as clue-less as to whether to do sensing and which sensing to do, as it is about which causative action to apply  Need heuristic support

Geffner’s model

5/1: Conditional Planning (contd) Midterms returned Monty Python on Conformant Planning Next class * REQUIRED READING* assigned Can we meet sometime on Monday (instead of reading class?)

Very simple Example A1 p=>r,~p A2 ~p=>r,p A3 r=>g O5 observe(p) Problem: Init: don’t know p Goal: g Plan: O5:p?[A1  A3][A2  A3] O5:p? A1 A3 A2 A3 Y N

nuPDDL—not yet a standard…  define (domain d)... (:predicates (P1) (P2) (P3) (P4) (P5) (P6))...)  (define (problem p).... (:init (and (P1) (oneof (and (P2) (P3)) (P4)) (unknown (P5))))....)  define (problem p).... (:effect (and (P1) (oneof (and (P2) (P3)) (P4)) (unknown (P5))))....)  (:observation wall_north - boolean :parameters () (iff (= wall_north 1) (or (= (robot_y) north) (= (robot_x) west))))  ;.... (:observation wall_east - boolean :parameters () (imply (= wall_east 0) (= (robot_x) west)) (imply (= wall_east 1) (true))  :weakgoal : it is required that the plan may reach the goal.  :stronggoal : it is required that every execution of the plan reaches the goal.  :strongcyclicgoal : it is required that every execution of the plan either reaches the goal, or at least always has a chance to do it  :postronggoal : it is required that every execution of the plan reaches the goal, using only the observations described in the domain  :conformantgoal : it is required that every execution of the plan reaches the goal, without ever observing  :ctlgoal : it is required that the CTL formula expressed as a goal is satisfied throughout every possible execution of the plan. Some examples of typical extended goals follow:  Do Reach p (``strong goal''): (af p)  Try Reach p (``weak goal''): (ef p)  Keep Trying Reach p (``strong cyclic goal''): (aw (ef p) p)

A Simple Progression Algorithm in the presence of pure sensing actions  Call the procedure Plan(B I,G,nil) where  Procedure Plan(B,G,P)  If B is a subset of B G (or any B’ in P that is marked “solved”) return P (propagate “solve” marking upwards)  Non-deterministically choose:  I. Non-deterministically choose a causative action a that is applicable in B.  Return Plan(a(B),G,P+a)  II. Non-deterministically choose a sensing action s that senses a formula f (could be a single state variable)  Let p’ = Plan(B f,G,nil); p’’=Plan(B ~f,G,nil)  /*B f is the set of states of B in which f is true */  Return P+(s?:p’;p’’) If we always pick I and never do II then we will produce conformant Plans (if we succeed).

Remarks on the progression with sensing actions  Progression is implicitly finding an AND subgraph of an AND/OR Graph  The amount of sensing done in the eventual solution plan is controlled by how often we pick step I vs. step II (if we always pick I, we get conformant solutions).  Progression is as clue-less as to whether to do sensing and which sensing to do, as it is about which causative action to apply  Need heuristic support

Cost models of conditional plans  The execution cost of a conditional plan is Cost of O5 + [Prob(p=T)* {cost of A1 + A3} + Prob(p=F)*{cost of A2 +A3} ]  Can take max(cost A1+A3; cost A2+A3 )  The planning cost of a conditional plan is however is proportional to the total size of the plan (num actions) O5:p? A1 A3 A2 Y N O5:p? A1 A2 Y N Need to estimate cost of leaf belief states

Similar processing can be done for regression (PO planning is nothing but least-committed regression planning)

Sensing: General observations  Sensing can be thought in terms of  Speicific state variables whose values can be found  OR sensing actions (with preconditions and causative effects) that evaluate truth of some boolean formula over the state variables.  Sense(p) ; Sense(pV(q&r))  A general action may have both causative effects and sensing effects  Sensing effect changes the agent’s knowledge, and not the world  Causative effect changes the world (and may give certain knowledge to the agent)  A pure sensing action only has sensing effects; a pure causative action only has causative effects.  The recent work on conditional planning has considered mostly simplistic sensing actions that have no preconditions and only have pure sensing effects.  When applied to a belief state, the sensing effects of an action wind up reducing the cardinality of that belief state  basically by removing all states that are not consistent with the sensed effects  Sensing actions introduce branches into the plans  If you apply Sense-A? to a belief state B, you get a partition of B: B A and B ~A  You will have to make a plan for both the branches. And/Or search in the space of belief states

Sensing: More things under the mat  Sensing extends the notion of goals too.  Check if Rao is awake vs. Wake up Rao  Presents some tricky issues in terms of goal satisfaction…!  Handling quantified effects and preconditions in the presence of sensing actions  Rm* can satisfy the effect forall files remove(file); without KNOWING what are the files in the directory!  Sensing actions can have preconditions (as well as other causative effects)  The problem of OVER-SENSING (Sort of like the initial driver; also Sphexishness) [XII/Puccini project]  Handling over-sensing using local-closedworld assumptions  Listing a file doesn’t destroy your knowledge about the size of a file; but compressing it does. If you don’t recognize it, you will always be checking the size of the file after each and every action  A general action may have both causative effects and sensing effects  Sensing effect changes the agent’s knowledge, and not the world  Causative effect changes the world (and may give certain knowledge to the agent)  A pure sensing action only has sensing effects; a pure causative action only has causative effects.  The recent work on conditional planning has considered mostly simplistic sensing actions that have no preconditions and only have pure sensing effects.  Sensing has cost!

Sensing: Limited Contingency planning  In many real-world scenarios, having a plan that works in all contingencies is too hard  An idea is to make a plan for some of the contingencies; and monitor/Replan as necessary.  Qn: What contingencies should we plan for?  The ones that are most likely to occur…(need likelihoods)  Qn: What do we do if an unexpected contingency arises?  Monitor (the observable parts of the world)  When it goes out of expected world, replan starting from that state.

“Triangle Tables”

NOT used beyond this point