Computing Superior Counter-Examples for Conformant Planning: Australian National University , February 8, 2020 Alban Grastien | alban.grastien@data61.csiro.au | Superb 1/18 Xiaodi Zhang, Alban Grastien, Enrico Scala 1 / 18
2/18 Problem: planning) Motivation: Conformant Planning — Motivation dangerous environments epistemic planning Alban Grastien | alban.grastien@data61.csiro.au | Superb • Conformant planning = fjnd a plan that leads to a given goal • Uncertainty in the initial state and no observability • No uncertainty on the action efgect (deterministic conformant • Useful for robots with little processing capability and in • Target language from probabilistic conformant planning and • The ideas will apply for more sophisticated problems 2 / 18 1
Superb Alban Grastien | alban.grastien@data61.csiro.au | Dispose (simplifjed): 3/18 Conformant Planning — Example • Three items 1 to 3 , four locations A to D • Initial location of each item unknown • Goal: drop all items in another location T • Actions: ◦ Go-to: moves the robot ◦ Pick-up: grabs the item if it is where the robot is ◦ Drop: drops the item if the robot is holding it • One solution: ◦ go-to A , pick-up 1 , pick-up 2 , pick-up 3 ◦ go-to B , pick-up 1 , pick-up 2 , pick-up 3 ◦ go-to C , pick-up 1 , pick-up 2 , pick-up 3 ◦ go-to D , pick-up 1 , pick-up 2 , pick-up 3 ◦ go-to T , drop 1 , drop 2 , drop 3 3 / 18 1
Conformant Planner: g cpces Assuming the problem is “easy” if the set of initial states is small Alban Grastien | alban.grastien@data61.csiro.au | Superb 4/18 • B := { } • repeat ◦ π := compute-plan ( B ) ◦ if no π • return unsolvable ◦ q := compute-counter-example ( π ) ◦ if no q • return π ◦ B := B ∪ { q } 4 / 18 1
Init loc of item A A A A A Init loc of item A A C A A A D C B B D g cpces — Example A Alban Grastien | alban.grastien@data61.csiro.au | D C B A A A A A A A Init loc of item A A A 10 5/18 9 Illustration on Dispose : ) counter-ex. 1 2 3 4 A B C D A B D C Superb 7 B C 8 D What happens in practice :( counter-ex. 1 A 2 3 4 5 6 Init loc of item 1 Init loc of item 2 Init loc of item 3 5 / 18 1
A C B C D A A A A A A A A A A B D 5/18 A A A A A A A A A A B C D Alban Grastien | alban.grastien@data61.csiro.au | g cpces — Example Superb 10 9 Illustration on Dispose :) counter-ex. 1 2 3 4 A B C D A B D C A 2 8 7 6 5 4 3 1 counter-ex. What happens in practice :( D C B Init loc of item 1 Init loc of item 2 Init loc of item 3 Init loc of item 1 Init loc of item 2 Init loc of item 3 5 / 18 1
Our Goal We want to minimise the number of counter-examples that are generated by g cpces 1. Fewer iterations 2. Smaller set of counter-examples 3. More diverse counter-examples Question: Alban Grastien | alban.grastien@data61.csiro.au | Superb 6/18 → faster (?) g cpces → better “explanation” → less “biased” plans when using non-admissible heuristics • How do we know that q ′ is a better counter-example than q ? 6 / 18 1
Superiority: Intuition g cpces Alban Grastien | alban.grastien@data61.csiro.au | Superb 7/18 • Let B 1 ⊂ B 2 ⊂ . . . be the sequence of samples built by • Then: Π( P [ B 1 ]) ⊃ Π( P [ B 2 ]) ⊃ · · · ⊇ Π( P ) • g cpces terminates when Π( P [ B ]) = Π( P ) (sometimes before) → To accelerate convergence, we want to minimise Π( P [ B i ]) at each i 7 / 18 1
Superiority: Intuition (continued) Alban Grastien | alban.grastien@data61.csiro.au | Superb 8/18 Properties we are looking for: if q ′ is superior to q (given B ) 1. Π( B ∪ { q } ) ⊇ Π( B ∪ { q ′ } ) ← so q ′ is better now 2. for all subset B ′ of initial states: Π( B ∪ { q } ∪ B ′ ) ⊇ Π( B ∪ { q ′ } ∪ B ′ ) ← so q ′ will be better I.e., q ′ is always better than q 8 / 18 1
9/18 (Palacios & Gefgner, 2009; Albore, Palacios, & Gefgner, 2010) Known Notions: Tags Example in dispose: context of a validity condition Alban Grastien | alban.grastien@data61.csiro.au | Superb • A plan is valid ifg ◦ all its actions’ preconditions are satisfjed when they are applied ◦ and the goal is satisfjed at the end → validity condition • The context of a validity condition ϕ is the list of all variables that ϕ depends on (including through other actions) ◦ Context of disposed( i ) = { disposed( i ), holding( i ), location( i ) } • A tag t is a possible initial assignment of the variables in the 9 / 18 1
Known Notions: Tags (continued) such that: Alban Grastien | alban.grastien@data61.csiro.au | Superb 10/18 • An initial state q exhibits a number of tags: Tags ( q ) • It is possible to associate each tag t with a set of plans Π( t ) • The set of valid plans of problem P is: � Π( P ) = Π( t ) t ∈ Tags ( q ) , q ∈ I 10 / 18 1
Tag-Based Superiority (defjnition) Remember: Alban Grastien | alban.grastien@data61.csiro.au | Superb 11/18 Tags ( B ) ⊆ Tags ( B ′ ) ⇒ Π( P [ B ]) ⊇ Π( P [ B ′ ]) • Let B ⊆ I be a sample • Let q and q ′ be two counter-examples • q ′ is superior to q (given B ) if: Tags ( B ∪ { q } ) ⊂ Tags ( B ∪ { q ′ } ) 11 / 18 1
Superb 12/18 Then Alban Grastien | alban.grastien@data61.csiro.au | Computing Superior Counter-Examples Let q be the current counter-example and B the sample Let C 1 , . . . , C k be the contexts Let t i, 1 , . . . , t i,p be the tags of C i in B Let t i be the tag of q for C i Let j be such that t i �∈ { t i, 1 , . . . , t i,p } is a new tag ifg i ≤ j � � � Initial_State ∧ t i ∧ ¬ t i,ℓ i ∈{ 1 ,...,j } i ∈{ j +1 ,...,k } ℓ ∈{ 1 ,...,p } is satisfjable ifg there is a counter-example superior to q 12 / 18 1
Experiments (setup) Planners: well when the contexts include only one unknown variable Alban Grastien | alban.grastien@data61.csiro.au | Superb 13/18 • g cpces (using z3 and ff ) • new CPCES: Superb (using z3 and ff ) • T1 , a planner based on Conformant FF that performs very 13 / 18 1
Experiments (expectations) Defjnitions: a problem instance is unknown (“width” = 1) We expect (“>” means “faster”): Alban Grastien | alban.grastien@data61.csiro.au | Superb 14/18 • vertical if all contexts include exactly one variable initially • horizontal if all contexts are identical • Vertical & horizontal: trivial problems • Vertical & non-horizontal: T1 > Superb > g cpces • Non-vertical & horizontal: g cpces = Superb > T1 • Non-vertical & non-horizontal: Superb > g cpces > T1 14 / 18 1
Experiments (benchmarks) (crudely) EmptyGrid , WallGrid , Dispose-One , LookAndGrab MAWallGrid Alban Grastien | alban.grastien@data61.csiro.au | Superb 15/18 • Vertical & non-horizontal: Dispose , Coins , Bomb , uts • Non-vertical & horizontal: BlockWorld , RaosKey , • Non-vertical & non-horizontal: (new domain!) 15 / 18 1
62 0.1 Bomb (9) 0.1 1.3 0.6 18 18 18 4 4 4 emptygrid (4) 0.9 9 0.7 18 18 18 4 18 18 wallgrid (18) 377 67 30 79 7 9 Experiments (results) 3 Alban Grastien | alban.grastien@data61.csiro.au | 6 259 580 212 184 184 8 6 4 dispose (11) 0.6 3 106 149 86 88 9 8 8 Coins (9) 0.1 4 96 101 106 68 4 16/18 LookAndGrab (18) 3 BlockWorld (3) 117 36 22 34 42 42 15 18 18 T1 2 S C T1 S C T1 S C Domain Planning Time Plan Quality Coverage 3 13 5 0.2 5 Dispose-One (10) 0.5 1.2 0.6 21 16 16 1 2 2 RaosKeyS (2) 4 13 3 41 36 36 11 13 13 UTS (15) 0.2 0.8 0.7 13 Superb 16 / 18 1
29 TO 10_10_3 TO 9.75 4.11 50 40 1876.62 874.49 10_10_2 NA TO NA NA NA TO TO 8_8_3 TO 3.31 2.74 TO NA Experiments (results, continued) TO Alban Grastien | alban.grastien@data61.csiro.au | TO NA NA NA NA TO TO 11_11_3 9.3 NA 6.09 38 43 1606.3 2287.07 11_11_2 TO NA NA 25 77.75 17/18 S 0.1 0.42 0.41 7 10 1.17 1.43 4_4_2 T1 Time C 20.02 S C S C Pro Sampling Time Iterations Planning Time mawallgrid 4_4_3 10.34 124.14 0.1 8_8_2 4.9 1.74 1.08 14 14 904.75 1037.74 6_6_3 1.14 19 0.7 12 13 4.25 4.29 6_6_2 0.3 1.09 0.86 11 Superb 17 / 18 1
18/18 than others in the context of g cpces counter-examples More broadly: Conclusion ( g cpces ) with a technique that leverages on the structure (superiority) Alban Grastien | alban.grastien@data61.csiro.au | Superb • We identify that some counter-examples are more informative • We show one characterisation of this relation (“superiority”) • We show how to compute maximally-superior • We show experimentally the benefjts of this approach • We combine a technique that is oblivious of the structure • Can we characterise informativeness more precisely? • Can we import this type of solution in other problems? 18 / 18 1
Recommend
More recommend
