Where Ignoring Delete Lists Works, Part II: Causal Graphs J org - - PowerPoint PPT Presentation

Where Ignoring Delete Lists Works, Part II: Causal Graphs

J¨

• rg Hoffmann

INRIA Nancy, France

June 14, 2011

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 1/23

Outline

◮ What happened? ◮ On causal graphs and h+ ◮ Guaranteed global analysis ◮ Approximate local analysis ◮ Diagnosis ◮ Conclusion

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 2/23

Outline

◮ What happened? ◮ On causal graphs and h+ ◮ Guaranteed global analysis ◮ Approximate local analysis ◮ Diagnosis ◮ Conclusion

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 3/23

FF

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 4/23

Where Ignoring Delete Lists Works

undirected Logistics [0,1] Ferry [0,1] Gripper [0,1] harmless recognized unrecognized Miconic−STRIPS [0,1] Movie [0,1] Simple−Tsp [0,0] Zenotravel [2,2] Satellite [4,4] Tyreworld [0,6] Grid [0] Rovers local minima ed <= c Hanoi [0] Blocksworld−NoArm [0] Transport [0] Blocksworld−Arm Depots Driverlog PSR Pipesworld−NoTank Mystery Mprime Freecell Airport Pipesworld−Tank Elevators [0,1] flat ed <= c

red: no local minima at all under h+

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 5/23

Can we recognize this automatically?

at A mv A B at B at C mv C D mv D C at D mv D E at E B C D E

1 EUR

mv B D A

== 1 EUR += 1 EUR

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 6/23

Can we recognize this automatically?

at A mv A B at B at C mv C D mv D C at D mv D E at E B C D E

1 EUR

mv B D A

== 1 EUR += 1 EUR

Works only in trivialities; explodes quickly

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 6/23

Time passes . . .

← me in 2002

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 7/23

Time passes . . .

← me in 2003

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 7/23

Time passes . . .

← me in 2004

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 7/23

Time passes . . .

← me in 2005

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 7/23

Time passes . . .

← me in 2006

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 7/23

Time passes . . .

← me in 2007

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 7/23

Time passes . . .

← me in 2008

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 7/23

Time passes . . .

← me in 2009

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 7/23

2009

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 8/23

2009

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 8/23

2009

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 8/23

Carlos & Luciana

Shortly after the presentation. Carlos, Luciana, and J¨

• rg sit around a
• table. The conversation goes like this:

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 9/23

Carlos & Luciana

Shortly after the presentation. Carlos, Luciana, and J¨

• rg sit around a
• table. The conversation goes like this:

Carlos/Luciana: “When we made PDDL models, it was very hard to know how to design them so that planners would perform better. Couldn’t one build a tool based on recognizing h+ toplogy?”

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 9/23

Carlos & Luciana

Shortly after the presentation. Carlos, Luciana, and J¨

• rg sit around a
• table. The conversation goes like this:

Carlos/Luciana: “When we made PDDL models, it was very hard to know how to design them so that planners would perform better. Couldn’t one build a tool based on recognizing h+ toplogy?” J¨

• rg: “Oh yeah, I already tried that during my PhD, but it didn’t work.”

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 9/23

Carlos & Luciana

Shortly after the presentation. Carlos, Luciana, and J¨

• rg sit around a
• table. The conversation goes like this:

Carlos/Luciana: “When we made PDDL models, it was very hard to know how to design them so that planners would perform better. Couldn’t one build a tool based on recognizing h+ toplogy?” J¨

• rg: “Oh yeah, I already tried that during my PhD, but it didn’t work.”

Carlos/Luciana: “But couldn’t we do something like XYZ?”

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 9/23

Carlos & Luciana

Shortly after the presentation. Carlos, Luciana, and J¨

• rg sit around a
• table. The conversation goes like this:

Carlos/Luciana: “When we made PDDL models, it was very hard to know how to design them so that planners would perform better. Couldn’t one build a tool based on recognizing h+ toplogy?” J¨

• rg: “Oh yeah, I already tried that during my PhD, but it didn’t work.”

Carlos/Luciana: “But couldn’t we do something like XYZ?” J¨

• rg: “Hm I don’t think so.”

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 9/23

Carlos & Luciana

Shortly after the presentation. Carlos, Luciana, and J¨

• rg sit around a
• table. The conversation goes like this:

Carlos/Luciana: “When we made PDDL models, it was very hard to know how to design them so that planners would perform better. Couldn’t one build a tool based on recognizing h+ toplogy?” J¨

• rg: “Oh yeah, I already tried that during my PhD, but it didn’t work.”

Carlos/Luciana: “But couldn’t we do something like XYZ?” J¨

• rg: “Hm I don’t think so.”

Carlos/Luciana: “αβγmaybe?”

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 9/23

Carlos & Luciana

Shortly after the presentation. Carlos, Luciana, and J¨

• rg sit around a
• table. The conversation goes like this:

Carlos/Luciana: “When we made PDDL models, it was very hard to know how to design them so that planners would perform better. Couldn’t one build a tool based on recognizing h+ toplogy?” J¨

• rg: “Oh yeah, I already tried that during my PhD, but it didn’t work.”

Carlos/Luciana: “But couldn’t we do something like XYZ?” J¨

• rg: “Hm I don’t think so.”

Carlos/Luciana: “αβγmaybe?” . . . [45 minutes later] . . .

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 9/23

Carlos & Luciana

Shortly after the presentation. Carlos, Luciana, and J¨

• rg sit around a
• table. The conversation goes like this:

Carlos/Luciana: “When we made PDDL models, it was very hard to know how to design them so that planners would perform better. Couldn’t one build a tool based on recognizing h+ toplogy?” J¨

• rg: “Oh yeah, I already tried that during my PhD, but it didn’t work.”

Carlos/Luciana: “But couldn’t we do something like XYZ?” J¨

• rg: “Hm I don’t think so.”

Carlos/Luciana: “αβγmaybe?” . . . [45 minutes later] . . . J¨

• rg: “Look, just consider Blocksworld and Logistics. One has local

minima, the other doesn’t. Still both have deletes.”

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 9/23

Carlos & Luciana

Shortly after the presentation. Carlos, Luciana, and J¨

• rg sit around a
• table. The conversation goes like this:

Carlos/Luciana: “When we made PDDL models, it was very hard to know how to design them so that planners would perform better. Couldn’t one build a tool based on recognizing h+ toplogy?” J¨

• rg: “Oh yeah, I already tried that during my PhD, but it didn’t work.”

Carlos/Luciana: “But couldn’t we do something like XYZ?” J¨

• rg: “Hm I don’t think so.”

Carlos/Luciana: “αβγmaybe?” . . . [45 minutes later] . . . J¨

• rg: “Look, just consider Blocksworld and Logistics. One has local

minima, the other doesn’t. Still both have deletes.” J¨

• rg: “And there is no other obvious difference in their structure . . . ”

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 9/23

Carlos & Luciana

Shortly after the presentation. Carlos, Luciana, and J¨

• rg sit around a
• table. The conversation goes like this:

Carlos/Luciana: “When we made PDDL models, it was very hard to know how to design them so that planners would perform better. Couldn’t one build a tool based on recognizing h+ toplogy?” J¨

• rg: “Oh yeah, I already tried that during my PhD, but it didn’t work.”

Carlos/Luciana: “But couldn’t we do something like XYZ?” J¨

• rg: “Hm I don’t think so.”

Carlos/Luciana: “αβγmaybe?” . . . [45 minutes later] . . . J¨

• rg: “Look, just consider Blocksworld and Logistics. One has local

minima, the other doesn’t. Still both have deletes.” J¨

• rg: “And there is no other obvious difference in their structure . . . ”

J¨

• rg: “. . .

Causal graphs!!!”

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 9/23

Blocksworld, Logistics, Causal Graphs

• n−A
• n−B
• n−C

clear−A clear−B clear−C pack1 pack2 truck

The causal graph of Blocksworld contains cycles; h+ local minima. That of Logistics doesn’t; h+ no local minima. Is there a general phenomenon behind this?

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 10/23

Outline

◮ What happened? ◮ On causal graphs and h+ ◮ Guaranteed global analysis ◮ Approximate local analysis ◮ Diagnosis ◮ Conclusion

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 11/23

On causal graphs and h+

Details:

[J. Hoffmann (2011). Analyzing Search Topology Without Running Any Search: On the Connection Between Causal Graphs and h+. Journal of Artificial Intelligence Research, Volume 41: 155-229. June 2nd ]

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 12/23

On causal graphs and h+

Details:

[J. Hoffmann (2011). Analyzing Search Topology Without Running Any Search: On the Connection Between Causal Graphs and h+. Journal of Artificial Intelligence Research, Volume 41: 155-229. June 2nd ]

CG acyclic & invertibility = ⇒ no local minima under h+

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 12/23

CG acyclic & invertibility = ⇒ no local minima under h+

T1 T1 T2 c c

1 2 1 2

x x x

L1 L2 L3 R3 R2 R1 g 0

x

1

x

2

x

d d d1

2 3

T2 c c

1 2 1 2

x x x

L1 L2 L3 R3 R2 R1 g 0

x

1

x

2

x

d d d1

2 3

• p0

◮ Finite-domain vars (“SAS+”) x0, x1, x2 ◮ Domain transition graphs ◮ Causal graph: top left ◮ Transitions invertible + no side effects ◮ Red: need this; Blue: how to get it; Green: where we are (state s) ◮ “Start” state s is not a local minimum! ◮ State s0: x1 = c1 and x2 = c2

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 13/23

CG acyclic & invertibility = ⇒ no local minima under h+

T1 T1 T2 c c

1 2 1 2

x x x

L1 L2 L3 R3 R2 R1 g 0

x

1

x

2

x

d d d1

2 3

T2 c c

1 2 1 2

x x x

L1 L2 L3 R3 R2 R1 g 0

x

1

x

2

x

d d d1

2 3

• p0

◮ Assume optimal relaxed plan P+(s) for s ◮ P+(s) must achieve c1, c2 via some paths T1, T2 ◮ If we remain within these paths, h+ never increases!

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 13/23

CG acyclic & invertibility = ⇒ no local minima under h+

T1 T1 T2 c c

1 2 1 2

x x x

L1 L2 L3 R3 R2 R1 g 0

x

1

x

2

x

d d d1

2 3

T2 c c

1 2 1 2

x x x

L1 L2 L3 R3 R2 R1 g 0

x

1

x

2

x

d d d1

2 3

• p0

◮ Assume optimal relaxed plan P+(s) for s ◮ P+(s) must achieve c1, c2 via some paths T1, T2 ◮ If we remain within these paths, h+ never increases! ◮ Wlog P+(s) = R1+, R2+, R3+ ◦ P+

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 13/23

CG acyclic & invertibility = ⇒ no local minima under h+

T1 T1 T1 T2 c c

1 2 1 2

x x x

L1 L2 L3 R3 R2 R1 g 0

x

1

x

2

x

d d d1

2 3

T2 c c

1 2 1 2

x x x

L1 L2 L3 R3 R2 R1 g 0

x

1

x

2

x

d d d1

2 3

T2 c c

1 2 1 2

x x x

L1 L2 L3 R3 R2 R1 g 0

x

1

x

2

x

d d d1

2 3

• p0

◮ Assume optimal relaxed plan P+(s) for s ◮ P+(s) must achieve c1, c2 via some paths T1, T2 ◮ If we remain within these paths, h+ never increases! ◮ Wlog P+(s) = R1+, R2+, R3+ ◦ P+ ◮ Say s′ := apply(s, R1, R2, R3)

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 13/23

CG acyclic & invertibility = ⇒ no local minima under h+

T1 T1 T1 T2 c c

1 2 1 2

x x x

L1 L2 L3 R3 R2 R1 g 0

x

1

x

2

x

d d d1

2 3

T2 c c

1 2 1 2

x x x

L1 L2 L3 R3 R2 R1 g 0

x

1

x

2

x

d d d1

2 3

T2 c c

1 2 1 2

x x x

L1 L2 L3 R3 R2 R1 g 0

x

1

x

2

x

d d d1

2 3

• p0

◮ Assume optimal relaxed plan P+(s) for s ◮ P+(s) must achieve c1, c2 via some paths T1, T2 ◮ If we remain within these paths, h+ never increases! ◮ Wlog P+(s) = R1+, R2+, R3+ ◦ P+ ◮ Say s′ := apply(s, R1, R2, R3) ◮ P+(s′) := L3+, L2+, L1+ ◦ P+ ◮ apply(s, R1+, R2+, R3+)[x1] = {d1, d2, d3, c1} =

apply(s′, L3+, L2+, L1+)[x1]

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 13/23

CG acyclic & invertibility = ⇒ no local minima under h+

T1 T1 T2 c c

1 2 1 2

x x x

L1 L2 L3 R3 R2 R1 g 0

x

1

x

2

x

d d d1

2 3

T2 c c

1 2 1 2

x x x

L1 L2 L3 R3 R2 R1 g 0

x

1

x

2

x

d d d1

2 3

• p0

◮ Say we’re in s0

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 13/23

CG acyclic & invertibility = ⇒ no local minima under h+

T1 T1 T2 c c

1 2 1 2

x x x

L1 L2 L3 R3 R2 R1 g 0

x

1

x

2

x

d d d1

2 3

T2 c c

1 2 1 2

x x x

L1 L2 L3 R3 R2 R1 g 0

x

1

x

2

x

d d d1

2 3

• p0

◮ Say we’re in s0 ◮ P+(s0) = op+

0 ◦ P+, and (from prev arg) |P+(s0)| ≤ |P+(s)|

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 13/23

CG acyclic & invertibility = ⇒ no local minima under h+

T1 T2 c c

1 2 1 2

x x x

L1 L2 L3 R3 R2 R1 g 0

x

1

x

2

x

d d d1

2 3

• p0

◮ Say we’re in s0 ◮ P+(s0) = op+

0 ◦ P+, and (from prev arg) |P+(s0)| ≤ |P+(s)|

◮ op0 is applicable now, leading to s1

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 13/23

CG acyclic & invertibility = ⇒ no local minima under h+

T1 T2 c c

1 2 1 2

x x x

L1 L2 L3 R3 R2 R1 g 0

x

1

x

2

x

d d d1

2 3

• p0

◮ Say we’re in s0 ◮ P+(s0) = op+

0 ◦ P+, and (from prev arg) |P+(s0)| ≤ |P+(s)|

◮ op0 is applicable now, leading to s1 ◮ P+(s1) := P+ (remove op0 from P+(s0)); thus h+(s1) < h+(s)!!

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 13/23

CG acyclic & invertibility = ⇒ no local minima under h+

T1 T2 c c

1 2 1 2

x x x

L1 L2 L3 R3 R2 R1 g 0

x

1

x

2

x

d d d1

2 3

• p0

◮ What does any of this have to do with causal graphs???

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 13/23

CG acyclic & invertibility = ⇒ no local minima under h+

T1 T2 c c

1 2 1 2

x x x

L1 L2 L3 R3 R2 R1 g 0

x

1

x

2

x

d d d1

2 3

• p0

◮ What does any of this have to do with causal graphs??? ◮ x0 is CG leaf

= ⇒ moving x0 does not affect relaxed plan, thus applying op0 in s0 decreases h+

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 13/23

CG acyclic & invertibility = ⇒ no local minima under h+

T1 T2 c c

1 2 1 2

x x x

L1 L2 L3 R3 R2 R1 g 0

x

1

x

2

x

d d d1

2 3

• p0

◮ What does any of this have to do with causal graphs??? ◮ x0 is CG leaf

= ⇒ moving x0 does not affect relaxed plan, thus applying op0 in s0 decreases h+

◮ Moving x0 involves only CG predecessors; if those have invertible

transitions & no cyclic dependencies = ⇒ can construct path to s0 with non-increasing h+

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 13/23

Is this useful for anything?

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 14/23

Is this useful for anything?

◮ Domain analysis! ◮ TorchLight ◮ Long-term goal: “automatic Hoffmann”

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 14/23

Is this useful for anything?

◮ Domain analysis! ◮ TorchLight ◮ Long-term goal: “automatic Hoffmann” ◮ Guaranteed global analysis ◮ Approximate local analysis ◮ Diagnosis

= ⇒ TorchLight demo today 17:30 – 20:00

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 14/23

Outline

◮ What happened? ◮ On causal graphs and h+ ◮ Guaranteed global analysis ◮ Approximate local analysis ◮ Diagnosis ◮ Conclusion

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 15/23

Guaranteed global analysis

◮ Prove absence of local minima & global bound on lookahead ◮ Criterion strictly more general than what we just saw ◮ Allows e.g. non-unary operators, provided any side-effects are

“harmless”

◮ Recognizes Logistics, Miconic-STRIPS, Movie, SimpleTSP ◮ Does not recognize anything else just yet . . . [ 4 12 domains]

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 16/23

Outline

◮ What happened? ◮ On causal graphs and h+ ◮ Guaranteed global analysis ◮ Approximate local analysis ◮ Diagnosis ◮ Conclusion

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 17/23

Approximate local analysis

◮ Local: Is state s not a local minimum? ◮ Analyze relaxed plan P+(s) ◮ Answer “yes” guaranteed correct if P+(s) is optimal ◮ Theoretically, given optimal P+(s) as input, recognizes

Ferry, Gripper, Elevators, Transport [+ global = 8

12 domains] ◮ Randomly sample states; fraction of “yes”: success rate

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 18/23

Approximate local analysis

◮ Local: Is state s not a local minimum? ◮ Analyze relaxed plan P+(s) ◮ Answer “yes” guaranteed correct if P+(s) is optimal ◮ Theoretically, given optimal P+(s) as input, recognizes

Ferry, Gripper, Elevators, Transport [+ global = 8

12 domains] ◮ Randomly sample states; fraction of “yes”: success rate ◮ Disclaimer:

◮ Success rates can also be obtained by trivial search probing ◮ Strong theoretical differences; some differences in benchmarks J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 18/23

Hoffmann vs. TorchLight

Airport Blocksworld−Arm Depots Driverlog Freecell Mprime Mystery Pipesworld−NoTank Pipesworld−Tank PSR Rovers Satellite Zenotravel Simple−Tsp Transport Tyreworld Elevators Ferry Gripper Hanoi Logistics Miconic−STRIPS Movie Grid Blocksworld−NoArm Zenotravel [95] Depots [81] Grid [80] Pipesworld−NoTank [76] Blocksworld−NoArm [57] Freecell [56] PSR [50] Mprime [49] Pipesworld−Tank [40] Mystery [39] Blocksworld−Arm [30] Airport [0] Hanoi [0] Ferry [100] Gripper [100] Elevators [100] Logistics [100] Miconic−STRIPS [100] Movie [100] Driverlog [100] Rovers [100] Satellite [100] Simple−Tsp [100] Transport [100] Tyreworld [100]

◮ Success rate: average

per-domain from single sample state per-instance

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 19/23

Hoffmann vs. TorchLight

Airport Blocksworld−Arm Depots Driverlog Freecell Mprime Mystery Pipesworld−NoTank Pipesworld−Tank PSR Rovers Satellite Zenotravel Simple−Tsp Transport Tyreworld Elevators Ferry Gripper Hanoi Logistics Miconic−STRIPS Movie Grid Blocksworld−NoArm Zenotravel [95] Depots [81] Grid [80] Pipesworld−NoTank [76] Blocksworld−NoArm [57] Freecell [56] PSR [50] Mprime [49] Pipesworld−Tank [40] Mystery [39] Blocksworld−Arm [30] Airport [0] Hanoi [0] Ferry [100] Gripper [100] Elevators [100] Logistics [100] Miconic−STRIPS [100] Movie [100] Driverlog [100] Rovers [100] Satellite [100] Simple−Tsp [100] Transport [100] Tyreworld [100]

◮ Not all domains are

“fully recognized” . . .

◮ . . . mostly because

Hoffmann is too

• ptimistic

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 19/23

Hoffmann vs. TorchLight

Airport Blocksworld−Arm Depots Driverlog Freecell Mprime Mystery Pipesworld−NoTank Pipesworld−Tank PSR Rovers Satellite Zenotravel Simple−Tsp Transport Tyreworld Elevators Ferry Gripper Hanoi Logistics Miconic−STRIPS Movie Grid Blocksworld−NoArm Zenotravel [95] Depots [81] Grid [80] Pipesworld−NoTank [76] Blocksworld−NoArm [57] Freecell [56] PSR [50] Mprime [49] Pipesworld−Tank [40] Mystery [39] Blocksworld−Arm [30] Airport [0] Hanoi [0] Ferry [100] Gripper [100] Elevators [100] Logistics [100] Miconic−STRIPS [100] Movie [100] Driverlog [100] Rovers [100] Satellite [100] Simple−Tsp [100] Transport [100] Tyreworld [100]

◮ Some new domains are

“fully recognized” . . .

◮ . . . mostly because

Hoffmann is too pessimistic

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 19/23

Hoffmann vs. TorchLight

Airport Blocksworld−Arm Depots Driverlog Freecell Mprime Mystery Pipesworld−NoTank Pipesworld−Tank PSR Rovers Satellite Zenotravel Simple−Tsp Transport Tyreworld Elevators Ferry Gripper Hanoi Logistics Miconic−STRIPS Movie Grid Blocksworld−NoArm Zenotravel [95] Depots [81] Grid [80] Pipesworld−NoTank [76] Blocksworld−NoArm [57] Freecell [56] PSR [50] Mprime [49] Pipesworld−Tank [40] Mystery [39] Blocksworld−Arm [30] Airport [0] Hanoi [0] Ferry [100] Gripper [100] Elevators [100] Logistics [100] Miconic−STRIPS [100] Movie [100] Driverlog [100] Rovers [100] Satellite [100] Simple−Tsp [100] Transport [100] Tyreworld [100]

◮ Success rates are more

than a “yes/no” answer!

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 19/23

Outline

◮ What happened? ◮ On causal graphs and h+ ◮ Guaranteed global analysis ◮ Approximate local analysis ◮ Diagnosis ◮ Conclusion

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 20/23

Diagnosis

◮ Which domain aspects cause local minima?

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 21/23

Diagnosis

◮ Which domain aspects cause local minima? ◮ Which unsatisfied conditions caused the analysis to fail?

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 21/23

Diagnosis

◮ Which domain aspects cause local minima? ◮ Which unsatisfied conditions caused the analysis to fail? ◮ Operator-name/predicate pairs (op, P) where op effect on P

prevented use as successful op0 in approximate local analysis

◮ Zenotravel: “fly,fuel-level” ◮ Mystery/Mprime: “feast,locale” ◮ Satellite: “switch-on,calibrated” ◮ Rovers: “take-image,calibrated” ◮ This is merely a first-shot technique!

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 21/23

Outline

◮ What happened? ◮ On causal graphs and h+ ◮ Guaranteed global analysis ◮ Approximate local analysis ◮ Diagnosis ◮ Conclusion

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 22/23

Conclusion

◮

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 23/23

Conclusion

◮

Improving TorchLight:

◮ Strengthen global anaylsis with complementary techniques ◮ Derive “good case” characterizations from local analysis?

Using TorchLight:

◮ Relaxed plan analysis =

⇒ macro actions

◮ Performance prediction (even online during search) ◮ Abstract by removing (some) harmful effects (diagnosis!) ◮ Modeling support for planning end-users (diagnosis!)

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 23/23

Last Slide

• Thanks. Questions?

p.s. There is an error in these slides. Where?

J¨

• rg Hoffmann

Where Ignoring Delete Lists Works, Part II: Causal Graphs 24/23