The Joy of Forgetting: Faster Anytime Search via Restarting

43 Pages·2010·0.33 MB·English

Introduction
ExperimentsinPlanning
ExperimentsinOtherDomains
Summary
The Joy of Forgetting:
Faster Anytime Search via Restarting
Silvia Richter
GriffithUniversity&NICTA,Australia
Jordan T. Thayer & Wheeler Ruml
UniversityofNewHampshire,US
ICAPS 2010
Introduction
ExperimentsinPlanning
ExperimentsinOtherDomains
Summary
Outline
1 Introduction
Anytime Weighted A∗
Low h-Bias
Restarting Weighted A∗
2 Experiments in Planning
3 Experiments in Other Domains
4 Summary
Introduction AnytimeWeightedA∗
ExperimentsinPlanning
Lowh-Bias
ExperimentsinOtherDomains RestartingWeightedA∗
Summary
Outline
1 Introduction
Anytime Weighted A∗
Low h-Bias
Restarting Weighted A∗
2 Experiments in Planning
3 Experiments in Other Domains
4 Summary
Introduction AnytimeWeightedA∗
ExperimentsinPlanning
Lowh-Bias
ExperimentsinOtherDomains RestartingWeightedA∗
Summary
Anytime Planning for IPC 2008
IPC 2008 requirement: find best possible plan within 30 minutes.
This suggested an anytime approach:
Find a solution as quickly as possible
(any solution is better than none).
(cid:32) greedy best-first search
While there is still time, try to improve the solution.
(cid:32) weighted A∗ with decreasing weights
Interesting finding:
A series of independent runs of weighted A∗ seemed to perform
better than one continued search.
Introduction AnytimeWeightedA∗
ExperimentsinPlanning
Lowh-Bias
ExperimentsinOtherDomains RestartingWeightedA∗
Summary
Continued WA∗
Basic algorithm:
1 Set weight and bound
bound = cost of best known solution, initially ∞
2 Update open list w.r.t. weight if necessary
3 Conduct WA∗ search, using bound for pruning
4 Upon new best solution: report solution, goto 1.
Variants used in literature:
Anytime A∗ (Zhou & Hansen 2001, 2004)
ARA∗ (Likhachev et al. 2003)
Introduction AnytimeWeightedA∗
ExperimentsinPlanning
Lowh-Bias
ExperimentsinOtherDomains RestartingWeightedA∗
Summary
Example: Blocksworld Task 11-2
Plan lengths found over time:
GBFS + iterated WA∗: 72 50 46 36 34
GBFS + continued WA∗: 72 68 46 38 34
Plan qualities (best length / current length):
1 34
36
0.9
38
q)
q*/ 0.8 h
uality ( 0.7 46 n lengt
q 50 a
n 0.6 Pl
a
Pl
0.5
iterated WA*
continued WA* 68
0.4 72
0.1 1 10
Time (s)
hff1’’-0--vvvaaaellluuuxepeesssa,,ndwwed==st21a.t5es(reduced weight)
glx(cid:32)2er9seseesxedgapaycearcncsnuehodrrlaaeulettdteesiodsstnthgasetrteaefetsuedrsyther from gohma=ulst3e.8xpanhd=for4.o0ptimal path
olbbbepuuesttttsswitmmeaaeffctaeaceenlnuscsytrfioiannosltutdpeoitileipnloonegnpnnsegttrlh1asisietstaetlsnsedfhtaevxepalonwdienrgf’r-ivgahltueof S
1380...876 397...867 386...867 497...000 4.0
x x
983...814 387...481 11320...005
x
297...629 286...629 286...629 286...629 617...8985 298...000 1290...000
x x x x
1280...692 176...867 176...867 176...867 176...867 617...8985 176...005 187...005
x x x x x x
1280...692 187...867 176...005 176...005 176...005 718...8985 176...005
x x x x
198...867 187...005 187...005 819...8985 187...005 187...005
x
Introduction AnytimeWeightedA∗
ExperimentsinPlanning
Lowh-Bias
ExperimentsinOtherDomains RestartingWeightedA∗
Summary
The Problem: Low-h Bias
S
g2
g1
hff1’’-0--vvvaaaellluuuxepeesssa,,ndwwed==st21a.t5es(reduced weight)
glx(cid:32)2er9seseesxedgapaycearcncsnuehodrrlaaeulettdteesiodsstnthgasetrteaefetsuedrsyther from gomaulst expand for optimal path
olbbbepuuesttttsswitmmeaaeffctaeaceenlnuscsytrfioiannosltutdpeoitileipnloonegnpnnsegttrlh1asisietstaetlsnsedfhtaevxepalonwdienrgf’r-ivgahltueof S
1380...876 397...867 386...867 497...000 4.0
x x
983...814 387...481 11320...005
x
297...629 286...629 286...629 286...629 617...8985 298...000 1290...000
x x x x
1280...692 176...867 176...867 176...867 176...867 617...8985 176...005 187...005
x x x x x x
1280...692 187...867 176...005 176...005 176...005 718...8985 176...005
x x x x
198...867 187...005 187...005 819...8985 187...005 187...005
x
Introduction AnytimeWeightedA∗
ExperimentsinPlanning
Lowh-Bias
ExperimentsinOtherDomains RestartingWeightedA∗
Summary
The Problem: Low-h Bias
h = 3.8 h = 4.0
S
g2
g1
hff1’’-0--vvvaaaellluuuxepeesssa,,ndwwed==st21a.t5es(reduced weight)
lx(cid:32)2e9ssesxegapacearcncnuehdrraaelettdeesdsstthgasetrteaefetsuedrsyther from gomaulst expand for optimal path
lbbbeuuestttsswtmeaaeffcteaceennuscytrfiiannosttdpeoiilepnlonegnpnsegttrlh1asisietstaetlsnsedfhtaevxepalonwdienrgf’r-ivgahltueof S
1380...876 397...867 386...867 497...000 4.0
x x
983...814 387...481 11320...005
x
297...629 286...629 286...629 286...629 617...8985 298...000 1290...000
x x x x
1280...692 176...867 176...867 176...867 176...867 617...8985 176...005 187...005
x x x x x x
1280...692 187...867 176...005 176...005 176...005 718...8985 176...005
x x x x
198...867 187...005 187...005 819...8985 187...005 187...005
x
Introduction AnytimeWeightedA∗
ExperimentsinPlanning
Lowh-Bias
ExperimentsinOtherDomains RestartingWeightedA∗
Summary
The Problem: Low-h Bias
greedy solution h = 3.8 h = 4.0
optimal solution
S
g2
g1
ff1’’0--vvaaelluuxpeessa,,ndwwed==st21a.t5es(reduced weight)
gx(cid:32)2r9eeesxedgpayearncsnehodrlaeuletdtesiodssntgastrteaeetsedsy hm=ust3e.8xpanhd=for4.o0ptimal path
obbbpuuettttswitmmeaefftaeaeenlnscsytfioinnoslutdpoitileipnlonegpnnsegtrl1asisitstaetsnsdhaevxepalonwdienrgf’r-ivgahltueof S
180..76 97..67 86..67 97..00
x x
98..81 87..81 1120..05
x
97..29 86..29 86..29 86..29 67..885 98..00 190..00
x x x x
180..92 76..67 76..67 76..67 76..67 67..885 76..05 87..05
x x x x x x
180..92 87..67 76..05 76..05 76..05 78..885 76..05
x x x x
98..67 87..05 87..05 89..885 87..05 87..05
x
Introduction AnytimeWeightedA∗
ExperimentsinPlanning
Lowh-Bias
ExperimentsinOtherDomains RestartingWeightedA∗
Summary
The Problem: Low-h Bias
h-values
less accurate the further from goal
less accurate on the left
3.8 3.8 3.8 S 4.0 4.0
3.4 3.4 3.0
2.6 2.6 2.6 2.6 1.9 2.0 2.0
2.6 1.8 1.8 1.8 1.8 1.9 1.0 1.0
2.6 1.8 1.0 1.0 1.0 1.9 1.0 g2
1.8 1.0 g1 1.0 1.9 1.0 1.0