PREDICTING THE EFFECTIVENESS OF BIDIRECTIONAL HEURISTIC SEARCH - - PowerPoint PPT Presentation

predicting the effectiveness of bidirectional heuristic
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PREDICTING THE EFFECTIVENESS OF BIDIRECTIONAL HEURISTIC SEARCH - - PowerPoint PPT Presentation

PREDICTING THE EFFECTIVENESS OF BIDIRECTIONAL HEURISTIC SEARCH Nathan R. Sturtevant, Canada CIFAR AI Chair, Amii, University of Alberta Shahaf Shperberg , Ben-Gurion University Ariel Felner , Ben-Gurion University Jingwei Chen, University of


slide-1
SLIDE 1

Moving AI Lab

PREDICTING THE EFFECTIVENESS OF BIDIRECTIONAL HEURISTIC SEARCH

Nathan R. Sturtevant, Canada CIFAR AI Chair, Amii, University of Alberta Shahaf Shperberg , Ben-Gurion University Ariel Felner , Ben-Gurion University Jingwei Chen, University of Alberta

slide-2
SLIDE 2

Q: When does bidirectional (heuristic) search perform well? A: Performance of bidirectional search is positively correlated with the number of states that have heuristics that are both low and inaccurate.

BIDIRECTIONAL SEARCH

Caveat: Not enough time in talk to be completely precise.

slide-3
SLIDE 3

A strong heuristic expands a majority

  • f the states in the first half of the

search. BK2: Unidirectional search

  • utperforms bidirectional search with

a strong heuristic.

BARKER AND KORF (2015)

slide-4
SLIDE 4

MM is guaranteed to meet in the middle. If |FF| > |RN|, A* will expand more states than MM if the heuristic is weak, fewer if the heuristic is accurate.

HOLTE ET AL (2017)

Start Goal

slide-5
SLIDE 5

MM is guaranteed to meet in the middle. If |FF| > |RN|, A* will expand more states than MM if the heuristic is weak, fewer if the heuristic is accurate.

HOLTE ET AL (2017)

FF Start Goal

slide-6
SLIDE 6

MM is guaranteed to meet in the middle. If |FF| > |RN|, A* will expand more states than MM if the heuristic is weak, fewer if the heuristic is accurate.

HOLTE ET AL (2017)

FF RN Start Goal

slide-7
SLIDE 7

Front-to-end bidirectional search

  • admissible heuristic
  • not necessarily consistent

Corresponds to finding a minimum vertex cover on a bipartite graph

ECKERLE ET AL (2017)

slide-8
SLIDE 8

Necessary expansions for a pair of states: ff(a) < C* fb(b) < C* gf(a) + gb(b) < C*

ECKERLE ET AL (2017)

slide-9
SLIDE 9

Necessary expansions for a pair of states: ff(a) < C* fb(b) < C* gf(a) + gb(b) < C*

ECKERLE ET AL (2017)

a

slide-10
SLIDE 10

Necessary expansions for a pair of states: ff(a) < C* fb(b) < C* gf(a) + gb(b) < C*

ECKERLE ET AL (2017)

b a

slide-11
SLIDE 11

Necessary expansions for a pair of states: ff(a) < C* fb(b) < C* gf(a) + gb(b) < C*

ECKERLE ET AL (2017)

?

b a

slide-12
SLIDE 12

EXPLANATION

1

1

19

2

342

3

5,391

4

31,924

5

53,120

6

31,819

7

11,686

8

3,159

9

715

10

128

11

23

12

3 1

1

19

2

342

3

3,396

4

10,697

5

11,586

6

6,604

7

2,634

8

810

9

213

10

47

11

13

12

2 gF gB

C* = 13

slide-13
SLIDE 13

EXPLANATION

1

1

19

2

342

3

5,391

4

31,924

5

53,120

6

31,819

7

11,686

8

3,159

9

715

10

128

11

23

12

3 1

1

19

2

342

3

3,396

4

10,697

5

11,586

6

6,604

7

2,634

8

810

9

213

10

47

11

13

12

2 gF gB

C* = 13 ff < C*

slide-14
SLIDE 14

EXPLANATION

1

1

19

2

342

3

5,391

4

31,924

5

53,120

6

31,819

7

11,686

8

3,159

9

715

10

128

11

23

12

3 1

1

19

2

342

3

3,396

4

10,697

5

11,586

6

6,604

7

2,634

8

810

9

213

10

47

11

13

12

2 gF gB

C* = 13 ff < C*

slide-15
SLIDE 15

EXPLANATION

1

1

19

2

342

3

5,391

4

31,924

5

53,120

6

31,819

7

11,686

8

3,159

9

715

10

128

11

23

12

3 1

1

19

2

342

3

3,396

4

10,697

5

11,586

6

6,604

7

2,634

8

810

9

213

10

47

11

13

12

2 gF gB

C* = 13 ff < C*

slide-16
SLIDE 16

EXPLANATION

1

1

19

2

342

3

5,391

4

31,924

5

53,120

6

31,819

7

11,686

8

3,159

9

715

10

128

11

23

12

3 1

1

19

2

342

3

3,396

4

10,697

5

11,586

6

6,604

7

2,634

8

810

9

213

10

47

11

13

12

2 gF gB

C* = 13 ff < C* fb < C*

slide-17
SLIDE 17

EXPLANATION

1

1

19

2

342

3

5,391

4

31,924

5

53,120

6

31,819

7

11,686

8

3,159

9

715

10

128

11

23

12

3 1

1

19

2

342

3

3,396

4

10,697

5

11,586

6

6,604

7

2,634

8

810

9

213

10

47

11

13

12

2 gF gB

C* = 13 ff < C* fb < C*

slide-18
SLIDE 18

EXPLANATION

1

1

19

2

342

3

5,391

4

31,924

5

53,120

6

31,819

7

11,686

8

3,159

9

715

10

128

11

23

12

3 1

1

19

2

342

3

3,396

4

10,697

5

11,586

6

6,604

7

2,634

8

810

9

213

10

47

11

13

12

2 gF gB

C* = 13 ff < C* fb < C*

slide-19
SLIDE 19

EXPLANATION

1

1

19

2

342

3

5,391

4

31,924

5

53,120

6

31,819

7

11,686

8

3,159

9

715

10

128

11

23

12

3 1

1

19

2

342

3

3,396

4

10,697

5

11,586

6

6,604

7

2,634

8

810

9

213

10

47

11

13

12

2 gF gB

C* = 13 ff < C* fb < C* gf(a) + gb(b) < C*

slide-20
SLIDE 20

EXPLANATION

1

1

19

2

342

3

5,391

4

31,924

5

53,120

6

31,819

7

11,686

8

3,159

9

715

10

128

11

23

12

3 1

1

19

2

342

3

3,396

4

10,697

5

11,586

6

6,604

7

2,634

8

810

9

213

10

47

11

13

12

2 gF gB

C* = 13 ff < C* fb < C* gf(a) + gb(b) < C*

slide-21
SLIDE 21

EXPLANATION

1

1

19

2

342

3

5,391

4

31,924

5

53,120

6

31,819

7

11,686

8

3,159

9

715

10

128

11

23

12

3 1

1

19

2

342

3

3,396

4

10,697

5

11,586

6

6,604

7

2,634

8

810

9

213

10

47

11

13

12

2 gF gB

C* = 13 ff < C* fb < C* gf(a) + gb(b) < C*

slide-22
SLIDE 22

EXPLANATION

1

1

19

2

342

3

5,391

4

31,924

5

53,120

6

31,819

7

11,686

8

3,159

9

715

10

128

11

23

12

3 1

1

19

2

342

3

3,396

4

10,697

5

11,586

6

6,604

7

2,634

8

810

9

213

10

47

11

13

12

2 gF gB

C* = 13 ff < C* fb < C* gf(a) + gb(b) < C*

slide-23
SLIDE 23

EXPLANATION

1

1

19

2

342

3

5,391

4

31,924

5

53,120

6

31,819

7

11,686

8

3,159

9

715

10

128

11

23

12

3 1

1

19

2

342

3

3,396

4

10,697

5

11,586

6

6,604

7

2,634

8

810

9

213

10

47

11

13

12

2 gF gB

C* = 13 ff < C* fb < C*

slide-24
SLIDE 24

EXPLANATION

36,364 36,363 36,369 36,664 41,842 72,956 123,442 148,657 148,757 141,219 138,538 138,324 138,328 138,330 1

1

19

2

342

3

5,391

4

31,924

5

53,120

6

31,819

7

11,686

8

3,159

9

715

10

128

11

23

12

3 1

1

19

2

342

3

3,396

4

10,697

5

11,586

6

6,604

7

2,634

8

810

9

213

10

47

11

13

12

2 gF gB

C* = 13

slide-25
SLIDE 25

RUBIK’S CUBE 7-TILE PDB

C* = 12

1

1

18

2

237

3

1,201

4

1,981

5

2,670

6

3,291

7

3,567

8

3,638

9

3,647

10

3,740

11

3,138 1

1

18

2

237

3

1,330

4

2,438

5

3,123

6

3,615

7

3,904

8

4,156

9

4,273

10

4,371

11

3,749 gF gB

slide-26
SLIDE 26

RUBIK’S CUBE 7-TILE PDB

C* = 12

1

1

18

2

237

3

1,201

4

1,981

5

2,670

6

3,291

7

3,567

8

3,638

9

3,647

10

3,740

11

3,138 1

1

18

2

237

3

1,330

4

2,438

5

3,123

6

3,615

7

3,904

8

4,156

9

4,273

10

4,371

11

3,749 gF gB

slide-27
SLIDE 27

RUBIK’S CUBE 7-TILE PDB

C* = 12

1

1

18

2

237

3

1,201

4

1,981

5

2,670

6

3,291

7

3,567

8

3,638

9

3,647

10

3,740

11

3,138 1

1

18

2

237

3

1,330

4

2,438

5

3,123

6

3,615

7

3,904

8

4,156

9

4,273

10

4,371

11

3,749 gF gB

slide-28
SLIDE 28

RUBIK’S CUBE 7-TILE PDB

C* = 12

1

1

18

2

237

3

1,201

4

1,981

5

2,670

6

3,291

7

3,567

8

3,638

9

3,647

10

3,740

11

3,138 1

1

18

2

237

3

1,330

4

2,438

5

3,123

6

3,615

7

3,904

8

4,156

9

4,273

10

4,371

11

3,749 gF gB

slide-29
SLIDE 29

RUBIK’S CUBE 7-TILE PDB

C* = 12

1

1

18

2

237

3

1,201

4

1,981

5

2,670

6

3,291

7

3,567

8

3,638

9

3,647

10

3,740

11

3,138 1

1

18

2

237

3

1,330

4

2,438

5

3,123

6

3,615

7

3,904

8

4,156

9

4,273

10

4,371

11

3,749 gF gB

slide-30
SLIDE 30

RUBIK’S CUBE 7-TILE PDB

C* = 12

1

1

18

2

237

3

1,201

4

1,981

5

2,670

6

3,291

7

3,567

8

3,638

9

3,647

10

3,740

11

3,138 1

1

18

2

237

3

1,330

4

2,438

5

3,123

6

3,615

7

3,904

8

4,156

9

4,273

10

4,371

11

3,749 gF gB

slide-31
SLIDE 31

RUBIK’S CUBE 7-TILE PDB

C* = 12

1

1

18

2

237

3

1,201

4

1,981

5

2,670

6

3,291

7

3,567

8

3,638

9

3,647

10

3,740

11

3,138 1

1

18

2

237

3

1,330

4

2,438

5

3,123

6

3,615

7

3,904

8

4,156

9

4,273

10

4,371

11

3,749 gF gB

slide-32
SLIDE 32

1

1

19

2

259

3

839

4

534

5

173

6

31

7

3 1

1

19

2

250

3

919

4

917

5

406

6

123

7

29

8

2 gF gB

PANCAKE GAP HEURISTIC

C* = 13

slide-33
SLIDE 33

PANCAKE GAP HEURISTIC

2,666 2,667 2,686 2,945 3,784 4,316 4,460 4,368 3,965 3,048 2,129 1,879 1,860 1,859 1

1

19

2

259

3

839

4

534

5

173

6

31

7

3

8 9 10 11 12

1

1

19

2

250

3

919

4

917

5

406

6

123

7

29

8

2

9 10 11 12

gF gB

C* = 13

slide-34
SLIDE 34

PANCAKE GAP HEURISTIC

2,666 2,667 2,686 2,945 3,784 4,316 4,460 4,368 3,965 3,048 2,129 1,879 1,860 1,859 1

1

19

2

259

3

839

4

534

5

173

6

31

7

3

8 9 10 11 12

1

1

19

2

250

3

919

4

917

5

406

6

123

7

29

8

2

9 10 11 12

gF gB

C* = 13

slide-35
SLIDE 35

PANCAKE GAP HEURISTIC

2,666 2,667 2,686 2,945 3,784 4,316 4,460 4,368 3,965 3,048 2,129 1,879 1,860 1,859 1

1

19

2

259

3

839

4

534

5

173

6

31

7

3

8 9 10 11 12

1

1

19

2

250

3

919

4

917

5

406

6

123

7

29

8

2

9 10 11 12

gF gB

C* = 13

slide-36
SLIDE 36

PANCAKE GAP HEURISTIC

2,666 2,667 2,686 2,945 3,784 4,316 4,460 4,368 3,965 3,048 2,129 1,879 1,860 1,859 1

1

19

2

259

3

839

4

534

5

173

6

31

7

3

8 9 10 11 12

1

1

19

2

250

3

919

4

917

5

406

6

123

7

29

8

2

9 10 11 12

gF gB

C* = 13

slide-37
SLIDE 37

PANCAKE GAP HEURISTIC

2,666 2,667 2,686 2,945 3,784 4,316 4,460 4,368 3,965 3,048 2,129 1,879 1,860 1,859 1

1

19

2

259

3

839

4

534

5

173

6

31

7

3

8 9 10 11 12

1

1

19

2

250

3

919

4

917

5

406

6

123

7

29

8

2

9 10 11 12

gF gB

C* = 13

slide-38
SLIDE 38

PANCAKE GAP HEURISTIC

2,666 2,667 2,686 2,945 3,784 4,316 4,460 4,368 3,965 3,048 2,129 1,879 1,860 1,859 1

1

19

2

259

3

839

4

534

5

173

6

31

7

3

8 9 10 11 12

1

1

19

2

250

3

919

4

917

5

406

6

123

7

29

8

2

9 10 11 12

gF gB

C* = 13

slide-39
SLIDE 39

PANCAKE GAP HEURISTIC

2,666 2,667 2,686 2,945 3,784 4,316 4,460 4,368 3,965 3,048 2,129 1,879 1,860 1,859 1

1

19

2

259

3

839

4

534

5

173

6

31

7

3

8 9 10 11 12

1

1

19

2

250

3

919

4

917

5

406

6

123

7

29

8

2

9 10 11 12

gF gB

C* = 13

slide-40
SLIDE 40

PANCAKE GAP HEURISTIC

2,666 2,667 2,686 2,945 3,784 4,316 4,460 4,368 3,965 3,048 2,129 1,879 1,860 1,859 1

1

19

2

259

3

839

4

534

5

173

6

31

7

3

8 9 10 11 12

1

1

19

2

250

3

919

4

917

5

406

6

123

7

29

8

2

9 10 11 12

gF gB

C* = 13

slide-41
SLIDE 41

CRITICAL STATES

  • Sample states near goal and

find heuristic inaccuracies

Goal

slide-42
SLIDE 42

CRITICAL STATES

  • Sample states near goal and

find heuristic inaccuracies

Goal

slide-43
SLIDE 43

CRITICAL STATES

  • Sample states near goal and

find heuristic inaccuracies

  • Sample the heuristic to find

how many low heuristic values there are

Goal

slide-44
SLIDE 44

CRITICAL STATES

  • Sample states near goal and

find heuristic inaccuracies

  • Sample the heuristic to find

how many low heuristic values there are

Goal

slide-45
SLIDE 45

ASYMMETRY

  • Sample states near goal and

find heuristic inaccuracies

  • Sample the heuristic to find

how many low heuristic values there are

  • Look at the asymmetry of the

state space

slide-46
SLIDE 46

EXAMPLE: TOH WITH PDB HEURISTIC

is close to the goal and has a low heuristic value is far from the goal Low heuristics are inaccurate Bidirectional heuristic search outperforms unidirectional search

ϕ(s) s

5 4 3 7 6 2 1 5 4 7 6

Problem State s PDB Abstraction ϕ(s)

slide-47
SLIDE 47

EXAMPLE: UNINFORMED SEARCH

Low and inaccurate heuristics for almost all states

slide-48
SLIDE 48

CONCLUSION

Critical states have both low and inaccurate heuristics Need critical states for bidirectional search to perform well More critical states → bidirectional search will do better

https://webdocs.cs.ualberta.ca/~nathanst/papers/sturtevant2020unibidi.pdf