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Table 1 Average and 95 % confidence interval of the time, in seconds, to solve each problem using ε=10−3

From: Reachability-based model reduction for Markov decision process

Problem

ReachMRFS-V2 + TVI

ReachMRFS-V2 + VI

ReachMRFS-V2 + LRTDP

MRFS + TVI

MRFS + VI

MRFS + LRTDP

Cross.

1

3.64 ±0.04

4.10 ± 0.03

5.71 ± 0.08

19.41 ± 0.60

19.87 ± 0.65

20.86 ± 0.59

 

2

3.65 ±0.03

4.14 ± 0.05

6.53 ± 0.16

19.36 ± 0.60

19.80 ± 0.58

21.82 ± 0.67

 

3

15.29 ±0.11

22.74 ± 0.21

26.72 ± 0.40

-

-

-

 

4

15.17 ±0.14

22.49 ± 0.34

25.05 ± 0.34

-

-

-

Elevators

1

4.45 ±0.04

4.90 ± 0.07

16.08 ± 0.33

100.10 ± 4.56

97.57 ± 5.49

101.99 ± 4.07

 

2

161.60 ± 1.42

155.99 ±1.35

1788.44 ± 14.60

-

-

-

 

3

146.87 ±1.04

149.76 ± 1.24

1468.64 ± 11.85

-

-

-

 

4

16.86 ± 0.65

15.35 ±0.26

146.66 ± 1.22

-

-

-

 

7

72.25 ±0.83

90.99 ± 0.86

3599.00 ± 0.11

-

-

-

Game

1

137.10 ±0.48

192.98 ± 0.80

215.95 ± 1.31

161.62 ± 1.04

211.74 ± 1.31

234.31 ± 1.65

 

2

118.89 ±0.35

174.03 ± 0.97

239.72 ± 1.27

140.83 ± 0.97

191.77 ± 1.16

260.07 ± 2.40

 

3

114.57 ±0.49

168.88 ± 0.48

233.54 ± 1.51

137.38 ± 0.83

187.54 ± 1.21

253.25 ± 1.87

Navigation

1

1.76 ±0.01

1.97 ± 0.01

2.41 ± 0.03

21.09 ± 0.76

20.36 ± 1.00

21.39 ± 0.82

 

2

2.29 ±0.02

2.59 ± 0.02

2.91 ± 0.03

189.90 ± 8.69

191.50 ± 6.66

194.26 ± 6.82

 

3

2.72 ±0.07

3.45 ± 0.03

3.26 ± 0.02

-

-

-

 

4

4.61 ±0.04

4.80 ± 0.04

4.83 ± 0.04

-

-

-

 

5

4.32 ±0.05

4.80 ± 0.05

5.18 ± 0.06

-

-

-

 

6

6.66 ±0.07

7.17 ± 0.07

8.03 ± 0.09

-

-

-

 

7

8.53 ±0.06

8.84 ± 0.07

9.64 ± 0.07

-

-

-

 

8

11.40 ±0.09

12.24 ± 0.11

13.39 ± 0.10

-

-

-

 

9

20.33 ±0.21

21.58 ± 0.21

22.94 ± 0.22

-

-

-

 

10

36.53 ±0.51

37.55 ± 0.47

38.55 ± 0.45

-

-

-

Skill

1

2.76 ±0.02

2.86 ± 0.03

4.48 ± 0.07

19.24 ± 1.17

18.98 ± 1.00

18.07 ± 0.85

 

2

2.75 ±0.04

2.87 ± 0.03

4.51 ± 0.12

18.72 ± 0.95

18.20 ± 0.87

17.46 ± 0.60

 

3

27.91 ± 0.23

26.15 ±0.23

112.63 ± 0.80

175.94 ± 5.73

176.50 ± 7.12

328.26 ± 11.62

 

4

27.55 ± 0.26

25.92 ±0.30

100.38 ± 0.79

178.21 ± 7.62

172.60 ± 7.85

311.95 ± 12.43

  1. If a solution is not found in the given time and memory thresholds, then ‘-’ is shown. Best performance over all planners (columns) is shown in bold font. In the columns, Algorithm ?? + Algorithm ?? refers to the algorithm used in reduction phase (Algorithm ??) and the algorithm used to solve the reduced MDP (Algorithm ??)