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140 lines
2.9 KiB
140 lines
2.9 KiB
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// maze example (POMDP)
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// slightly extends that presented in
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// Littman, Cassandra and Kaelbling
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// Learning policies for partially observable environments: Scaling up
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// Technical Report CS, Brown University
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// gxn 29/01/16
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// state space (value of variable "s")
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// 0 1 2 3 4
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// 5 6 7
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// 8 9 10
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// 11 13 12
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// 13 is the target
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pomdp
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// can observe the walls and target
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observables
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o
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endobservables
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// o=0 - observation in initial state
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// o=1 - west and north walls (s0)
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// o=2 - north and south walls (s1 and s3)
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// o=3 - north wall (s2)
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// o=4 - east and north way (s4)
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// o=5 - east and west walls (s5, s6, s7, s8, s9 and s10)
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// o=6 - east, west and south walls (s11 and s12)
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// o=7 - the target (s13)
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module maze
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s : [-1..13];
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o : [0..7];
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// initialisation
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[] s=-1 -> 1/13 : (s'=0) & (o'=1)
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+ 1/13 : (s'=1) & (o'=2)
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+ 1/13 : (s'=2) & (o'=3)
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+ 1/13 : (s'=3) & (o'=2)
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+ 1/13 : (s'=4) & (o'=4)
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+ 1/13 : (s'=5) & (o'=5)
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+ 1/13 : (s'=6) & (o'=5)
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+ 1/13 : (s'=7) & (o'=5)
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+ 1/13 : (s'=8) & (o'=5)
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+ 1/13 : (s'=9) & (o'=5)
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+ 1/13 : (s'=10) & (o'=5)
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+ 1/13 : (s'=11) & (o'=6)
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+ 1/13 : (s'=12) & (o'=6);
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// moving around the maze
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[east] s=0 -> (s'=1) & (o'=2);
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[west] s=0 -> (s'=0);
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[north] s=0 -> (s'=0);
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[south] s=0 -> (s'=5) & (o'=5);
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[east] s=1 -> (s'=2) & (o'=3);
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[west] s=1 -> (s'=0) & (o'=1);
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[north] s=1 -> (s'=1);
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[south] s=1 -> (s'=1);
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[east] s=2 -> (s'=3) & (o'=2);
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[west] s=2 -> (s'=1) & (o'=2);
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[north] s=2 -> (s'=2);
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[south] s=2 -> (s'=6) & (o'=5);
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[east] s=3 -> (s'=4) & (o'=4);
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[west] s=3 -> (s'=2) & (o'=3);
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[north] s=3 -> (s'=3);
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[south] s=3 -> (s'=3);
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[east] s=4 -> (s'=4);
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[west] s=4 -> (s'=3) & (o'=2);
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[north] s=4 -> (s'=4);
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[south] s=4 -> (s'=7) & (o'=5);
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[east] s=5 -> (s'=5);
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[west] s=5 -> (s'=5);
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[north] s=5 -> (s'=0) & (o'=1);
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[south] s=5 -> (s'=8);
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[east] s=6 -> (s'=6);
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[west] s=6 -> (s'=6);
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[north] s=6 -> (s'=2) & (o'=3);
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[south] s=6 -> (s'=9);
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[east] s=7 -> (s'=7);
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[west] s=7 -> (s'=7);
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[north] s=7 -> (s'=4) & (o'=4);
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[south] s=7 -> (s'=10);
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[east] s=8 -> (s'=8);
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[west] s=8 -> (s'=8);
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[north] s=8 -> (s'=5);
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[south] s=8 -> (s'=11) & (o'=6);
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[east] s=9 -> (s'=9);
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[west] s=9 -> (s'=9);
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[north] s=9 -> (s'=6);
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[south] s=9 -> (s'=13) & (o'=7);
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[east] s=10 -> (s'=10);
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[west] s=10 -> (s'=10);
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[north] s=10 -> (s'=7);
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[south] s=10 -> (s'=12) & (o'=6);
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[east] s=11 -> (s'=11);
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[west] s=11 -> (s'=11);
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[north] s=11 -> (s'=8) & (o'=5);
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[south] s=11 -> (s'=11);
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[east] s=12 -> (s'=12);
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[west] s=12 -> (s'=12);
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[north] s=12 -> (s'=10) & (o'=5);
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[south] s=12 -> (s'=12);
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// loop when we reach the target
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[done] s=13 -> true;
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endmodule
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// reward structure (number of steps to reach the target)
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rewards
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[east] true : 1;
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[west] true : 1;
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[north] true : 1;
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[south] true : 1;
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endrewards
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// target observation
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label "goal" = o=7;
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label "bad" = o=6;
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