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Commit d3b6a07e authored by Michael Leuschel's avatar Michael Leuschel
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add MCTS example

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Algorithms/MCTS/Bucket_Game.def 0 → 100644
+ 8
− 0
View file @ d3b6a07e
DEFINITIONS
/* a particular game tree : simple bucket example */
GAME_DEFINITIONS ==
min_node = 1 & max_node = 10 &
root = 1 &
moves = [{2,3,4}, {5,6}, {7,8}, {9,10}, {},{},{},{},{},{}] &
utility = {5 |-> -50, 6|-> 50, 7|->1, 8|->3, 9|->10, 10 |->-5} &
maxplayer_nodes = {1, 5,6, 7,8, 9,10}
Algorithms/MCTS/CustomGraph.def 0 → 100644
+ 32
− 0
View file @ d3b6a07e
DEFINITIONS
"LibraryStrings.def";
perc_wins(s) == IF number_of_visits(s)=0 THEN 0.0 ELSE real(number_of_wins(s)) / real(number_of_visits(s)) END;
node_string(s) == (IF n:terminal_nodes THEN FORMAT_TO_STRING("~w (val=~w)",[n,utility(n)]) ELSE TO_STRING(n) END)
^
(IF n=state THEN "*" ELSE "" END);
CUSTOM_GRAPH_NODES1 ==
ran(%n.(n:terminal_nodes | rec(color:IF utility(n)>0 THEN "green3" ELSE "burlywood" END,
value:n,shape:"box",label:node_string(n))));
CUSTOM_GRAPH_NODES2 ==
ran(%n.(n:expanded_nodes | rec(color:IF perc_wins(n) > 0.5 THEN "green3" ELSE "burlywood" END,
value:n,
shape:"record",
style:IF n=state THEN "bold" ELSE "rounded" END,
label:FORMAT_TO_STRING("|{~w\\n|w=~w\\n|n=~w\\n|exp=~w\\n|ucb=~w}|",
[node_string(n),TO_STRING(number_of_wins(n)),
TO_STRING(number_of_visits(n)),
REAL_TO_DEC_STRING(Exploration(n),2),
REAL_TO_DEC_STRING(UCBtot(n),2)]))));
CUSTOM_GRAPH_NODES3 ==
ran(%n.(n:nodes\terminal_nodes\expanded_nodes | rec(color:"gray",
value:n,shape:"box",
label:TO_STRING(n))));
CUSTOM_GRAPH_EDGES1 ==
rec(label:"",
style:"dotted",
value:{x,y|x:nodes & y:(moves(x)) & IsBestMove(x,y)=FALSE});
CUSTOM_GRAPH_EDGES2 ==
rec(label:"best",
style:"bold",
value:{x,y|x:nodes & y:(moves(x)) & IsBestMove(x,y)=TRUE});
Algorithms/MCTS/MCTS.mch 0 → 100644
+ 138
− 0
View file @ d3b6a07e
MACHINE MCTS
// an attempt at modelling Monte-Carlo Tree Search in B for ProB
// by Michael Leuschel (c) 2022
DEFINITIONS
VISB_JSON_FILE == "MCTS_visb.json";
terminal_nodes == dom(utility);
"Bucket_Game.def";
"LibraryStrings.def";
"LibraryRandom.def";
"LibraryReals.def";
"CustomGraph.def";
IsBestMove(from,to) == bool(to:expanded_nodes & to:(moves(from)) &
number_of_visits(to) = max(number_of_visits[(moves(from))]));
UpdateState(s,SimValue) == // update state after a simulation with value SimValue
BEGIN
number_of_visits(s) := number_of_visits(s) + 1;
IF (s/:maxplayer_nodes & SimValue >0 ) or
(s:maxplayer_nodes & SimValue <0 ) THEN // we adapt the value for the parent node !
number_of_wins(s) := number_of_wins(s) + 1 // TO DO: treat value 0 as 0.5 for wins
END
END;
UCBtot(s) == IF s:expanded_nodes & s/= root THEN UCB(s) ELSE 0.0 END; // total version of UCB
INFINITY == 10000.0;
Exploration(s) == IF number_of_visits(s) = 0 or s=root THEN
INFINITY
ELSE RSQRT(2.0 * RLOGe(real(number_of_visits(parent(s))))
/
real(number_of_visits(s)))
END;
UCB(s) == // Upper Confidence Bound Formula
LET ni BE ni = number_of_visits(s) IN
IF ni=0 THEN
INFINITY
ELSE
real(number_of_wins(s)) / real(ni) // Exploitation
+
RSQRT(2.0 * RLOGe(real(number_of_visits(parent(s))))
/
real(ni))
END // IF
END;
ABSTRACT_CONSTANTS rollout
CONSTANTS root, nodes, min_node, max_node, moves, utility, parent, maxplayer_nodes
PROPERTIES
root : nodes &
max_node : NATURAL1 &
nodes = min_node..max_node &
moves: nodes --> POW(nodes) &
utility: nodes +-> INTEGER &
!s.(s:nodes => (moves(s)={} => s:terminal_nodes)) &
parent: nodes \ {root} --> nodes &
!(p,c).(p:nodes & c:(moves(p)) => c|->p : parent) &
rollout = %n.(n:nodes | IF n:terminal_nodes THEN
utility(n)
ELSE
rollout(random_element(moves(n)))
END ) &
/* a particular game tree : simple bucket example*/
!(p,c).(p:nodes & c:(moves(p)) => p<c) /*@desc "Ensures we have no cycles" */ &
GAME_DEFINITIONS
VARIABLES cur_root,
state,
selected,
expanded_nodes,
number_of_visits,
number_of_wins
INVARIANT
cur_root:nodes &
state:nodes &
selected:BOOL /*@desc "TRUE if state has been selected" */ &
expanded_nodes <: nodes &
number_of_visits : expanded_nodes --> NATURAL &
number_of_wins : expanded_nodes --> NATURAL
INITIALISATION cur_root := root ||
state := root ||
selected := TRUE ||
expanded_nodes := {root} ||
number_of_visits := {root} * {0} ||
number_of_wins := {root} * {0}
OPERATIONS
// PHASE 1: Select children from cur_root with best UCB value
Select(ucb,child) = SELECT selected=FALSE &
state : expanded_nodes &
ucb = %(i).(i:(moves(state)) | UCB(i)) &
child: moves(state) &
// ucb(nr) = max(ran(ucb))
!o.(o:ran(ucb) => ucb(child) >= o)
THEN
state := child ||
selected := bool(number_of_visits(child) = 0 or child:terminal_nodes)
END;
// PHASE 2: Expand the selected node
Expand(newchildren) = SELECT selected=TRUE &
newchildren = (moves(state)) \ expanded_nodes & newchildren /= {} THEN
expanded_nodes := expanded_nodes \/ newchildren ||
number_of_visits := number_of_visits <+ (newchildren*{0}) ||
number_of_wins := number_of_wins <+ (newchildren*{0})
END;
// PHASE 3: Run a simulation and backpropagate result back to cur_root
Simulate(value) = SELECT selected=TRUE &
(moves(state)) <: expanded_nodes &
value = rollout(state) /* perform random simulation */
THEN
UpdateState(state,value);
VAR backstate IN
BEGIN
backstate := state;
WHILE backstate : dom(parent) DO
backstate := parent(backstate);
UpdateState(backstate,value)
INVARIANT backstate:nodes
VARIANT backstate
END // WHILE
END // BEGIN
END; //VAR
state,selected := cur_root, FALSE // Restart selecting nodes at the root
END; //SELECT
ChooseBestMove(To) = SELECT 1=2 & state=cur_root & IsBestMove(cur_root,To)=TRUE THEN
cur_root := To || // refocus on new root state of game
state := To
END
// Query operations to inspect state:
/*
;
res <-- GameOver = SELECT state:terminal_nodes THEN
res := utility(state)
END
*/
END
Algorithms/MCTS/MCTS_visb.json 0 → 100644
+ 58
− 0
View file @ d3b6a07e
{
"svg":"MCTS_visb.svg",
"comment": "VisB Visualization for MCTS",
"items": [
{
"id": "w_%0",
"attr": "text",
"value": "\"w=\"^IF %0:dom(number_of_wins) THEN TO_STRING(number_of_wins(%0)) ELSE \"-\" END",
"for": {"from":1, "to":10}
},
{
"id": "n_%0",
"attr": "text",
"value": "\"n=\"^IF %0:dom(number_of_visits) THEN TO_STRING(number_of_visits(%0)) ELSE \"-\" END",
"for": {"from":1, "to":10}
},
{
"id": "exp_%0",
"attr": "text",
"value": "\"exp=\"^IF %0:dom(number_of_visits) THEN REAL_TO_DEC_STRING(Exploration(%0),2) ELSE \"-\" END",
"for": {"from":1, "to":10}
},
{
"id": "ucb_%0",
"attr": "text",
"value": "\"ucb=\"^IF %0:dom(number_of_visits) THEN REAL_TO_DEC_STRING(UCBtot(%0),2) ELSE \"-\" END",
"for": {"from":1, "to":10}
},
{
"id": "node%0",
"attr": "stroke-width",
"value": "IF %0=state THEN 3 ELSE 1 END",
"for": {"from":1, "to":10}
},
{
"id": "feedback_text",
"attr": "text",
"value": "\"Next: \"^IF GET_IS_ENABLED(\"Simulate\")=TRUE THEN \"SIMULATE\" ELSIF GET_IS_ENABLED(\"Select\")=TRUE THEN \"SELECT\" ELSE \"EXPAND\" END"
}
],
"events": [
{
"id": "feedback_text",
"event": "Select"
},
{
"id": "feedback_text",
"event": "Expand"
},
{
"id": "feedback_text",
"event": "Simulate"
}
]
}
Algorithms/MCTS/MCTS_visb.svg 0 → 100644
+ 238
− 0
View file @ d3b6a07e
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
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-->
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<!-- 0 -->
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<!-- 1 -->
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<title>1</title>
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<title>3</title>
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<title>4</title>
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<title>5</title>
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<text id="exp_9" text-anchor="middle" x="433" y="-98.9" font-family="Times,serif" font-size="12.00">exp=1.67</text>
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<text id="ucb_9" text-anchor="middle" x="433" y="-77.9" font-family="Times,serif" font-size="12.00">ucb=1.67</text>
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<!-- 6 -->
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<title>6</title>
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<!-- 7 -->
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<title>7</title>
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<text id="ucb_2" text-anchor="middle" x="181" y="-438.9" font-family="Times,serif" font-size="12.00">ucb=1.70</text>
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</g>
<!-- 6&#45;&gt;7 -->
<g id="edge6" class="edge">
<title>6&#45;&gt;7</title>
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<!-- 8 -->
<g id="node4" class="node">
<title>8</title>
<path fill="none" stroke="burlywood" d="M322,-431.5C322,-431.5 400,-431.5 400,-431.5 406,-431.5 412,-437.5 412,-443.5 412,-443.5 412,-524.5 412,-524.5 412,-530.5 406,-536.5 400,-536.5 400,-536.5 322,-536.5 322,-536.5 316,-536.5 310,-530.5 310,-524.5 310,-524.5 310,-443.5 310,-443.5 310,-437.5 316,-431.5 322,-431.5"/>
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<text id="node_4" text-anchor="middle" x="361" y="-522.9" font-family="Times,serif" font-size="12.00">4</text>
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<text id="w_4" text-anchor="middle" x="361" y="-501.9" font-family="Times,serif" font-size="12.00">w=2</text>
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<text id="n_4" text-anchor="middle" x="361" y="-480.9" font-family="Times,serif" font-size="12.00">n=4</text>
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<text id="exp_4" text-anchor="middle" x="361" y="-459.9" font-family="Times,serif" font-size="12.00">exp=1.20</text>
<polyline fill="none" stroke="burlywood" points="330,-452.5 392,-452.5 "/>
<text id="ucb_4" text-anchor="middle" x="361" y="-438.9" font-family="Times,serif" font-size="12.00">ucb=1.70</text>
<polyline fill="none" stroke="burlywood" points="392,-431.5 392,-536.5 "/>
</g>
<!-- 6&#45;&gt;8 -->
<g id="edge7" class="edge">
<title>6&#45;&gt;8</title>
<path fill="none" stroke="blue" stroke-dasharray="1,5" d="M361,-792.18C361,-727.26 361,-616.14 361,-546.84"/>
<polygon fill="blue" stroke="blue" points="364.5,-546.51 361,-536.51 357.5,-546.51 364.5,-546.51"/>
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<!-- 9 -->
<g id="node3" class="node">
<title>9</title>
<polygon fill="none" stroke="#00cd00" points="504,-431.5 504,-536.5 606,-536.5 606,-431.5 504,-431.5"/>
<polyline fill="none" stroke="#00cd00" points="524,-431.5 524,-536.5 "/>
<text id="node_3" text-anchor="middle" x="555" y="-522.9" font-family="Times,serif" font-size="12.00">3</text>
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<text id="w_3" text-anchor="middle" x="555" y="-501.9" font-family="Times,serif" font-size="12.00">w=9</text>
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<text id="n_3" text-anchor="middle" x="555" y="-480.9" font-family="Times,serif" font-size="12.00">n=9</text>
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<text id="exp_3" text-anchor="middle" x="555" y="-459.9" font-family="Times,serif" font-size="12.00">exp=0.80</text>
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<text id="ucb_3" text-anchor="middle" x="555" y="-438.9" font-family="Times,serif" font-size="12.00">ucb=1.80</text>
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</g>
<!-- 6&#45;&gt;9 -->
<g id="edge1" class="edge">
<title>6&#45;&gt;9</title>
<path fill="none" stroke="blue" stroke-width="2" d="M389,-792.18C424.3,-726.86 484.87,-614.77 522.27,-545.57"/>
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<text text-anchor="middle" x="467.5" y="-660.9" font-family="Times,serif" font-size="12.00">best</text>
</g>
<!-- 7&#45;&gt;1 -->
<g id="edge2" class="edge">
<title>7&#45;&gt;1</title>
<path fill="none" stroke="blue" stroke-width="2" d="M162.81,-431.18C139.93,-365.99 100.71,-254.23 76.41,-184.99"/>
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<text text-anchor="middle" x="127.5" y="-300.9" font-family="Times,serif" font-size="12.00">best</text>
</g>
<!-- 7&#45;&gt;2 -->
<g id="edge8" class="edge">
<title>7&#45;&gt;2</title>
<path fill="none" stroke="blue" stroke-dasharray="1,5" d="M181,-431.18C181,-366.26 181,-255.14 181,-185.84"/>
<polygon fill="blue" stroke="blue" points="184.5,-185.51 181,-175.51 177.5,-185.51 184.5,-185.51"/>
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<!-- 8&#45;&gt;0 -->
<g id="edge5" class="edge">
<title>8&#45;&gt;0</title>
<path fill="none" stroke="blue" stroke-width="2" d="M353.21,-431.18C343.42,-366.13 326.66,-254.69 316.24,-185.42"/>
<polygon fill="blue" stroke="blue" stroke-width="2" points="319.7,-184.88 314.75,-175.51 312.77,-185.92 319.7,-184.88"/>
<text text-anchor="middle" x="343.5" y="-300.9" font-family="Times,serif" font-size="12.00">best</text>
</g>
<!-- 8&#45;&gt;5 -->
<g id="edge9" class="edge">
<title>8&#45;&gt;5</title>
<path fill="none" stroke="blue" stroke-dasharray="1,5" d="M371.39,-431.18C384.44,-366.13 406.79,-254.69 420.68,-185.42"/>
<polygon fill="blue" stroke="blue" points="424.13,-186 422.67,-175.51 417.27,-184.63 424.13,-186"/>
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<!-- 9&#45;&gt;3 -->
<g id="edge3" class="edge">
<title>9&#45;&gt;3</title>
<path fill="none" stroke="blue" stroke-width="2" d="M555,-431.18C555,-366.26 555,-255.14 555,-185.84"/>
<polygon fill="blue" stroke="blue" stroke-width="2" points="558.5,-185.51 555,-175.51 551.5,-185.51 558.5,-185.51"/>
<text text-anchor="middle" x="564.5" y="-300.9" font-family="Times,serif" font-size="12.00">best</text>
</g>
<!-- 9&#45;&gt;4 -->
<g id="edge4" class="edge">
<title>9&#45;&gt;4</title>
<path fill="none" stroke="blue" stroke-width="2" d="M572.32,-431.18C594.07,-366.13 631.32,-254.69 654.47,-185.42"/>
<polygon fill="blue" stroke="blue" stroke-width="2" points="657.93,-186.11 657.78,-175.51 651.29,-183.89 657.93,-186.11"/>
<text text-anchor="middle" x="624.5" y="-300.9" font-family="Times,serif" font-size="12.00">best</text>
</g>
</g>
<g id="feedback" class="node">
<title>feed</title>
<text id="feedback_text" text-anchor="middle" x="100" y="90"
font-family="Times,serif" font-size="12.00">ACTION</text>
</g>
</svg>
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