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  1. open System
  2.  
  3. let random = new Random()                                     
  4.  
  5. let flip f a b = f b a
  6.  
  7. let keepLeft f (x,y) = x, f y
  8.  
  9. let keepRight f (x,y) = f x, y
  10.  
  11. let fst3 (a,_,_) = a
  12.  
  13. let fst_snd3 (a,b,_) = a,b
  14.  
  15. let scaleTo rmin rmax rangemin rangemax value =
  16.    let adjrmin, adjrmax, adjval = 
  17.        if rangemin < 0. then 0., -rangemin + rangemax , -rangemin + value 
  18.        else rangemin, rangemax , value //translate to 0
  19.  
  20.    (adjval - adjrmin)/(adjrmax - adjrmin) * (rmax-rmin) + rmin
  21.  
  22. module Array =
  23.   let inline normalize (a: _[]) = 
  24.       let tot = Array.sum a
  25.       Array.map (flip (/) tot) a           
  26.  
  27.   let inline normalizeWeights (a: ('a * 'b) []) = 
  28.       let tot = Array.sumBy snd a
  29.       Array.map (keepLeft (flip (/) tot)) a
  30.  
  31.  
  32. let cdf p = 
  33.     p |> Array.fold (fun (total, list) v -> 
  34.                 let cd = v + total
  35.                 cd, cd::list) (0., []) 
  36.       |> snd 
  37.       |> Array.ofList 
  38.  
  39. let getDiscreteSampleFromCDF (pcdf:float[]) = 
  40.     let k, pcdlen = random.NextDouble() * pcdf.[0], pcdf.Length - 1
  41.  
  42.     let rec cummProb idx = if k > pcdf.[idx] then cummProb (idx - 1) else idx
  43.  
  44.     abs(cummProb pcdlen - pcdlen) 
  45.  
  46.  
  47. let discreteSample p = cdf p |> getDiscreteSampleFromCDF  
  48.  
  49.  
  50. let round (n:int) (x:float) = Math.Round(x,n)                                                                               
  51.  
  52.  
  53. //////////////////////////////   
  54.  
  55. type Go = ``Do 🛑`` | ``Do 🚙``
  56.  
  57. type Decision = ``Do 😏`` of float [] | ``Do 🚦``    
  58.  
  59. let moves = [|``Do 🛑``;``Do 🚙``|]
  60.  
  61. let multiplicativeWeightsUpdate rate minAmount maxAmount (oldweights:float []) (results:seq<float>) =      
  62.     let lossbounded = scaleTo -1. 1. minAmount maxAmount 
  63.     results |> Seq.mapi (fun i r -> oldweights.[i] * (1. + rate * lossbounded (min r maxAmount)))
  64.             |> Seq.toArray 
  65.             |> Array.normalize
  66.  
  67. let learningExpert2 prevWeights rate res = multiplicativeWeightsUpdate rate -100. 1. prevWeights res
  68.  
  69. let sampleLight p = if random.NextDouble() < p then ``Do 🛑``,``Do 🚙`` else ``Do 🚙``,``Do 🛑``
  70.  
  71. let randomLight () = if random.NextDouble() < 0.5 then ``Do 🛑`` else ``Do 🚙``
  72. let faultyLight p2 p = if random.NextDouble() < p then randomLight(),randomLight() else sampleLight p2
  73.  
  74.  
  75. //============
  76.  
  77. let drive =
  78.     function 
  79.       | (``Do 🛑``,``Do 🛑``) -> (0.,0.)
  80.       | (``Do 🛑``,``Do 🚙``)   -> (0.,1.) 
  81.       | (``Do 🚙``,``Do 🛑``)   -> (1.,0.)
  82.       | (``Do 🚙``,``Do 🚙``)   -> (-100.,-100.)
  83.  
  84. let inline getExpertVerbose indicated signal (rules:_[]) = 
  85.     printfn "Signal = %A" signal
  86.     let other = match indicated with None -> "N/A" | Some a -> string a
  87.     printfn "Other signal: %s" other
  88.  
  89.     let cs = [|for (p,r,f) in rules do 
  90.                match f indicated signal with
  91.                  | Some e -> printfn "Rule %s with weight %A matched" r p; yield e, p 
  92.                  | None -> ()|] 
  93.               |> Array.normalizeWeights 
  94.  
  95.     printfn "Normalized %A" cs
  96.     let cs' = Array.groupBy fst cs |> Array.map (fun (s,c) -> s, Array.sumBy snd c)
  97.     printfn "%A" cs'
  98.     let ps = Array.map snd cs
  99.  
  100.     fst (cs.[discreteSample ps])
  101.  
  102. let inline getExpert2 indicated signal (rules:_[]) = 
  103.     let cs = [|for (p,_,f) in rules do 
  104.                match f indicated signal with 
  105.                 | Some c -> yield c,p 
  106.                 | None -> ()|] |> Array.normalizeWeights
  107.     let ps = Array.map snd cs
  108.     fst(cs.[discreteSample ps])
  109.  
  110.  
  111. let learnExperts3 signal rate opmove (rules:_[]) =
  112.     let costs = 
  113.         [|for (p,_,f) in rules do 
  114.             match f (Some opmove) signal with //<== change (Some opmove) to (None), see what happens
  115.               | Some choice -> yield (p * fst(drive (choice,opmove))) 
  116.               | None -> yield 0.|]
  117.  
  118.     let w = Array.map fst3 rules
  119.  
  120.     Array.Copy(learningExpert2 w rate costs,w,w.Length)   
  121.  
  122.     for i in 0..w.Length - 1 do
  123.       let _,name,f = rules.[i]
  124.       rules.[i] <- w.[i],name,f
  125.  
  126.  
  127. let learnExpertsVerbose signal rate opmove (rules:_[]) =
  128.     let costs = [|for (p,hh,f) in rules do 
  129.                     match f (Some opmove) signal with 
  130.                      | Some choice -> 
  131.                       printfn "%A" ((p ,hh,opmove,choice, fst(drive (choice,opmove))) )
  132.                       yield (p * fst(drive (choice,opmove))) 
  133.                      | None -> yield 0.|]
  134.     let w = Array.map fst3 rules
  135.     Array.Copy(learningExpert2 w rate costs,w,w.Length)   
  136.     for i in 0..w.Length - 1 do
  137.       let _,name,f = rules.[i]
  138.       rules.[i] <- w.[i],name,f
  139.  
  140.  
  141. let rules =   
  142.     let num_moves = (float moves.Length)*(float moves.Length)*(float moves.Length)
  143.     [|for m in moves do
  144.       for m2 in moves do
  145.       for m3 in moves ->
  146.         let rulename = sprintf "if signal=%A && other=%A then %A" m m2 m3
  147.  
  148.         1./num_moves, 
  149.         rulename, 
  150.         fun other signal -> 
  151.         match other with
  152.          | None -> if signal = m then Some m3 else None
  153.          | Some indicated -> if signal = m && indicated = m2 then Some m3 else None|]
  154.  
  155.  
  156. let gatherStats n look1 look2 otherweight heroweights = 
  157.     let lists = ResizeArray()
  158.     for i in 0..n do
  159.       let light1, light2 = sampleLight 0.5  
  160.       let p1mov = getExpert2 (if look1 then Some light2 else None) light1 heroweights
  161.       let p2mov = getExpert2 (if look2 then Some p1mov else None) light2 otherweight
  162.       lists.Add(p1mov,p2mov)
  163.     lists
  164.  
  165. let round100 x = sprintf "%A%%" (round 2 ((float x)*100.))
  166.  
  167. let learner2 () =
  168.     let mutable heroweights = Array.map id rules
  169.     let mutable otherweight = Array.map id rules
  170.  
  171.     let rate = 0.5
  172.  
  173.     for _ in 0..99999 do
  174.         let light1, light2 = sampleLight 0.5   
  175.  
  176.         let p1mov = getExpert2 (Some light2) light1 heroweights // <== Change (Some light2) to None 
  177.         let p2mov = getExpert2 (Some p1mov) light2 otherweight
  178.         learnExperts3 light1 rate p2mov heroweights
  179.         learnExperts3 light2 rate p1mov otherweight        
  180.  
  181.     let gathered = gatherStats 999 true true otherweight heroweights
  182.  
  183.     gathered.ToArray() 
  184.     |> Array.groupBy id    
  185.     |> Array.map (keepLeft (Array.length >> float))
  186.     |> Array.normalizeWeights 
  187.     |> Array.map (keepLeft round100)
  188.     |> printfn "%A\n"
  189.  
  190.     printfn "Rules 1: %A" (Array.map fst_snd3 heroweights |> Array.filter (fst >> round 2 >> (<>) 0.) |> Array.map (keepRight round100))
  191.     printfn "Rules 2: %A" (Array.map fst_snd3 otherweight |> Array.filter (fst >> round 2 >> (<>) 0.) |> Array.map (keepRight round100))
  192.  
  193. learner2()
  194.  
Success #stdin #stdout 0.75s 135232KB
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[|((Do 🚙, Do 🛑), "48.2%"); ((Do 🛑, Do 🚙), "51.0%"); ((Do 🚙, Do 🚙), "0.8%")|]

Rules 1: [|("100.0%", "if signal=Do 🚙 && other=Do 🛑 then Do 🚙")|]
Rules 2: [|("100.0%", "if signal=Do 🚙 && other=Do 🛑 then Do 🚙")|]
https://ideone.com/Tn3LeS
language:
F# (mono 4.1)
created:
6 years ago
visibility:
public

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