Changes for saamplig wwith a bayesian prior

bayesian_normal.jl

@@ -0,0 +1,63 @@
+using Plots
+using Random
+using Distributions
+
+mutable struct Bandit
+    true_mean::Number  
+    predicted_mean::Number
+    λ::Number
+    sum_x::Number
+    τ::Number
+    N::Number #Number of samples
+    Bandit(true_mean) = new(true_mean,0,1,0,1,0)
+end
+
+function pull(ban::Bandit)
+   return (rand(Normal(0,1)) / √(ban.τ)) + ban.true_mean
+end
+
+function sample(ban::Bandit)
+    return (rand(Normal(0,1)) / √(ban.λ)) + ban.predicted_mean
+end
+
+function update(ban::Bandit, x::Number) #x is a sample number
+    ban.λ += ban.τ
+    ban.sum_x += x
+    ban.predicted_mean = ban.τ * ban.sum_x / ban.λ
+    ban.N += 1
+end
+
+function ban_plot(bandits::Array,trial::Number)
+    plt = plot()
+    x = convert(Array,LinRange(-3,6,200))
+    for b in bandits
+        y = pdf(Normal(b.predicted_mean,√(1.0/b.λ)),x)
+        plot!(plt,x,y, title="Bandit distributions after $trial trials",label="Real mean: $(b.true_mean), Num of plays: $(b.N)")
+    end
+    display(plt)
+end
+
+num_trials = 2000;
+bandit_means = [1,2,3];
+
+bandits = [Bandit(p) for p in bandit_means];
+sample_points = [5,10,20,50,100,200,500,1000,1500,1999];
+rewards = zeros(num_trials);
+
+for i in 1:num_trials
+    # Thomson sampling
+    j = argmax([sample(b) for b in bandits])
+
+    if i in sample_points
+        ban_plot(bandits,i)
+    end
+
+    x = pull(bandits[j])
+    rewards[i] = x
+    update(bandits[j],x)
+end
+
+cumulative_average = cumsum(rewards) ./ Array(1:num_trials);
+plot(cumulative_average,xaxis=:log)
+plot!(ones(num_trials) .* max(bandit_probs...))
+