diff --git a/.gitignore b/.gitignore
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+*.tex
+*.bib
+/Pics
+*.log
+*.bbl
+*.synctex.gz
+*.toc
+*.blg
+*.aux
+*.log
+.DS_Store
+/WorkingDoc
diff --git a/Algorithm-comparison.R b/Algorithm-comparison.R
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+####################################
+######## Initialize functions ######
+####################################
+
+Get_Convergence = function(mus) {
+  sortedMaxRewards = sort(mus, decreasing = TRUE)
+  
+  return(sortedMaxRewards[1] - sortedMaxRewards[2])
+}
+normalize = function(vec) {
+  
+  print(sd(vec))
+  if (sd(vec) != 0) {
+    return((vec - mean(vec)/sd(vec)))
+  } else {
+    return(vec)
+  }
+  
+}
+Convergence_Means <- function (samples) {
+  means <- numeric()
+  for (i in 1:length(samples)) {
+    means[i] <- mean(samples[1:i])
+  }
+  return(means)
+}
+
+ret_epsilon = function(mode = 1, t = NULL, c = 1) {
+  if (mode == 1) {
+    return(0.5)
+  } else if (mode == 2) {
+    return(min(1,c/sqrt(t)))
+  } else if (mode == 3) {
+    return(min(1,c/log(t)))
+  } else if (mode == 4) {
+    # Another suggestion?
+  }
+}
+
+epsilonGreedy = function(k, mus, sigma2) {
+  
+  epsilon = ret_epsilon(mode = 1)
+  
+  # Set all mu estimates to 0.5 first.
+  muEstimates = rep(0.5, k)
+  
+  # Set probability to pick each arm to epsilon/k, 
+  probabilities = rep(epsilon/k, k)
+  
+  # Set the best arm's probability to 1 - epsilon + e/k, i.e. add 1 - epsilon
+  # In this case, all
+  # Initialize vectors to store information
+  rewards = as.numeric()
+  armChosen = as.numeric()
+  t = 1
+  while (t <= T) {
+    
+    # update epsilon 
+    epsilon = ret_epsilon(epsilonMode, t = t)
+    
+    
+    # Sample an arm
+    armChosen[t] = sample(seq(1, k, 1), size = 1, prob = probabilities)
+    
+    rewards[t] = rnorm(n=1,mean = mus[armChosen[t]], sd = sqrt(sigma2))
+    
+    
+    # Update muEstimates
+    muEstimates[armChosen[t]] = sum(rewards[armChosen == armChosen[t]])/sum(armChosen == armChosen[t])
+    
+    # Update probabilities
+    probabilities = rep(epsilon/k, k)
+    # Set the best arm's probability to 1 - epsilon + e/k, i.e. add 1 - epsilon
+    probabilities[which.max(muEstimates)] = probabilities[which.max(muEstimates)] + 1 - epsilon
+    
+    t = t + 1
+  }
+  
+  data = data.frame(armChosen, rewards)
+  colnames(data) = c("ArmChosen", "Rewards")
+  return(data)
+}
+
+SoftMax = function(k, mus, sigma2, c = NULL) {
+  muEstimates = rep(0.5, k)
+  
+  # Initialize vectors to store information
+  rewards = as.numeric()
+  armChosen = as.numeric()
+  n_k_t = rep(0,k)
+  
+  for (t in 1:T) {
+    if (!is.null(c)) {
+      eta_t = c/t
+    } else {
+      eta_t = 0.9
+    }
+    
+    
+    probs = exp(eta_t*muEstimates)
+    
+    
+    if(any(is.na(probs))) {
+      print(probs)
+      print(muEstimates)
+      muEstimates = normalize(muEstimates)
+      print(muEstimates)
+      probs = exp(eta_t*muEstimates)/sum(exp(eta_t*muEstimates))
+      print(probs)
+    }
+    armChosen[t] = sample(seq(1,k,1), size = 1, prob = probs)
+    rewards[t] = rnorm(n=1,mean = mus[armChosen[t]], sd = sqrt(sigma2))
+    n_k_t[armChosen[t]] = n_k_t[armChosen[t]] + 1
+    muEstimates[armChosen[t]] = sum(rewards[armChosen == armChosen[t]])/(n_k_t[armChosen[t]] + max(0, 1 - n_k_t[armChosen[t]]))
+  }
+  data = data.frame(armChosen, rewards)
+  colnames(data) = c("ArmChosen", "Rewards")
+  return(data)
+}
+
+
+UCB = function(k, mus, sigma2) {
+  
+  muEstimates = rep(0.5, k)
+  
+  # Initialize vectors to store information
+  rewards = as.numeric()
+  armChosen = as.numeric()
+  n_k_t = rep(0,k)
+  
+  t = 1
+  while (t <= T) {
+    
+    # Generate the ucbs. We need the indices for this, hence the for loop.
+    ucbs = as.numeric()
+    for (i in 1:k) {
+      
+      ucbs[i] = muEstimates[i] + sqrt(2*log(t)/(n_k_t[i] + max(0, 1 - n_k_t[i])))
+    }
+
+    # Choose arm from the one with highest UCB
+    armChosen[t] = which.max(ucbs)
+    # update n_k_t
+    n_k_t[armChosen[t]] = n_k_t[armChosen[t]] + 1
+    
+    # Sample reward
+    rewards[t] = rnorm(n=1, mean = mus[armChosen[t]], sd = sqrt(sigma2))
+    
+    
+    # Update muEstimates
+    
+    muEstimates[armChosen[t]] = sum(rewards[armChosen == armChosen[t]])/(n_k_t[armChosen[t]] + max(0, 1 - n_k_t[armChosen[t]]))
+    
+    t = t + 1
+    
+  }
+  
+  data = data.frame(armChosen, rewards)
+  colnames(data) = c("ArmChosen", "Rewards")
+  return(data)
+}
+
+calc_regret = function(muStar, armChosen, mus) {
+  
+  return(apply(as.matrix(armChosen), 2, function(row, muStar) {
+    return(muStar - mus[armChosen])
+  }, muStar))
+}
+
+cumRegret = function(regrets) {
+  cumRegrets = as.numeric()
+  for (i in 1:length(regrets)) {
+    cumRegrets[i] = sum(regrets[1:i])
+  }
+  return(cumRegrets)
+}
+
+analyze = function(k, sigma2, regretsEps1, regretsEps2, regretsEps3, regretsUCB, regretsSM1, regretsSM10, avgBestArmEps1, avgBestArmEps2, avgBestArmEps3, avgBestArmUCB, avgBestArmSM1, avgBestArmSM10) {
+  xSeq = seq(1, length(regretsEps1),1)
+  plot(x=xSeq, y = Convergence_Means(regretsEps1), type = "l", lwd = 2, xlab = "Iteraciones", ylab = "Arrepentimiento promedio", col = "blue", ylim = c(0,max(Convergence_Means(regretsEps1), Convergence_Means(regretsUCB))),main = paste("K = ",k, ", ", expression(sigma), " = ", sigma2))
+  lines(Convergence_Means(regretsUCB), lwd = 2, col = "red")
+  lines(Convergence_Means(regretsEps2), lwd = 2, col = "green")
+  lines(Convergence_Means(regretsEps3), lwd = 2, col = "black")
+  lines(Convergence_Means(regretsSM1), lwd = 2, col = "purple")
+  lines(Convergence_Means(regretsSM10), lwd = 2, col = "yellow")
+  cumulativeRegretEpsilon1 = cumRegret(regretsEps1)
+  cumulativeRegretEpsilon2 = cumRegret(regretsEps2)
+  cumulativeRegretEpsilon3 = cumRegret(regretsEps3)
+  cumulativeRegretUCV = cumRegret(regretsUCB)
+  cumulativeRegretSM1 = cumRegret(regretsSM1)
+  cumulativeRegretSM10 = cumRegret(regretsSM10)
+  
+  legend("top",
+         col = c("blue", "red", "green", "black", "purple", "yellow"), 
+         lwd = c(2,2), 
+         legend = c(expression(paste(epsilon,"-greedy, ", epsilon, " = 0.5")),
+                    "UCB",
+                    expression(paste(epsilon," = 1/",sqrt(t))),
+                    expression(paste(epsilon, "= 1/log(t)")),
+                    expression(paste("Softmax, ",eta," = 0.9")),
+                    expression(paste("Softmax, ",eta," = 10/t"))
+         ))
+  plot(x=xSeq, y = cumulativeRegretEpsilon1, type = "l", lwd = 2, xlab = "Iteraciones", ylab = "Arrepentimiento cumulativo", col = "blue", ylim = c(min(cumulativeRegretUCV, cumulativeRegretEpsilon1),max(cumulativeRegretUCV, cumulativeRegretEpsilon1)),main = paste("K = ",k, ", ", expression(sigma), " = ", sigma2))
+  lines(cumulativeRegretUCV, lwd = 2, col = "red")
+  lines(cumulativeRegretEpsilon2, lwd = 2, col = "green")
+  lines(cumulativeRegretEpsilon3, lwd = 2, col = "black")
+  lines(cumulativeRegretSM1, lwd = 2, col = "purple")
+  lines(cumulativeRegretSM10, lwd = 2, col = "yellow")
+  legend("top",
+         col = c("blue", "red", "green", "black", "purple", "yellow"), 
+         lwd = c(2,2), 
+         legend = c(expression(paste(epsilon,"-greedy, ", epsilon, " = 0.5")),
+                    "UCB",
+                    expression(paste(epsilon," = 1/",sqrt(t))),
+                    expression(paste(epsilon, "= 1/log(t)")),
+                    expression(paste("Softmax, ",eta," = 0.9")),
+                    expression(paste("Softmax, ",eta," = 10/t"))
+                    ))
+  
+  ## Plot best arm
+  
+  plot(x=xSeq, y = avgBestArmEps1, type = "l", lwd = 2, xlab = "Iteraciones", ylab = "Veces mejor brazo elegido", col = "blue", ylim = c(0,max(avgBestArmEps1, avgBestArmEps2, avgBestArmEps3, avgBestArmUCB)),main = paste("K = ",k, ", ", expression(sigma), " = ", sigma2))
+  lines(avgBestArmUCB, lwd = 2, col = "red")
+  lines(avgBestArmEps2, lwd = 2, col = "green")
+  lines(avgBestArmEps3, lwd = 2, col = "black")
+  lines(avgBestArmSM1, lwd = 2, col = "purple")
+  lines(avgBestArmSM10, lwd = 2, col = "yellow")
+  legend("top",
+         col = c("blue", "red", "green", "black", "purple", "yellow"), 
+         lwd = c(2,2), 
+         legend = c(expression(paste(epsilon,"-greedy, ", epsilon, " = 0.5")),
+                    "UCB",
+                    expression(paste(epsilon," = 1/",sqrt(t))),
+                    expression(paste(epsilon, "= 1/log(t)")),
+                    expression(paste("Softmax, ",eta," = 0.9")),
+                    expression(paste("Softmax, ",eta," = 10/t"))
+         ))
+}
+
+bestArmPlayed = function(armPlayed, mus) {
+  percArmPlayed = as.numeric()
+  for (i in 1:length(armPlayed)) {
+    tmp = armPlayed[1:i]
+    percArmPlayed[i] = sum(tmp == which.max(mus))
+  }
+  return(percArmPlayed)
+}
+
+############################################
+######## Initialize and run ################
+############################################
+
+set.seed(123)
+# Set parameters
+
+K = c(5,10,25,50)
+
+sigma2 = c(0.01^2,0.1^2,1^2, 10^2)
+
+## Set algorithm specifications
+# Set epsilon mode. Sets which way the epsilon is decided. 1 for fixed, 2 for epsilon = 1/t, 3 for epsilon = 1/sqrt(t), 4 for epsilon = 1/log(t)
+epsilonMode = 1
+c = 1
+#Setting number of max iterations and convergence criteria. Problem will run until convergence or for the max nr iterations specified.
+T = 2000
+nRuns = 1
+convergence = Get_Convergence(mus)
+# Generate results
+for (k in K) {
+  for (sig in sigma2) {
+    for (i in 1:nRuns) {
+      # Get results for the run in terms of ArmChosen and reward
+      mus = runif(k, min = 0, max = 1)
+      epsilonMode = 1
+      epsilonResults1 = epsilonGreedy(k, mus, sig)
+      epsilonMode = 2
+      epsilonResults2 = epsilonGreedy(k, mus, sig)
+      epsilonMode = 3
+      epsilonResults3 = epsilonGreedy(k, mus, sig)
+      UCBResults = UCB(k, mus, sig)
+      if (sig != 10^2) {
+        softMaxC1 = SoftMax(k, mus, sig)
+        softMaxC10 = SoftMax(k, mus, sig, c = 10)
+      }
+      # Now, convert to AVERAGE regret over the 1000 iterations. 
+      if (i == 1) {
+        avgRegretEps1 = calc_regret(mus[which.max(mus)], epsilonResults1$ArmChosen, mus)
+        avgRegretEps2 = calc_regret(mus[which.max(mus)], epsilonResults2$ArmChosen, mus)
+        avgRegretEps3 = calc_regret(mus[which.max(mus)], epsilonResults3$ArmChosen, mus)
+        avgRegretUCB = calc_regret(mus[which.max(mus)], UCBResults$ArmChosen, mus)
+        avgRegretSM1 = calc_regret(mus[which.max(mus)], softMaxC1$ArmChosen, mus)
+        avgRegretSM10 = calc_regret(mus[which.max(mus)], softMaxC10$ArmChosen, mus)
+        
+        avgBestArmEps1 = bestArmPlayed(epsilonResults1$ArmChosen, mus)
+        avgBestArmEps2 = bestArmPlayed(epsilonResults2$ArmChosen, mus)
+        avgBestArmEps3 = bestArmPlayed(epsilonResults3$ArmChosen, mus)
+        avgBestArmUCB = bestArmPlayed(UCBResults$ArmChosen, mus)
+        avgBestArmSM1 = bestArmPlayed(softMaxC1$ArmChosen, mus)
+        avgBestArmSM10 = bestArmPlayed(softMaxC10$ArmChosen, mus)
+      } else {
+        avgRegretEps1 = avgRegretEps1*(i-1)/i + calc_regret(mus[which.max(mus)], epsilonResults1$ArmChosen, mus)/i
+        avgRegretEps2 = avgRegretEps2*(i-1)/i + calc_regret(mus[which.max(mus)], epsilonResults2$ArmChosen, mus)/i
+        avgRegretEps3 = avgRegretEps3*(i-1)/i + calc_regret(mus[which.max(mus)], epsilonResults3$ArmChosen, mus)/i
+        avgRegretUCB = avgRegretUCB*(i-1)/i + calc_regret(mus[which.max(mus)], UCBResults$ArmChosen, mus)/i
+        avgRegretSM1 = avgRegretSM1*(i-1)/i + calc_regret(mus[which.max(mus)], softMaxC1$ArmChosen, mus)/i
+        avgRegretSM10 = avgRegretSM10*(i-1)/i + calc_regret(mus[which.max(mus)], softMaxC10$ArmChosen, mus)/i
+        
+        avgBestArmEps1 = avgBestArmEps1*(i-1)/i + bestArmPlayed(epsilonResults1$ArmChosen,mus)/i
+        avgBestArmEps2 = avgBestArmEps2*(i-1)/i + bestArmPlayed(epsilonResults2$ArmChosen,mus)/i
+        avgBestArmEps3 = avgBestArmEps3*(i-1)/i + bestArmPlayed(epsilonResults3$ArmChosen,mus)/i
+        avgBestArmUCB = avgBestArmUCB*(i-1)/i + bestArmPlayed(UCBResults$ArmChosen,mus)/i
+        avgBestArmSM1 = avgBestArmSM1*(i-1)/i + bestArmPlayed(softMaxC1$ArmChosen,mus)/i
+        avgBestArmSM10 = avgBestArmSM10*(i-1)/i + bestArmPlayed(softMaxC10$ArmChosen,mus)/i
+      }
+      
+      print(i)
+    }
+    
+    analyze(k, sqrt(sig), avgRegretEps1, avgRegretEps2, avgRegretEps3, avgRegretUCB, avgRegretSM1, avgRegretSM10, avgBestArmEps1, avgBestArmEps2, avgBestArmEps3, avgBestArmUCB, avgBestArmSM1, avgBestArmSM10)
+    
+  }
+}
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