From 158ec547f9b65f5c5514c48a82f43e13ecd4a4a9 Mon Sep 17 00:00:00 2001 From: Filip Cornell Date: Fri, 11 Jan 2019 12:23:25 +0100 Subject: [PATCH] Added the whole project, more or less --- .gitignore | 12 ++ Algorithm-comparison.R | 322 +++++++++++++++++++++++++++++++++++++++++ TrabajoTHSP18.pdf | Bin 0 -> 2121546 bytes 3 files changed, 334 insertions(+) create mode 100644 .gitignore create mode 100644 Algorithm-comparison.R create mode 100644 TrabajoTHSP18.pdf diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..de50eb2 --- /dev/null +++ b/.gitignore @@ -0,0 +1,12 @@ +*.tex +*.bib +/Pics +*.log +*.bbl +*.synctex.gz +*.toc +*.blg +*.aux +*.log +.DS_Store +/WorkingDoc diff --git a/Algorithm-comparison.R b/Algorithm-comparison.R new file mode 100644 index 0000000..21dbc27 --- /dev/null +++ b/Algorithm-comparison.R @@ -0,0 +1,322 @@ +#################################### +######## 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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