this is what I have so far based on our chat:
set.seed(1)
getRewardsGaussian <- function(arms, plays) {
## assuming each action has a normal distribution
# first generate new means
QStar <- rnorm(arms, 0, 1)
# then for each mean, generate `play`-many samples
sapply(QStar, function(u)
rnorm(plays, u, 1))
}
CalculateRewardsPerMethod <- function(arms=7, epsi1=0.01, epsi2=0.1
, plays=1000, methods=c("greedy", "epsi1", "epsi2")) {
# names for easy handling
names(methods) <- methods
arm.names <- paste0("Arm", ifelse((1:arms)<10, 0, ""), 1:arms)
# this could be different if not all actions' rewards have a gaussian dist.
rewards.source <- getRewardsGaussian(arms, plays)
# Three dimensional array to track running averages of each method
running.avgs <-
array(0, dim=c(plays, arms, length(methods))
, dimnames=list(PlayNo.=NULL, Arm=arm.names, Method=methods))
# Three dimensional array to track the outcome of each play, according to each method
rewards.received <-
array(NA_real_, dim=c(plays, 2, length(methods))
, dimnames=list(PlayNo.=seq(plays), Outcome=c("Arm", "Reward"), Method=methods))
# define the function internally to not have to pass running.avgs
chooseAnArm <- function(p) {
# Note that in a tie, which.max returns the lowest value, which is what we want
maxes <- apply(running.avgs[p, ,methods, drop=FALSE], 3, which.max)
# Note: deliberately drawing two separate random numbers and keeping this as
# two lines of code to accent that the two draws should not be related
if(runif(1) < epsi1)
maxes["epsi1"] <- sample(arms, 1)
if(runif(1) < epsi2)
maxes["epsi2"] <- sample(arms, 1)
return(maxes)
}
## TODO: Perform each action at least once, then select according to algorithm
## Starting points. Everyone starts at machine 3
choice <- c(3, 3, 3)
reward <- rewards.source[1, choice]
## First run, slightly different
rewards.received[1,,] <- rbind(choice, reward)
running.avgs[1, choice, ] <- reward # if different starting points, this needs to change like below
## HERE IS WHERE WE START PULLING THE LEVERS ##
## ----------------------------------------- ##
for (p in 2:plays) {
choice <- chooseAnArm(p)
reward <- rewards.source[p, choice]
# Note: When dropping a dim, the methods will be the columns
# and the Outcome info will be the rows. Use `rbind` instead of `cbind`.
rewards.received[p,,names(choice)] <- rbind(choice, reward)
## Update the running averages.
## For each method, the current running averages are the same as the
## previous for all arms, except for the one chosen this round.
## Thus start with last round's averages, then update the one arm.
running.avgs[p,,] <- running.avgs[p-1,,]
# The updating is only involved part (due to lots of array-indexing)
running.avgs[p,,][cbind(choice, 1:3)] <-
sapply(names(choice), function(m)
# Update the running average for the selected arm (for the current play & method)
mean( rewards.received[ 1:p,,,drop=FALSE][ rewards.received[1:p,"Arm",m] == choice[m],"Reward",m])
)
} # end for-loop
## DIFFERENT RETURN OPTIONS ##
## ------------------------ ##
## All rewards received, in simplifed matrix (dropping information on arm chosen)
# return(rewards.received[, "Reward", ])
## All rewards received, along with which arm chosen:
# return(rewards.received)
## Running averages of the rewards received by method
return( apply(rewards.received[, "Reward", ], 2, cumsum) / (1:plays) )
}
### EXECUTION (AND SIMULATION)
## PARAMETERS
arms <- 10
plays <- 1000
epsi1 <- 0.01
epsi2 <- 0.1
simuls <- 50 # 2000
methods=c("greedy", "epsi1", "epsi2")
## Single Iteration:
### we can run system time to get an idea for how long one will take
tme <- system.time( CalculateRewardsPerMethod(arms=arms, epsi1=epsi1, epsi2=epsi2, plays=plays) )
cat("Expected run time is approx: ", round((simuls * tme[["elapsed"]]) / 60, 1), " minutes")
## Multiple iterations (simulations)
rewards.received.list <- replicate(simuls, CalculateRewardsPerMethod(arms=arms, epsi1=epsi1, epsi2=epsi2, plays=plays), simplify="array")
## Compute average across simulations
rewards.received <- apply(rewards.received.list, 1:2, mean)
## RESULTS
head(rewards.received, 17)
MeanRewards <- rewards.received
## If using an alternate return method in `Calculate..` use the two lines below to calculate running avg
# CumulRewards <- apply(rewards.received, 2, cumsum)
# MeanRewards <- CumulRewards / (1:plays)
## PLOT
plot.ts(MeanRewards[, "greedy"], col = 'red', lwd = 2, ylim = range(MeanRewards), ylab = 'Average reward', xlab="Plays")
lines(MeanRewards[, "epsi1"], col = 'orange', lwd = 2)
lines(MeanRewards[, "epsi2"], col = 'navy', lwd = 2)
grid(col = 'darkgray')
legend('bottomright', c('greedy', paste("epsi1 =", epsi1), paste("epsi2 =", epsi2)), col = c('red', 'orange', 'navy'), lwd = 2, cex = 0.8)
