/
model_functions_FQ.R
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model_functions_FQ.R
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#----------------------------------------------------------#
# Model functions (for parameter fit)
#----------------------------------------------------------#
# standard Q-learning
func_qlearning <- function(param, data, prior = NULL)
{
alpha <- param[1]
beta <- param[2]
c <- data$choice
r <- data$reward
T <- length(c)
pA <- numeric(T)
# set Q values (#option x T)
Q <- matrix(numeric(2*T), nrow=2, ncol=T)
# initialize log-likelihood
ll <- 0
for (t in 1:T) {
# choosing prob 1
pA[t] <- 1/(1+exp(-beta * (Q[1,t]-Q[2,t])))
pA[t] <- max(min(pA[t], 0.9999), 0.0001)
ll <- ll + (c[t]==1) * log(pA[t]) + (c[t]==2) * log(1-pA[t])
# update values
if (t < T) {
Q[c[t],t+1] <- Q[c[t],t] + alpha * (r[t] - Q[c[t],t] )
# for unchosen option
Q[3-c[t],t+1] <- Q[3-c[t],t]
}
}
# log prior density
if (is.null(prior)) {
lprior <- 0
} else {
lprior <- dbeta(alpha,prior$alpha_a, prior$alpha_b,log = T) +
dgamma(beta,shape=prior$beta_shape, scale=prior$beta_scale,log = T)
}
return(list(negll = -ll - lprior,Q = Q, pA = pA))
}
# forgetting Q-learning
func_fqlearning <- function(param, data, prior = NULL)
{
alpha <- param[1]
alphaF <- param[1]
beta <- param[2]
c <- data$choice
r <- data$reward
T <- length(c)
pA <- numeric(T)
# set Q values (#option x T)
Q <- matrix(numeric(2*T), nrow=2, ncol=T)
# initialize log-likelihood
ll <- 0
for (t in 1:T) {
# choosing prob 1
pA[t] <- 1/(1+exp(-beta * (Q[1,t]-Q[2,t])))
pA[t] <- max(min(pA[t], 0.9999), 0.0001)
ll <- ll + (c[t]==1) * log(pA[t]) + (c[t]==2) * log(1-pA[t])
# update values
if (t < T) {
Q[c[t],t+1] <- Q[c[t],t] + alpha * (r[t] - Q[c[t],t] )
# for unchosen option
Q[3-c[t],t+1] <- (1 - alphaF) * Q[3-c[t],t]
}
}
# log prior density
if (is.null(prior)) {
lprior <- 0
} else {
lprior <- dbeta(alpha,prior$alpha_a, prior$alpha_b,log = T) +
dgamma(beta,shape=prior$beta_shape, scale=prior$beta_scale,log = T)
}
return(list(negll = -ll - lprior,Q = Q, pA = pA))
}
# differential forgetting Q-learning
func_dfqlearning <- function(param, data, prior = NULL)
{
alpha <- param[1]
alphaF <- param[2]
beta <- param[3]
c <- data$choice
r <- data$reward
T <- length(c)
pA <- numeric(T)
# set Q values (#option x T)
Q <- matrix(numeric(2*T), nrow=2, ncol=T)
# initialize log-likelihood
ll <- 0
for (t in 1:T) {
# choosing prob 1
pA[t] <- 1/(1+exp(-beta * (Q[1,t]-Q[2,t])))
pA[t] <- max(min(pA[t], 0.9999), 0.0001)
ll <- ll + (c[t]==1) * log(pA[t]) + (c[t]==2) * log(1-pA[t])
# update values
if (t < T) {
Q[c[t],t+1] <- Q[c[t],t] + alpha * (r[t] - Q[c[t],t] )
# for unchosen option
Q[3-c[t],t+1] <- (1 - alphaF) * Q[3-c[t],t]
}
}
# log prior density
if (is.null(prior)) {
lprior <- 0
} else {
lprior <- dbeta(alpha,prior$alpha_a, prior$alpha_b,log = T) +
dbeta(alphaF,prior$alpha_a, prior$alpha_b,log = T) +
dgamma(beta,shape=prior$beta_shape, scale=prior$beta_scale,log = T)
}
return(list(negll = -ll - lprior,Q = Q, pA = pA))
}
# 事前分布のリスト
priorList <- list(
list(alpha_a = 2, alpha_b = 2, beta_shape = 2, beta_scale = 3), # Q-learning
list(alpha_a = 2, alpha_b = 2, beta_shape = 2, beta_scale = 3), # FQ-learning
list(alpha_a = 2, alpha_b = 2, beta_shape = 2, beta_scale = 3) # DFQ-learning
)
# モデル関数のリスト
modelfunctions <- c(func_qlearning, func_fqlearning, func_dfqlearning)
# パラメータ数のリスト
nParamList <- c(2,2,3)
# モデル数
nModel <- length(nParamList)
# 動作確認用
# source("parameter_fit_functions.R")
# paramfitML(modelfunctions, nParamList)