binaryRL (version 0.9.8)

func_pi: Function: Upper-Confidence-Bound

Description

Unlike epsilon-greedy, which explores indiscriminately, UCB is a more intelligent exploration strategy. It biases the value of each action based on how often it has been selected. For options chosen fewer times, or those with high uncertainty, a larger "uncertainty bonus" is added to their estimated value. This increases their selection probability, effectively encouraging the exploration of potentially optimal, yet unexplored actions. A higher pi indicates a greater bias toward giving less-chosen options.

Usage

func_pi(
  i,
  L_freq,
  R_freq,
  L_pick,
  R_pick,
  L_value,
  R_value,
  var1,
  var2,
  LR,
  pi,
  alpha,
  beta
)

Value

The probability of choosing this option

Arguments

i

The current row number.

L_freq

The frequency of left option appearance

R_freq

The frequency of right option appearance

L_pick

The number of times left option was picked

R_pick

The number of times left option was picked

L_value

The value of the left option

R_value

The value of the right option

var1

[character] Column name of extra variable 1. If your model uses more than just reward and expected value, and you need other information, such as whether the choice frame is Gain or Loss, then you can input the 'Frame' column as var1 into the model.

default: var1 = "Extra_Var1"

var2

[character] Column name of extra variable 2. If one additional variable, var1, does not meet your needs, you can add another additional variable, var2, into your model.

default: var2 = "Extra_Var2"

LR

Are you calculating the probability for the left option or the right option?

pi

[vector] Parameter used in the Upper-Confidence-Bound (UCB) action selection formula. func_pi controls the degree of exploration by scaling the uncertainty bonus given to less-explored options. A larger value of pi (denoted as c in Sutton and Barto(1998) ) increases the influence of this bonus, leading to more exploration of actions with uncertain estimated values. Conversely, a smaller pi results in less exploration.

$$ A_t = \arg \max_{a} \left[ V_t(a) + \pi \sqrt{\frac{\ln(t)}{N_t(a)}} \right] $$

default: pi = NA

alpha

[vector] Extra parameters that may be used in functions.

beta

[vector] Extra parameters that may be used in functions.

Examples

if (FALSE) {
func_tau <- function(
  # Trial number
  i,
  # Number of times this option has appeared
  L_freq,
  R_freq,
  # Number of times this option has been chosen
  L_pick,
  R_pick,
  # Current value of this option
  L_value,
  R_value,
  # Extra variables
  var1 = NA,
  var2 = NA,
  
  # Whether calculating probability for left or right choice
  LR,
  
  # Free parameter
  pi = 0.1,
  # Extra parameters
  alpha,
  beta
){
############################ [ at least 1 ] #################################
  if (is.na(x = pi)) {
    if (L_pick == 0 & R_pick == 0) {
      bias <- 0
    }
    else if (LR == "L" & L_pick == 0 & R_pick > 0) {
      bias <- 1e+4
    }
    else if (LR == "R" & R_pick == 0 & L_pick > 0) {
      bias <- 1e+4
    }
    else {
      bias <- 0
    }
  }
############################ [ bias value ] #################################
  else if (!(is.na(x = pi)) & LR == "L") {
    bias <- pi * sqrt(log(L_pick + exp(1)) / (L_pick + 1e-10))
  }
  else if (!(is.na(x = pi)) & LR == "R") {
    bias <- pi * sqrt(log(R_pick + exp(1)) / (R_pick + 1e-10))
  }
############################## [ error ] ####################################
  else {
    bias <- "ERROR"
  }
 
  return(bias)
}
}