Simple utility-theoretic planning for eye-movements

util_et.R

library(purr)
library(tidyverse)
library(stringr)


# constants
locations <- 1:3
timestep <- 1
t_end <- 6
t <- seq(0, t_end, timestep)

# utility cost of shifting
u_shift <- function() {
  return(-1)
}

# utility of staying on any salient target
u_stay <- function(len) {
  ts <- timestep:len
  return(sum(ts^-.7))
}

# score plan
score_plan <- function(d) {

  u <- d %>% 
    group_by(epoch) %>%
    summarise(u_stay = u_stay(n() * timestep)) %>%
    rowwise %>%
    mutate(u_shift = ifelse(epoch == 1, 0, u_shift())) %>%
    ungroup %>%
    summarise(u_total = sum(u_stay) + sum(u_shift)) 
  
  d$u_total <- u$u_total

  return(d)
}

# do stuff
plans <- expand.grid(t0 = locations, 
            t1 = locations, 
            t2 = locations, 
            t3 = locations, 
            t4 = locations, 
            t5 = locations, 
            t6 = locations) %>%
  mutate(plan_num = 1:n()) %>%
  gather(t, location, t0:t6) %>%
  arrange(plan_num) %>%
  mutate(t = as.numeric(str_sub(t, 2, 2))) %>%
  group_by(plan_num) %>%
  mutate(shift = c(0,diff(location) != 0), 
         epoch = cumsum(shift) + 1) %>%
  split(.$plan_num) %>%
  map_df(score_plan)
  

# analyze paths
plans %>%
  ungroup %>%
  filter(u_total == max(u_total))

# n_shifts
n_shifts <- plans %>%
  group_by(plan_num) %>%
  summarise(n_shifts = sum(shift), 
            u_total = u_total[1]) 

ggplot(n_shifts, aes(x = n_shifts, y = u_total)) + 
  geom_jitter()