It's no problem to initialize a reactiveValues object at startup. To access a value you need a reactive context, unless you use isolate. See below and also the help of reactiveValues (?reactiveValues)
library(shiny)
ui <- fluidPage(
textOutput("myvalue")
)
server <- function(input, output) {
values <- reactiveValues(a = 1)
output$myvalue <- renderText({
paste("My value is: ", values$a)
})
cat(paste("My value is: ", isolate(values$a)))
}
shinyApp(ui, server)