[Rd] R optim(method="L-BFGS-B"): unexpected behavior when working with parent environments

[Serguei Sokol]

On 02/05/2019 21:35, Florian Gerber wrote:
> Dear all,
>
> when using optim() for a function that uses the parent environment, I
> see the following unexpected behavior:
>
> makeFn <- function(){
>      xx <- ret <- NA
>      fn <- function(x){
>         if(!is.na(xx) && x==xx){
>             cat("x=", xx, ", ret=", ret, " (memory)", fill=TRUE, sep="")
>             return(ret)
>         }
>         xx <<- x; ret <<- sum(x^2)
>         cat("x=", xx, ", ret=", ret, " (calculate)", fill=TRUE, sep="")
>         ret
>      }
>      fn
> }
> fn <- makeFn()
> optim(par=10, fn=fn, method="L-BFGS-B")
> # x=10, ret=100 (calculate)
> # x=10.001, ret=100.02 (calculate)
> # x=9.999, ret=100.02 (memory)
> # $par
> # [1] 10
> #
> # $value
> # [1] 100
> # (...)
>
> I would expect that optim() does more than 3 function evaluations and
> that the optimization converges to 0.
>
> Same problem with optim(par=10, fn=fn, method="BFGS").
>
> Any ideas?
I don't have an answer but may be an insight. For some mysterious reason 
xx is getting changed when in should not. Consider:
 > fn=local({n=0; xx=ret=NA; function(x) {n <<- n+1; cat(n, "in 
x,xx,ret=", x, xx, ret, "\n"); if (!is.na(xx) && x==xx) ret else {xx <<- 
x; ret <<- x**2; cat("out x,xx,ret=", x, xx, ret, "\n"); ret}}})
 > optim(par=10, fn=fn, method="L-BFGS-B")
1 in x,xx,ret= 10 NA NA
out x,xx,ret= 10 10 100
2 in x,xx,ret= 10.001 10 100
out x,xx,ret= 10.001 10.001 100.02
3 in x,xx,ret= 9.999 9.999 100.02
$par
[1] 10

$value
[1] 100

$counts
function gradient
        1        1

$convergence
[1] 0

$message
[1] "CONVERGENCE: NORM OF PROJECTED GRADIENT <= PGTOL"

At the third call, xx has value 9.999 while it should have kept the 
value 10.001.

Serguei.