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

[Serguei Sokol]

On 03/05/2019 10:31, Serguei Sokol wrote:
> 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.
>
A little follow-up: if you untie the link between xx and x by replacing 
the expression "xx <<- x" by "xx <<- x+0" it works as expected:
 > 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+0; 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 10.001 100.02
out x,xx,ret= 9.999 9.999 99.98
4 in x,xx,ret= 9 9.999 99.98
out x,xx,ret= 9 9 81
5 in x,xx,ret= 9.001 9 81
out x,xx,ret= 9.001 9.001 81.018
6 in x,xx,ret= 8.999 9.001 81.018
out x,xx,ret= 8.999 8.999 80.982
7 in x,xx,ret= 1.776357e-11 8.999 80.982
out x,xx,ret= 1.776357e-11 1.776357e-11 3.155444e-22
8 in x,xx,ret= 0.001 1.776357e-11 3.155444e-22
out x,xx,ret= 0.001 0.001 1e-06
9 in x,xx,ret= -0.001 0.001 1e-06
out x,xx,ret= -0.001 -0.001 1e-06
10 in x,xx,ret= -1.334475e-23 -0.001 1e-06
out x,xx,ret= -1.334475e-23 -1.334475e-23 1.780823e-46
11 in x,xx,ret= 0.001 -1.334475e-23 1.780823e-46
out x,xx,ret= 0.001 0.001 1e-06
12 in x,xx,ret= -0.001 0.001 1e-06
out x,xx,ret= -0.001 -0.001 1e-06
$par
[1] -1.334475e-23

$value
[1] 1.780823e-46

$counts
function gradient
        4        4

$convergence
[1] 0

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

Serguei.