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

[Duncan Murdoch]

Your results below make it look like a bug in optim():  it is not 
duplicating a value when it should, so changes to x affect xx as well.

Duncan Murdoch

On 03/05/2019 4:41 a.m., Serguei Sokol wrote:
> 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.
> 
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