Bug in optim for specific orders of magnitude

FWIW, I suspect the problem might have something to do with:
1/1e-308
[1] 1e+308
1/1e-309
[1] Inf
1e-309 > 0
[1] TRUE
1e-324 > 0
[1] FALSE

That is 1e-309 starts being treated as zero by division, but not by comparison (which happens at 1e-324).? This is not quite the range of values you were seeing the anomaly, but close.

This is on a 6th gen Skylake on MacOS.? 

Best,

B.
Thanks for all of your replies.

I would like to clarify that I am not expecting optim to return a good
result in these cases, as I am aware of the difficulties that come with the
numerical precision for such small numbers. I would be happy for optim to
take zero steps and return the initial value after it sees the gradient as
close enough to 0. What I think is a bug is for optim to return an error
for a specific range of numbers between 1e-309 and 1e-320 while not giving
an error for values on either side. I think the behavior should be the same
as for smaller numbers where it simply returns the starting point after
estimating the gradient to be 0.

To give an idea of where I was seeing the error, consider a function that
is mostly near 0, but has some areas of interest, for example:
f <- function(x) {-exp(-sum(x^2))}

As long as the starting point is near the peak, optim works fine, but if
you give it a bad starting point it will see the function as flat and
return the starting point.

Again, it is fine that it is not able to find the optimum in the scenario
of starting far from the peak, but I believe that it should NOT return an
error when the initial value falls within a specific range. The bug is that
it returns an error, not that it fails to optimize.

Thanks,
Collin

On Fri, Dec 23, 2022 at 1:52 PM Duncan Murdoch <murdoch.duncan at gmail.com>
wrote:
The optim help page mentions scaling in the discussion of the "control"
argument.? Specifically under the parscale description:

"Optimization is performed on par/parscale and these should be
comparable in the sense that a unit change in any element produces about
a unit change in the scaled value."

In your function a unit change in x[1] makes a change of 1e-317 in the
function value, and changing x[2] has no effect at all.

It would be nice if violating the rule only led to inefficiencies or
poor stopping decisions, but the numbers you are working with are close
to the hardware limits (the smallest positive number with full precision
is .Machine$double.xmin, about 2e-308), and sometimes that means
assumptions in the code about how arithmetic works are violated, e.g.
things like x*1.1 > x may not be true for positive x below
.Machine$double.xmin .

Duncan Murdoch

On 23/12/2022 12:30 p.m., Collin Erickson wrote:
Hello,

I've come across what seems to be a bug in optim that has become a
nuisance
for me.

To recreate the bug, run:

optim(c(0,0), function(x) {x[1]*1e-317}, lower=c(-1,-1), upper=c(1,1),
method='L-BFGS-B')

The error message says:

Error in optim(c(0, 0), function(x) { :
? ? non-finite value supplied by optim

What makes this particularly treacherous is that this error only occurs
for
specific powers. By running the following code you will find that the
error
only occurs when the power is between -309 and -320; above and below that
work fine.

p <- 1:1000
giveserror <- rep(NA, length(p))
for (i in seq_along(p)) {
? ? tryout <- try({
? ? ? optim(c(0,0), function(x) {x[1]*10^-p[i]}, lower=c(-1,-1),
upper=c(1,1), method='L-BFGS-B')
? ? })
? ? giveserror[i] <- inherits(tryout, "try-error")
}
p[giveserror]

Obviously my function is much more complex than this and usually doesn't
fail, but this reprex demonstrates that this is a problem. To avoid the
error I may multiply by a factor or take the log, but it seems like a
legitimate bug that should be fixed.

I tried to look inside of optim to track down the error, but the error
lies
within the external C code:

.External2(C_optim, par, fn1, gr1, method, con, lower,
? ? ? ? ? upper)

For reference, I am running R 4.2.2, but was also able to recreate this
bug
on another device running R 4.1.2 and another running 4.0.3.

Thanks,
Collin Erickson

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Bug in optim for specific orders of magnitude

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