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From S├ębastien Brisard <sebastien.bris...@m4x.org>
Subject Re: [math] Making last iteration data available when iterative algorithms fail to converge (MATH-902)
Date Sun, 18 Nov 2012 09:53:59 GMT
Hi,


2012/11/17 Gilles Sadowski <gilles@harfang.homelinux.org>

> On Sat, Nov 17, 2012 at 12:34:30PM -0800, Phil Steitz wrote:
> > I think MATH-902 makes a reasonable request, but I don't think the
> > exception is the right place to communicate last iteration data.
> > When iterative algorithms fail to converge and TooManyEvaluations or
> > other iteration bounds exceptions are thrown, the request in
> > MATH-902 is to make the last iterate available as a field in the
> > exception.  My inclination would be to not to do this, but instead
> > to adopt the convention that the class doing the iteration should
> > maintain last iteration state information.
>
> I understand the temptation to provide such a facility but it will make
> the implementation more complicated (additional bookkeeping) than necessary
> for the regular case, by which I mean that inputs were passed that don't
> lead to failure.
> Indeed, correct usage rests on the user, who is responsible for providing
> compatible values for maximum number of evaluations and the convergence
> criteria.
> The current design stems from the consideration that is "maxEval" is
> reached, it means that something has gone wrong: it took more evaluations
> than the _user_ was expecting.
> If this check gets in the way (as suggested by MATH-902), the user can
> always pass "Integer.MAX_VALUE", thereby disabling the safe-guard; but he
> must accept that he might wait a long time...
>
> It would be easier to figure out which approach is correct if we could have
> a concrete use-case.[1]
>
> The same issue also occurs with iterative linear solvers. I have concrete
use-cases, in this instance. Some of the systems I try to invert are quite
large (as in 128 * 128 * 128 * 6 unknowns). If the system is
ill-conditioned and the requirements on the stopping criterion is too
stringent, then the whole inversion will fail because of the maximum number
of iterations being reached. Now, failure is so "brutal" (meaning: nothing
is returned) that you can't even know how close the best estimate of the
solution is to the true solution, so you don't even know how to alter the
parameters of your solvers for failure not to happen again. Since these
iterations take a long time, this is a bit annoying.

With iterative solvers, there is a work-around, using the event handling
that is provided, which allows access to the *current* estimate of the
solution.

So I agree with Phil that it would be nice to retrieve the "best" estimate
of the solution, even if crash occurs. But I also agree with Gilles that
this must be done carefully. All the iterative solvers implemented so far
are almost state-less. The only class variables are related to the stopping
criterion. No data relating to the current system being inverted is stored
as a class variable (and is therefore not accessible). Again, event
handlers might be the way to go, we could add an event which is fired prior
to throwing the failure exception.

Best regards,
S├ębastien


Regards,
> Gilles
>
> [1] There is a similar situation with "CMAESOptimizer":
>       https://issues.apache.org/jira/browse/MATH-873
>     It behaves as the reporter of MATH-902 would like all optimizers to,
>     but it changes completely the meaning of "maxEval" (instead of a
>     safe-guard, it becomes a "normal" termination condition and the user
>     must check whether the convergence criteria have been met or not).
>
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