Re: Convex Optimization of Noisy Objective

From: Steve K. (c81058_at_uibk.ac.at)
Date: 11/18/04 

Date: Thu, 18 Nov 2004 18:59:22 +0000 (UTC)

On Thu, 18 Nov 2004 15:10:31 +0000 (UTC), Peter Spellucci wrote:
>
>In article <lov9e9kset6q@legacy>,
> c81058@uibk.ac.at ("Steve K.") writes:
> >I have and objective f: R^n -> R (n is in the 100s or a few 1000s)
> >which I wish to minimize (no constraints). I know the Hessian is
> >positive definite.
> >The problem arises from the fact that f, its gradient \nabla f and
the
> >Hessian H, can only be estimated pointwise through quite expensive
and
> >laborious stochastic simulations.
> >Unavoidably there is noise in these estimates (particularly in H
which
> >can become singular or non-positive definite).
> >
> >I am looking for suggestions with regard to minimizing as much as
> >possible the expensive calls for the evaluation of f and its
> >derivatives. I've been using a variation of conjugate gradients
with
> >considerable success but it is not as robust as I would like it.
> >
> >Any information would be greatly appreciated.
> >
>
>try snobfit:
><a
href="http://www.mat.univie.ac.at/~neum/software/snobfit/">http://www.mat.univie.ac.at/~neum/software/snobfit/>
>hth
>peter

Thanks for the information. If I understand correctly SNOBIF uses a
quadratic fit in successive boxes which are accordingly minimized
without gradient calculation. In my case I would need to have the
gradients because they represent the "interesting quantities". I can
calculate them (with noise, which is reduced the longer I let the
stochastic simulation run) and I think it would be beneficial to
utilize the information they carry. Of course I might be wrong on
that.