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From Luc Maisonobe <...@spaceroots.org>
Subject Re: [Math] Old to new API ("MultivariateDifferentiable(Vector)Function")
Date Sat, 01 Dec 2012 21:33:41 GMT


Konstantin Berlin <kberlin@gmail.com> a écrit :

>Hi,
>
>
>
>> Hello.
>>
>>>
>>> Now that I have some time, let me try to make my case clearly. First
>I want to say that this is not some attack on the
>automatic-differentation package. I love automatic-differentation and
>symbolic packages. I personally cannot compute a derivative without a
>computer for the life of me. And I am also glad we are finally starting
>to agree on something :)
>>
>> I don't think that we disagreed about the fact that there was a
>problem with
>> the interface to the user application. [_I_ started this thread
>hinting that
>> there was a problem (at least for me as a user, based on my
>use-case).]
>>
>> [Then there were several misunderstandings about what was the problem
>and how
>> to solve it...]
>>
>>>
>>> This discussion is about figuring out how an incorrect framework and
>storage affects the performance of an optimization. That is why I am so
>worried.
>>
>> I can understand that this is an important point for your use-case.
>> There are now two vantage points (at least) on two aspects to
>consider: You
>> seem to have experience where storage matter (while I don't); you
>worry
>> about "small" objects allocation (while I don't, anymore).
>>
>> I'm not saying that your worries do not count; quite the contrary. CM
>is not
>> my "toolbox"; it's a library based on the knowledge of its developers
>> (obviously).
>> If you bring actual use-cases (i.e. unit tests or real application
>code
>> that can be benchmarked) that will show worrying behaviour, it will
>> certainly trigger swift corrective action. [This has happened
>recently.]
>>
>> In this area (performance), the problem is that intuition (or
>educated
>> guess, however you want to name it) is not a substitute for actual
>runs,
>> sometimes by a large amount. [When I started to use CM, I raised the
>issue
>> that a 3D vector was immutable (so that I had to create a new one
>whenever
>> its coordinates were changing). Surely this was a performance hit!
>Actually
>> it wasn't.]
>
>This is not the same case. You take a function that a user normally
>expresses as a two dimensional array or a vector, you force them to
>allocate 10K+ new objects that you then have to unwrap back into the
>structure the user would have happily supplied you in the first place.
>The second issue you missed is one of scale. The difference between
>modifying a 3 variable array and creating a copy is not large. Try
>doing this with a 10k+ vector, where you don't actually need to modify
>any of the entries but are just doing copies for the hell of it. This
>is a known critical component of an optimization and should be
>optimized for performance itself.
>
>>
>> Again, that does not mean that you are wrong in this case. It's just
>that we
>> cannot jump and change the code every time someone comes up with what
>> amounts to "conventional wisdom". If the person comes with a patch
>that
>> readily proves the point (at least marginally through
>microbenchmarking),
>> then we all benefit.
>>
>
>This is not "conventional wisdom", this is 60 years of research, so you
>better provide a good reason for you increased level of abstraction. I
>asked you why you would indirectly wrap a Hessian or a Jacobian in a
>much heaver class that provides no useful features for a newton
>optimizer. I don't think you gave me an answer. I do not believe that
>good OO design is to have as many abstract layers as you can think of.
>Good OO design is just like any good engineering design, its about
>having things clean, simple, and not be dependent on components that
>are not required. In addition, if you are working on a code that is
>called thousands of times, you should think really careful about memory
>performance.
>
>>>
>>> So lets start with the basics. A Newton method must compute a
>descent step by solving a linear equation
>>>
>>> H*p = -g, (1)
>>>
>>> where H is the Hessian, g is the gradient, and p is the desired
>descent step. What I am about to say also holds for non-linear least
>squares method, where Hessian is approximated using the Jacobian as
>>>
>>> H \approx J^T*J+\lambda I.
>>>
>>> Now, if you are not solving a simple optimization problem that you
>keep giving examples for, you can easily have a Hessian be a very large
>matrix,
>>> like 1000x1000 or larger. Now, you better hope that you are storing
>H using your linear algebra framework, otherwise eq. (1) computation is
>going to take a while.
>>> This is actually a very active area of research, and that is why
>having sparse linear algebra (aren't you removing this? ;) ) and
>iterative solvers is important to a lot of people.
>>
>> Yes we are removing it because it is buggy and _nobody_ stepped up to
>say
>> that it was important for CM users, and to help solve the problems in
>a way
>> consistent with real-life usage of such a feature.
>> As Sébastien said, you are warmly welcome to help us find a way to
>keep the
>> feature.
>
>I personally do not use sparse linear algebra. I was just pointing out
>how important computation of eq. 1 is in general. I wish I had the time
>to help :(
>
>>
>>>
>>> What you are proposing as good OO style
>>
>> This discussion has really nothing to do with "OO style", merely code
>reuse;
>> and it was my big misunderstanding (partly because of my lack of
>knowledge,
>> partly because of the lack of documentation on the targetted usages
>of
>> "DerivativeStructure", which IIUC now, are outside CM) that I
>believed
>> that the new "MultivariateDifferentiableFunction" was the way to go.
>>
>> [Also, Luc had been moving very fast on this. And I couldn't keep up
>> although I had wondered earlier why this had to impact usage in the
>> "optimization" package.]
>>
>>> is that if someone has a function that they want to optimize, they
>need to take what is probably already a RealMatrix or [][], and create
>1000x1000 DerivativeStructure objects, that,
>>
>> IIUC, that would be 1000 "DerivativeStructure" (not 1000x1000). If
>so, for
>increase
>> in storage memory.
>
>Ok 1000. I guess it's really hard to understand this
>DerivativeStructure without further documentation. You can change my
>problem to least-squares problem with a very large number of
>observables. Same problem will pop-up again.
>
>>
>>> within the next 10 lines in the optimizer, are going to be converted
>back to a RealMatrix? Not only have you just fragmented your heap
>>> is going crazy, and you are wasting an incredible amount of memory.
>>
>> This is the kind of assertions that really needs support from actual
>code.
>> [Again, I don't claim to know better; I think that it would really be
>useful
>> to accumulate a list of "do and don't" for Java and CM, in the form
>of
>> reproducible user experience.]
>>
>>> Now imagine if your Jacobian is actually very simple to compute but
>large, then this whole conversion back and forth actually takes much
>longer than the function evaluation.
>>
>> We are willing to take this into account, but since I cannot see the
>> behaviour in my use-case (where the evaluation time overwhelms, by
>several
>> orders of magnitude, all such considerations), I do not have any
>incentive
>> to change what seems to be "efficient enough" (for the actually known
>> cases).
>> Again, your experience with other use-cases would be very valuable to
>> analyze the efficiency of the CM implementations and improve them, if
>> necessary.
>>
>>>
>>> So, why exactly are you insisting on taking this performance
>penalty?
>>
>> It's the other way around. Until the performance penalty is proven,
>we've
>> decided that it's up to the developer willing to do the work to
>decide.
>> Again, if there is patch, it makes the matter much easier to decide
>on.
>>
>> I admit that we decided to change the internal working of the
>optimizers, so
>> _we_ should have proved that it does not impact usability. Hence,
>again, the
>> usefulness of having a test suite of "real" applications which could
>be
>> benchmarked regularly in order to have performance regressions
>induced by
>> otherwise welcome changes.
>> [I raised that issue several times on the ML.]
>
>It's not about usability. When you tests your components you should not
>test on small problems, because any bad software will work on that.
>Create a case where you have 10K+ observations and 10K+ variable and
>see how your change effects the solution. I wish I would have time to
>do it myself, but I don't. As a user I can tell you that scalability is
>an important issue.
>
>>
>>> You claim that the optimizer can work better if it gets a
>DerivativeStructure, why?
>>
>> This was (supposed to be) an improvement of the _internal_ design.
>[Several
>> weeks ago, Luc posted the problems he was encountering.]
>>
>>> Where is the fact that you are holding a DerivativeStructure come
>into effect for a Newton method? Can you provide any literature in that
>regard? The classical optimization bottleneck, if not the actual
>function evaluation, is eq. (1). The optimization methodology is build
>on top of years of research in computational linear algebra concepts,
>and does not care how the matrices are actually computed. Efficient
>memory usage and speed is critical here because in Newton optimizations
>eq. (1) is evaluated thousands of times. The goal of the Jacobian is
>not to store derivatives it is to store a matrix of numbers that allows
>>
>> OK. Then Luc's proposal seems appropriate.
>> There would be new interfaces defining the "optimize" method
>appropriately.
>> For algorithms that need the gradient, it must be provided in an
>> argument, of type "MultivariateVectorFunction"; for those that need,
>the
>> Jacobian, the argument would be of type "MultivariateMatrixFunction".
>> Do you agree?
>>
>
>I keep saying that there are cases when evaluating value gradient
>Hessian is faster together than as a separate function. So no, I do not
>agree. I do agree it is better than having DerivativeStructure, but I
>think it is worse than what you had in 3.0. The proposal is pretty much
>like before in 3.0, but now I need to create two classes every time I
>want to optimize a function. Why are you doing this? I don't understand
>why this change needs to happen.

I would propose to simply revert my changes on the optimization package
and prepare for a reorganization for 4.0. I understand I focused only on
the type of problems Gilles and myself routinely use, i .e. small size problems
where the cost of the evaluation is several orders of magnitude larger than the
data copying. I forgot the dual case with  very large data sets. I apologize for that.

When 3.1 will be out, we will have to solve this so both  cases are handled efficiently,
and this would probably be implemented in 4.0.

Does this seems reasonable?

Best regards
Luc

>
>I don't see a problem at all. All that has to happen is that the
>function in gradient based methods overwrites the optimization
>function, such that it now takes a subclass of the function that is
>function to be implemented.
>
>>>
>>> You guys are focusing on people using finite differences and trying
>to optimize a newton method to use finite differences. This is not what
>the main purpose of a newton method is. If you want a method that
>dynamically adjusts finite differences step size, you should switch to
>BOBYQA, which was designed for this case.
>>
>> Another misunderstanding probably. [The "stepSize" discussion was
>sort of
>> a digression.]
>>
>>>
>>> Derivatives can be computed by a computer using a symbolic toolbox a
>priori (something that I was referring to when I accidentally said
>auto-differenation). They can also be efficiently simplified by that
>toolbox before being pasted back into you program. Auto-diff could also
>be an important tool for people if their problem is simple or they are
>not concerned with optimal efficiency . This can easily be handled by a
>wrapper and has nothing to do with Newton optimization.
>>
>> Maybe we should also change the "NewtonSolver" (in package
>> "o.a.c.m.analysis.solvers"). [In the same way we'll do for the
>optimizer
>> with derivatives. Actually those two packages were improved in
>parallel so
>> that the interface would be very similar from a usage point of view.]
>>
>
>Not sure what you mean.
>
>>> If you want to talk about proper OO design and internal
>simplification then you should focus on being able to pass a linear
>solver into your optimization method. This way you allow people to use
>iterative and sparse solvers when needed.
>>
>> This is a new feature; contributions are welcome. [CM is primarily
>> developed by people who use (part of) it; if they don't need that
>feature,
>> or don't know how to implement it, or do not have the time to
>implement it,
>> it won't be implemented.]
>>
>>> If you are concerned about people getting derivatives wrong, you can
>do what MATLAB does, which is to add an option to check the derivatives
>using finite differences when debugging.
>>
>> IMHO, the top-priority feature to help in debugging is to introduce
>logging
>> statements!
>
>I would go further than that. I think the user should be able to get
>back all the iterations steps back, and the associated rmsd values, etc
>if so desired. But that is sort of a wish.
>
>>
>>>
>>> This brings me to my second issue. There are important problems
>where computation
>>> of the derivatives combined with the actual function evaluation is
>*significantly*
>>> faster than computing each alone. I am not clear why I am hitting
>such resistance
>>> with this. [...]
>>
>> [If you think that you were met with strong resistance, I'd suggest
>that you
>> look in the archives for the discussions about exceptions in CM...]
>>
>> Unless I'm mistaken, CM does not prevent you to write a class that
>takes
>> advantage of combining the computations.
>
>How would I write that class? You optimizer first requests function
>value , then separately the Jacobian. It is not done at the same time.
>I could try to cache intermediately results, see if you are requesting
>a Jacobian for the same values you called my value function for, but
>that is very dirty.
>
>>
>>> What I suggested as function interfaces was just an initial quick
>suggestion
>>> that I would be happy for anyone to change in a way that everyone
>feels positive
>>> about. I just don't want my second issue to be ignored like a
>non-issue.
>>
>> I'm getting confused. Could you please restate what where those first
>and
>> second issue?
>
>First issue is you are creating extra layers of conversion for the user
>that is bad for performance, and there is not a single specific reason
>given for why its a good idea. Second issue is that computing value
>gradient Hessian might be faster for some functions together rather
>than in two unconnected calls.
>
>Thanks,
>Konstantin
>
>
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