[mlpack] Query regarding constrained and unconstrained methods

Sat Jan 20 05:19:49 EST 2018

Hello Marcus,

I have done some research on C++ lambda functions. Did you mean to use these instead of the standard accessors and mutators? From what I have found, lambda functions are used for writing an anonymous inline functor right into the spot where it is called, like in this example below (source<https://stackoverflow.com/a/7627218>):

std::for_each(v.begin(), v.end(), [](int) { /* do something here */ });

Although they can be used to modify the parameters (passed in a capture list) by using the mutable keyword, I don't know what advantage this would have over the standard accessors and mutators. If you had a different use in mind, please let me know.

Yes, a policy based design seems like a much better option for implementing the optimizer. We could create a base class named PSO and use its methods in another class, for instance, LBPSO; using the former class' object. This would be more intuitive if other variants of PSO are to be implemented in the future.

I have read some sections from the Velocity Adaptation in Particle Swarm Optimization paper. The PSO variant presented there is somewhat similar to PSO with inertia weight in Looking Inside Particle Swarm Optimization in Constrained Search Spaces paper. The algorithm presented in section 4 for PSO with Velocity Adaptation uses Velocity Length l for scaling the particle velocity based on its current behavior. There are various initialization methods for setting the initial value of velocity length, such as l = r, l = r / sqrt(n). If I opt to implement this PSO variant in my GSoC application, would I leave it to the user for specifying the value of l, or set it by default following a heuristic, or maybe a combination of both?

Thank you,
Adeel

________________________________
From: Marcus Edel <marcus.edel at fu-berlin.de>
Sent: Thursday, January 18, 2018 6:51 PM
To: Adeel Ahmad
Cc: mlpack at lists.mlpack.org
Subject: Re: [mlpack] Query regarding constrained and unconstrained methods

Hello Adeel,

I have read the research paper you linked. In the paper, two variants of PSO are
mentioned -- inertia weight and constriction factor based. It is stated that the
local-best particle swarm optimizer (LBPSO) with constriction k produces the
best results. I assume all variants must be implemented for GSoC, however, in
the paper a modified version of PSO is presented (MPSO), which dynamically
updates two hyper-parameters, k and c2 (acceleration constant for social
elements in the swarm), should this be implemented as well? I suppose this won't
be time consuming if vanilla PSO is already in place.

I'm not sure it would be reasonable to implement every variant mentioned in the
paper over the summer, keep in mind that each method has to be tested (writing
good tests is time-consuming). So my recommendation is, focus on a single
variant, in your proposal you can point out that if there is time left you aim
for another variant. But at the end it's up to you, choose the methods you think
are interesting. Also, there is another interesting paper that might be
interesting as well: "Particle Swarm Optimization with Velocity Adaptation" by S.
Helwig et al. (let me know if you can't access the paper).

Regarding the design of the optimizer itself, it was pointed out earlier by Ryan
that the SDP (semidefinite program) optimizer supports constraints. In there,
the constraints are specified as Armadillo matrices, and set using setters. I
think the same methodology could be applied for PSO.

Right, as pointed out on the ideas page a matrix representation is definitely
one option another would be to use C++11 lambda functions:
https://en.wikipedia.org/wiki/C%2B%2B11#Lambda_functions_and_expressions which I
C++11 - Wikipedia<https://en.wikipedia.org/wiki/C%2B%2B11#Lambda_functions_and_expressions>
en.wikipedia.org
C++11 is a version of the standard for the programming language C++. It was approved by International Organization for Standardization (ISO) on 12 August 2011 ...

think would be easier to use as someone could naturally define the constraints.
Let me know what you think, coming up with a good structure is part of the
project.

For specifying whether the
PSO is local or global, a boolean could be used. However, the constriction
factor k should only be created in case of constriction based PSO, I'm not sure
what would be the best design for this.

Another option would be to use a policy based design, provide a separate class
for each method and reuse as much code as possible internally. We do something
similar for Adam, RmsProp, etc. each optimizer basically uses the SGD class and
all we do is to provide a wrapper class to set optimizer specific parameter. Let
me know what you think.

Would it be possible for us to discuss the optimizer architecture in more detail
on the mailing list?

Absolutely, we are here to help.

Thanks,
Marcus

On 18. Jan 2018, at 08:54, Adeel Ahmad <adeelahmad14 at hotmail.com<mailto:adeelahmad14 at hotmail.com>> wrote:

Hello Marcus,

I have read the research paper you linked. In the paper, two variants of PSO are mentioned -- inertia weight and constriction factor based. It is stated that the local-best particle swarm optimizer (LBPSO) with constriction k produces the best results. I assume all variants must be implemented for GSoC, however, in the paper a modified version of PSO is presented (MPSO), which dynamically updates two hyper-parameters, k and c2 (acceleration constant for social elements in the swarm), should this be implemented as well? I suppose this won't be time consuming if vanilla PSO is already in place.

Regarding the design of the optimizer itself, it was pointed out earlier by Ryan that the SDP (semidefinite program) optimizer supports constraints. In there, the constraints are specified as Armadillo matrices, and set using setters. I think the same methodology could be applied for PSO. For specifying whether the PSO is local or global, a boolean could be used. However, the constriction factor k should only be created in case of constriction based PSO, I'm not sure what would be the best design for this.

Would it be possible for us to discuss the optimizer architecture in more detail on the mailing list?

Thank you,
Adeel

________________________________
From: Marcus Edel <marcus.edel at fu-berlin.de<mailto:marcus.edel at fu-berlin.de>>
Sent: Wednesday, January 17, 2018 5:39 PM
To: Adeel Ahmad
Cc: mlpack at lists.mlpack.org<mailto:mlpack at lists.mlpack.org>
Subject: Re: [mlpack] Query regarding constrained and unconstrained methods

Hello Adeel,

sorry for the slow reponse on this one. There are various approaches to solve
constrained problems; one is the use of a penalty function. The constrained
problem is transformed to an unconstrained one, by penalizing the constraints so
that it can be solved using an unconstrained optimization method. You might take
a look at: "Looking Inside Particle Swarm Optimization in Constrained Search
Spaces" by Jorge Isacc Flores-Mendoza and Efrén Mezura-Montes they describe
various PSO method to solve constrained problems.

I apologize if I misunderstood what constrained problems are, but can't we apply
constraints to the methods already present in "src/mlpack/methods/*" directory?
Or, are these unrelated? In the latter case, are there some specialized methods
for constrained problems that need to be implemented for this project?

Currently, mlpack does not implement an optimizer that can handle constrained
problems. So for example, if you like to solve the constrained (cube, line)
Rosenbrock function:

f(x, y) = (1 - x)^2 + 100(y - x^2)^2

with constraints (x - 1)^3 - y +1 < 0 and x + y - 2 < 0

Currently, there is no structure to represent the problem and there is no
optimizer that can solve the constrained problem. Comming up with a structure is
one part of the project implementing an optimizer (PSO) that can handle
constrained problems is the other part. But as pointed out in the project idea,
it's recommended to start with a PSO implementation for unconstrained problems
and to extend the work later on.

Regarding the test cases structuring, I've found that in some cases a
test_function.cpp or <method_name>_test_function.cpp file is present in the main
method directory, such as here (https://github.com/mlpack/mlpack/blob/master/src
[https://avatars3.githubusercontent.com/u/10216045?s=400&v=4]<https://github.com/mlpack/mlpack/blob/master/src>

mlpack/mlpack<https://github.com/mlpack/mlpack/blob/master/src>
github.com<http://github.com/>
mlpack: a scalable C++ machine learning library --

/mlpack/core/optimizers/gradient_descent/test_function.cpp). Later, an object of
this class is created in the main tests directory ("src/mlpack/tests/*"), in
this case, here (https://github.com/mlpack/mlpack/blob/master/src/mlpack/tests/g
radient_descent_test.cpp). So, my question is this, what is the preferred
structure for writing test cases? In this case, I think this could have been
directly tested without the need of a separate GDTestFunction class, however,
this might not have been a neat alternative.

There is an open PR which consolidates different problems into one folder
(https://github.com/mlpack/mlpack/pull/1151); the benefit for not implementing
[https://avatars0.githubusercontent.com/u/4209744?s=400&v=4]<https://github.com/mlpack/mlpack/pull/1151>

Optimization Test Problems by zoq · Pull Request #1151 · mlpack/mlpack<https://github.com/mlpack/mlpack/pull/1151>
github.com<http://github.com/>
Common functions used for testing optimization algorithms, will add more functions and test integrations once we agree on this.

the test function inside the test itself, is that someone could reuse the
functionality for other methods/tests. One example is the SGDTestFunction which
is used to test Adam, SGD, RMSProp, etc.

I hope this is helpful, let us know if we should clarify anything.

Thanks,
Marcus

On 16. Jan 2018, at 19:58, Adeel Ahmad <adeelahmad14 at hotmail.com<mailto:adeelahmad14 at hotmail.com>> wrote:

Greetings,

I'm following a potential idea for GSoC 2018 titled "Particle swarm optimization". I have read a few documents and familiarized myself with the algorithm. It's listed in the idea description: "So this project is divided into two parts: First implement one or two unconstrained methods and afterwards takes a look at one --contained-- (constrained [?]) method". I apologize if I misunderstood what constrained problems are, but can't we apply constraints to the methods already present in "src/mlpack/methods/*" directory? Or, are these unrelated? In the latter case, are there some specialized methods for constrained problems that need to be implemented for this project?

Regarding the test cases structuring, I've found that in some cases a test_function.cpp or <method_name>_test_function.cpp file is present in the main method directory, such as here (<https://github.com/mlpack/mlpack/blob/3d3d733ba3c41c4f51764f44185767384ab6d9c7/src/mlpack/core/optimizers/gradient_descent/test_function.cpp>https://github.com/mlpack/mlpack/blob/master/src/mlpack/core/optimizers/gradient_descent/test_function.cpp). Later, an object of this class is created in the main tests directory ("src/mlpack/tests/*"), in this case, here (<https://github.com/mlpack/mlpack/blob/97fd47de5e0a51adf3c01957f6646eb5cc3651d5/src/mlpack/tests/gradient_descent_test.cpp>https://github.com/mlpack/mlpack/blob/master/src/mlpack/tests/gradient_descent_test.cpp). So, my question is this, what is the preferred structure for writing test cases? In this case, I think this could have been directly tested without the need of a separate GDTestFunction class, however, this might not have been a neat alternative.

Thank you,
Adeel
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