[mlpack] GSoC'22 Project Proposal: Enhance CMA-ES

[Nhật Hoàng Phan]

I’m Phan Nhat Hoang, a freshman computer science student at Nanyang
Technological University. I’m familiar with multivariate statistical
analysis, matrix analysis and C++ programming as well which are all
relevant to CMA-ES (quite linear algebra intensive IMO). I would like to
contribute into CMA-ES expansion and ensmallen repository as a project for
Google Summer of Code 2022. I’ve read throughout the original paper
(”Completely Derandomized Self-Adaption in Evolution Strategies”), the
tutorial about CMA-ES in 2016 (”The CMA Evolution Strategy: A Tutorial”) as
well as some recent variations including the saACM-ES, IPOP-CMA-ES,
Active-CMA-ES, Cholesky-CMA-ES (2016) and some large-scale variants of it
including LM-CMA-ES, sep-CMA-ES. For the implementation part, I’ve examined
the CMA-ES implementation in ensmallen. Although, in cmaes/cmaes_impl.hpp,
authors mentioned this is implementation of "Completely Derandomized
Self-Adaption in Evolution Strategies” paper, I realized that many detail
implementations are inspired by "Efficient covariance matrix update for
variable metric evolution strategies” by Suttorp et al. Some of them are
Cholensky decomposition, hyperparameters choices and multi-objective
functions adaption. Furthermore, the lambda (size of population) in the
ensmallen is 10(4+round(3log(N)) meanwhile to the extent of my knowledge,
lambda is mostly set by 4+round(3log(N)). Therefore I think we need some
clarifications on which theoretical source is used for ensmallen
implementation. Besides to current implementation, the test
functions,currently only Rosenbrock and Logistic Regression functions, are
needed to be extended to Sphere (important), Cigar, Ellipsoid and Different
Powers for reliable benchmark. For the enhancement implementations of
CMA-ES, I would choose 2-3 algorithms (possibly IPOP-CMA-ES, Active-CMA-ES
and LM-CMA-ES) to improve the scalability, speed of adaption and globality
of original CMA-ES along with an intensive benchmark for them. The current
documentation is also lack of mathematical information, my plan also
includes mathematical documentations and how to use them for toy functions
and even scalable applications. Lastly, I’m writing a detail proposal on
how to leverage ensmallen APIs to implement aforementioned algorithms,
documentation and testing plan. In this thread, I’m looking for your
comments on my current directions and how original CMA-ES is implemented.
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