Optimization Project: Seeking Community Advice

Hello, ResearchHub community.

For some time now, I've wanted to publish a personal project and obtain funding through this platform. However, doing science isn't easy, and it's often undervalued, which makes sharing and validating new ideas difficult.

I've been working on a project focused on providing tools and a different perspective on how to tackle black-box optimization problems. Anyone who has worked with gradient optimizers, metaheuristics, or issues related to neural network training knows how complex it is to face these kinds of problems: from the need for computational resources to achieving an optimal adjustment of the algorithm's parameters. With the proliferation of AI, it has become clear how difficult it is to solve high-dimensional problems. Finding solutions that involve millions of variables is not trivial and requires specialized hardware. For these types of problems, the algorithms that have been developed are primarily based on gradient techniques. While other robust methods like CMA-ES exist, their use in very complex problems is extremely difficult due to the computational cost.

Given the above, my ideas are based on a reconstruction of optimization problems through a geometric approach. Using Fourier or Laplace transforms as an analogy, the approach to black-box problems is carried out by conceptually separating the domain and codomain. This transformation allows for visualizing the problem from a new perspective and designing search methods that rely solely on information from the objective function's domain. From this, I have developed my own theoretical framework where some optimization concepts like exploration and exploitation are reinterpreted.

But theory alone is not easily accepted in the scientific community or traditional systems. For this reason, I've also developed an own algorithm based on this theoretical framework, which introduces concepts with a geometric interpretation. The preliminary results are quite good. Problems with up to 100,000 variables have been analyzed to verify the proposal's stability and scalability. Of the developed algorithm, I could highlight the following:

Progressive improvement of a single solution, without the need for populations
Required parameters are adjusted adaptively
The algorithm's computational complexity grows linearly, O(n), with respect to the problem size
Stability, scalability, and efficient hardware usage

Some of the problems analyzed include classic benchmark functions, Pentamodel (a framework for optimizing the parameters of the Stockfish chess engine through simulations), and benchmark datasets like CIFAR-10.

However, everything I've mentioned and what is presented in the project can generate skepticism in the scientific community for many reasons. Therefore, before presenting it for funding, I'm looking for your advice on how to present it so that the idea's potential can be appreciated. I'm also interested in having an open interaction with the community and exploring possible collaborations.

From my end, I can offer transparency, results, data, and their reproducibility.

Thank you for your attention. If you'd like to learn more, you can find a previous post on the Giveth platform: https://giveth.io/project/towards-scalable-geometric-optimization

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Optimization Project: Seeking Community Advice