Frequently asked questions

TBA.

There are too many tools for hyperparameter search of ML. Why do you propose yet another one?

There are many important differences between the PyTorch-BSF and other hyperparameter search tools. First, the domain of a Bezier simplex is a (bounded) simplex, whereas other tools assume a (non-bounded) Euclidean space. Thus, the Bezier simplex can represent a compact subspace of the ambient space.

Second, for hyperparameter search tasks, the Bezier simplex has a strong limitation that its only optimizable type of hyperparameters is coefficients in the objective function. However, this limitation offers a great advantage in speed. While black-box optimization algorithms do not use properties of the objective function, the Bezier simplex takes advantage of it. As a result, the Bezier simplex fitting requires fewer solutions to fit the entire Pareto set and front, which will be suitable for hyperparameter search. And also you will find such a type of hyperparameters is quite ubiquitous. In designing software, there is always a trade-off between generality and efficiency.

Are approximation results always reliable?

No, not always. The approximation theorem says nothing about the approximation accuracy of the Bezier simplex of fixed degree. After fitting a Bezier simplex, you need to check the goodness of fit by using your domain knowledge.

Are there any applications other than multiobjective optimization?

Not yet, but possibly yes. I believe Bezier simplices arise everywhere we need high-dimensional shape representation. If you find a new application, then please let me know it. Your application will be documented in the application section.