liveBook · Manning

C-convex function

As explained in Optimization Algorithms: AI techniques for design, planning, and control problems

A c-convex function is a synthetic optimization function defined on a sphere whose parameterized components can be sampled for training.

A c-convex function is a synthetic optimization problem defined on a sphere. Its parameterized components can be sampled to create training problems for supervised learning. section 11.6

A PyTorch implementation specifies:

  • n_components components, a gamma aggregation parameter, and an optional seed for reproducibility. section 11.6
  • Random unit vectors ys and scalar alphas between 0 and 0.7, concatenated into a parameter vector. section 11.6
  • A forward calculation that evaluates the function at a three-dimensional point on the sphere. section 11.6

Learning spherical optima

Several seeded c-convex functions provide parameter vectors and losses. An amortized multilayer perceptron maps each parameter vector to a normalized three-dimensional output, then trains with Adam to reduce the corresponding function values.

How Optimization Algorithms: AI techniques for design, planning, and control problems covers it

How deep it goes
Explains parameter generation, spherical evaluation, sampling, and amortized training, but omits formal derivations.
Examples
Uses seeded function instances, unit vectors, spherical coordinates, and a multilayer perceptron producing normalized three-dimensional outputs.
What it assumes
Assumes basic supervised learning, neural networks, vectors, and sphere coordinates while demonstrating the implementation workflow.
What you can do after
Build it from scratch as a trainable PyTorch module and use sampled instances to train an amortized optimizer.
How it connects
Connects Riemannian distance, supervised learning, PyTorch, neural networks, and amortized optimization.
Cover of Optimization Algorithms: AI techniques for design, planning, and control problems
liveBookmanning.com
Read Optimization Algorithms: AI techniques for design, planning, and control problems on liveBook Get the book at manning.com

This explainer was generated by Manning's knowledge graph from the text of Optimization Algorithms: AI techniques for design, planning, and control problems. The section links point to the parts of the book it draws on.