Learned inexact alternating minimization bounds optimality gap for convex problems

The paper learns an inexact alternating minimization scheme in which neural networks approximate each subproblem solution. For convex problems with quadratic coupling and a quadratic growth condition, it derives a worst-case optimality-gap bound exposing the per-iteration error networks are trained to minimise greedily.

Why it matters

It could speed coupled optimisation by replacing costly inner solvers with learned approximations while retaining theoretical guarantees.

Analysis

Alternating minimisation is standard, but inner solvers dominate cost. Learning them is promising, and a worst-case bound tied to trainable per-iteration error gives a principled target. Main uncertainty is whether the bound is tight and useful in practice, and whether learned solvers generalise across problem instances.

Source: arXiv

AI disclosure: this article was produced with AI assistance and reviewed for accuracy.