Sharp bounds in perturbed smooth optimization
Optimization and Control
2025-06-08 v1 Statistics Theory
Statistics Theory
Abstract
This paper studies the problem of perturbed convex and smooth optimization. The main results describe how the solution and the value of the problem change if the objective function is perturbed. Examples include linear, quadratic, and smooth additive perturbations. Such problems naturally arise in statistics and machine learning, stochastic optimization, stability and robustness analysis, inverse problems, optimal control, etc. The results provide accurate expansions for the difference between the solution of the original problem and its perturbed counterpart with an explicit error term.
Cite
@article{arxiv.2505.02002,
title = {Sharp bounds in perturbed smooth optimization},
author = {Vladimir Spokoiny},
journal= {arXiv preprint arXiv:2505.02002},
year = {2025}
}
Comments
arXiv admin note: substantial text overlap with arXiv:2404.14227