On the power of adaption and randomization
Numerical Analysis
2025-09-24 v2 Computational Complexity
Numerical Analysis
Functional Analysis
Abstract
We present bounds on the maximal gain of adaptive and randomized algorithms over non-adaptive, deterministic ones for approximating linear operators on convex sets. If the sets are additionally symmetric, then our results are optimal. For non-symmetric sets, we unify some notions of -widths and s-numbers, and show their connection to minimal errors. We also discuss extensions to non-linear widths and approximation based on function values, and conclude with a list of open problems.
Cite
@article{arxiv.2406.07108,
title = {On the power of adaption and randomization},
author = {David Krieg and Erich Novak and Mario Ullrich},
journal= {arXiv preprint arXiv:2406.07108},
year = {2025}
}