Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.15867 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- We introduce a new generalization of relative entropy to non-negative vectors with sums $\gt 1$. We show in a purely combinatorial setting, with no probabilistic considerations, that in the presence of linear constraints defining a convex polytope, a concentration phenomenon arises for this generalized relative entropy, and we quantify the concentration precisely. We also present a probabilistic formulation, and extend the concentration results to it. In addition, we provide a number of simplifications and improvements to our previous work, notably in dualizing the optimization problem, in the concentration with respect to $\ell_{\infty}$ distance, and in the relationship to generalized KL-divergence. A number of our results apply to general compact convex sets, not necessarily polyhedral.