Improved Distribution Estimation in $ell_infty$

arXiv:2605.30509v1 Announce Type: new
Abstract: We present improved bounds for estimating discrete probability distributions under the $ell_infty$ norm. These include minimax bounds in expectation and high-probability tail bounds. We resolve some of the open questions posed in Kontorovich and Painsky (JMLR, 2025) — including a fully empirical version of the tightest risk bound they presented and identifying the form of the worst-case extremal distribution. Encouraging empirical results are reported as well.