Rank-Induced PL Mirror Descent: A Rank-Faithful Second-Order Algorithm for Sleeping Experts
Machine Learning
2025-09-24 v1
Abstract
We introduce a new algorithm, \emph{Rank-Induced Plackett--Luce Mirror Descent (RIPLM)}, which leverages the structural equivalence between the \emph{rank benchmark} and the \emph{distributional benchmark} established in \citet{BergamOzcanHsu2022}. Unlike prior approaches that operate on expert identities, RIPLM updates directly in the \emph{rank-induced Plackett--Luce (PL)} parameterization. This ensures that the algorithm's played distributions remain within the class of rank-induced distributions at every round, preserving the equivalence with the rank benchmark. To our knowledge, RIPLM is the first algorithm that is both (i) \emph{rank-faithful} and (ii) \emph{variance-adaptive} in the sleeping experts setting.
Cite
@article{arxiv.2509.18138,
title = {Rank-Induced PL Mirror Descent: A Rank-Faithful Second-Order Algorithm for Sleeping Experts},
author = {Tiantian Zhang},
journal= {arXiv preprint arXiv:2509.18138},
year = {2025}
}