Rank-Induced PL Mirror Descent: A Rank-Faithful Second-Order Algorithm for Sleeping Experts

We introduce a new algorithm, Rank-Induced Plackett--Luce Mirror Descent (RIPLM), which leverages the structural equivalence between the rank benchmark and the distributional benchmark established in citetBergamOzcanHsu2022. Unlike prior approaches that operate on expert identities, RIPLM updates directly in the 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) rank-faithful and (ii) variance-adaptive in the sleeping experts setting.