2016/07/11 by Nick Gravin, Yuval Peres, Gravin, Nick +3 · 1 citation
Computer Science · Mathematics · #Coding theory and cryptography #FOS: Computer and information sciences #Machine Learning (cs.LG) #Mathematical Approximation and Integration #cs.LG
paper · pdf · doi:10.48550/arxiv.1607.02834
openalex publication_date 2016/07/11 · arxiv created 2016/07/14 · arxiv updated 2016/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the fundamental problem of prediction with expert advice and develop regret lower bounds for a large family of algorithms for this problem. We develop simple adversarial primitives, that lend themselves to various combinations leading to sharp lower bounds for many algorithmic families. We use these primitives to show that the classic Multiplicative Weights Algorithm (MWA) has a regret of √((T ln k)/(2)), there by completely closing the gap between upper and lower bounds. We further show a regret lower bound of (2)/(3)√((Tln k)/(2)) for a much more general family of algorithms than MWA, where the learning rate can be arbitrarily varied over time, or even picked from arbitrary distributions over time. We also use our primitives to construct adversaries in the geometric horizon setting for MWA to precisely characterize the regret at (0.391)/(√δ) for the case of 2 experts and a lower bound of (1)/(2)√((ln k)/(2δ)) for the case of arbitrary number of experts k.