2017/06/13 by Siddharth Barman, Barman, Siddharth, Aditya Gopalan +3
Computer Science · Decision Sciences · #Advanced Bandit Algorithms Research #Cognitive Radio Networks and Spectrum Sensing #Distributed Sensor Networks and Detection Algorithms #FOS: Computer and information sciences #Machine Learning (cs.LG)
paper · pdf · doi:10.48550/arxiv.1706.04125
openalex publication_date 2017/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider prediction with expert advice when the loss vectors are assumed to lie in a set described by the sum of atomic norm balls. We derive a regret bound for a general version of the online mirror descent (OMD) algorithm that uses a combination of regularizers, each adapted to the constituent atomic norms. The general result recovers standard OMD regret bounds, and yields regret bounds for new structured settings where the loss vectors are (i) noisy versions of points from a low-rank subspace, (ii) sparse vectors corrupted with noise, and (iii) sparse perturbations of low-rank vectors. For the problem of online learning with structured losses, we also show lower bounds on regret in terms of rank and sparsity of the source set of the loss vectors, which implies lower bounds for the above additive loss settings as well.