Improved Algorithms for Environment friendly Lively Studying Halfspaces with Massart and Tsybakov noise
Authors: Chicheng Zhang, Yinan Li
Summary: We give a computationally-efficient PAC lively studying algorithm for d-dimensional homogeneous halfspaces that may tolerate Massart noise (Massart and Nédélec, 2006) and Tsybakov noise (Tsybakov, 2004). Specialised to the η-Massart noise setting, our algorithm achieves an information-theoretically near-optimal label complexity of O~(d(1−2η)2polylog(1ε)) underneath a variety of unlabeled knowledge distributions (particularly, the household of “structured distributions” outlined in Diakonikolas et al. (2020)). Beneath the more difficult Tsybakov noise situation, we determine two subfamilies of noise circumstances, underneath which our environment friendly algorithm gives label complexity ensures strictly decrease than passive studying algorithms
