ActiveHedge: Hedge meets Active Learning
Bhuvesh Kumar, Jacob D Abernethy, Venkatesh Saligrama
Abstract
We consider the classical problem of multi-class prediction with expert advice, but with an active learning twist. In this new setting the learner will only query the labels of a small number of examples, but still aims to minimize regret to the best expert as usual; the learner is also allowed a very short "burn-in" phase where it can fast-forward and query certain highly-informative examples. We design an algorithm that utilizes Hedge (aka Exponential Weights) as a subroutine, and we show that under a very particular combinatorial constraint on the matrix of expert predictions we can obtain a very strong regret guarantee while querying very few labels. This constraint, which we refer to as $\zeta$-compactness, or just compactness, can be viewed as a non-stochastic variant of the disagreement coefficient, another popular parameter used to reason about the sample complexity of active learning in the IID setting. We also give a polynomial-time algorithm to calculate the $\zeta$-compactness of a matrix up to an approximation factor of 3.
BibTeX
@InProceedings{pmlr-v162-kumar22a,
title = {{A}ctive{H}edge: Hedge meets Active Learning},
author = {Kumar, Bhuvesh and Abernethy, Jacob D and Saligrama, Venkatesh},
booktitle = {Proceedings of the 39th International Conference on Machine Learning},
pages = {11694--11709},
year = {2022},
editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan},
volume = {162},
series = {Proceedings of Machine Learning Research},
month = {17--23 Jul},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v162/kumar22a/kumar22a.pdf},
url = {https://proceedings.mlr.press/v162/kumar22a.html},
abstract = {We consider the classical problem of multi-class prediction with expert advice, but with an active learning twist. In this new setting the learner will only query the labels of a small number of examples, but still aims to minimize regret to the best expert as usual; the learner is also allowed a very short "burn-in" phase where it can fast-forward and query certain highly-informative examples. We design an algorithm that utilizes Hedge (aka Exponential Weights) as a subroutine, and we show that under a very particular combinatorial constraint on the matrix of expert predictions we can obtain a very strong regret guarantee while querying very few labels. This constraint, which we refer to as $\zeta$-compactness, or just compactness, can be viewed as a non-stochastic variant of the disagreement coefficient, another popular parameter used to reason about the sample complexity of active learning in the IID setting. We also give a polynomial-time algorithm to calculate the $\zeta$-compactness of a matrix up to an approximation factor of 3.}
}