Abstract
We present a PTAS for agnostically learning halfspaces w.r.t. the uniform distribution on the d dimensional sphere. Namely, we show that for every μ > 0 there is an algorithm that runs in time poly (d, 1/ϵ) , and is guaranteed to return a classifier with error at most (1 + μ)opt + μ, where opt is the error of the best halfspace classifier. This improves on Awasthi, Balcan and Long Awasthi et al. (2014) who showed an algorithm with an (unspecified) constant approximation ratio. Our algorithm combines the classical technique of polynomial regression (e.g. Linial et al. (1989); Kalai et al. (2005)), together with the new localization technique of Awasthi et al. (2014).
| Original language | English |
|---|---|
| Pages (from-to) | 484-502 |
| Number of pages | 19 |
| Journal | Proceedings of Machine Learning Research |
| Volume | 40 |
| State | Published - 2015 |
| Event | 28th Conference on Learning Theory, COLT 2015 - Paris, France Duration: 2 Jul 2015 → 6 Jul 2015 |
Bibliographical note
Publisher Copyright:© 2015 A. Agarwal & S. Agarwal.
Keywords
- Agnostic learning
- Approximation algorithms
- Halfspaces
- Localization
- Polynomial approximation
- Polynomial regression
- Uniform distribution