Statistics Papers

Document Type

Conference Paper

Date of this Version

2013

Publication Source

JMLR: Workshop and Conference Proceedings

Volume

30

Start Page

993

Last Page

1019

Abstract

We present methods for online linear optimization that take advantage of benign (as opposed to worst-case) sequences. Specifically if the sequence encountered by the learner is described well by a known “predictable process”, the algorithms presented enjoy tighter bounds as compared to the typical worst case bounds. Additionally, the methods achieve the usual worst-case regret bounds if the sequence is not benign. Our approach can be seen as a way of adding prior knowledge about the sequence within the paradigm of online learning. The setting is shown to encompass partial and side information. Variance and path-length bounds Hazan and Kale (2010); Chiang et al. (2012) can be seen as particular examples of online learning with simple predictable sequences.

We further extend our methods to include competing with a set of possible predictable processes (models), that is “learning” the predictable process itself concurrently with using it to obtain better regret guarantees. We show that such model selection is possible under various assumptions on the available feedback.

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Date Posted: 27 November 2017

This document has been peer reviewed.