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arXiv · 1801.00101

Parameter-free online learning via model selection

Dylan J. Foster·Satyen Kale·Mehryar Mohri·Karthik Sridharan
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Abstract

We introduce an efficient algorithmic framework for model selection in online learning, also known as parameter-free online learning. Departing from previous work, which has focused on highly structured function classes such as nested balls in Hilbert space, we propose a generic meta-algorithm framework that achieves online model selection oracle inequalities under minimal structural assumptions. We give the first computationally efficient parameter-free algorithms that work in arbitrary Banach spaces under mild smoothness assumptions; previous results applied only to Hilbert spaces. We further derive new oracle inequalities for matrix classes, non-nested convex sets, and $\mathbb{R}^{d}$ with generic regularizers. Finally, we generalize these results by providing oracle inequalities for arbitrary non-linear classes in the online supervised learning model. These results are all derived through a unified meta-algorithm scheme using a novel "multi-scale" algorithm for prediction with expert advice based on random playout, which may be of independent interest.

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Dylan J. Foster, Satyen Kale, Mehryar Mohri, Karthik Sridharan. 2017-12-30. Parameter-free online learning via model selection. https://arxiv.org/abs/1801.00101

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