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arXiv · 1605.07018

Online Learning with Feedback Graphs Without the Graphs

Alon Cohen·Tamir Hazan·Tomer Koren
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Abstract

We study an online learning framework introduced by Mannor and Shamir (2011) in which the feedback is specified by a graph, in a setting where the graph may vary from round to round and is \emph{never fully revealed} to the learner. We show a large gap between the adversarial and the stochastic cases. In the adversarial case, we prove that even for dense feedback graphs, the learner cannot improve upon a trivial regret bound obtained by ignoring any additional feedback besides her own loss. In contrast, in the stochastic case we give an algorithm that achieves $\widetilde Θ(\sqrt{αT})$ regret over $T$ rounds, provided that the independence numbers of the hidden feedback graphs are at most $α$. We also extend our results to a more general feedback model, in which the learner does not necessarily observe her own loss, and show that, even in simple cases, concealing the feedback graphs might render a learnable problem unlearnable.

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Alon Cohen, Tamir Hazan, Tomer Koren. 2016-05-23. Online Learning with Feedback Graphs Without the Graphs. https://arxiv.org/abs/1605.07018

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