Second-order quantile methods for experts and combinatorial games

Koolen, Wouter M. & Van Erven, Tim (2015) Second-order quantile methods for experts and combinatorial games. (Unpublished)

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We aim to design strategies for sequential decision making that adjust to the difficulty of the learning problem. We study this question both in the setting of prediction with expert advice, and for more general combinatorial decision tasks. We are not satisfied with just guaranteeing minimax regret rates, but we want our algorithms to perform significantly better on easy data. Two popular ways to formalize such adaptivity are second-order regret bounds and quantile bounds. The underlying notions of 'easy data', which may be paraphrased as "the learning problem has small variance" and "multiple decisions are useful", are synergetic. But even though there are sophisticated algorithms that exploit one of the two, no existing algorithm is able to adapt to both.

In this paper we outline a new method for obtaining such adaptive algorithms, based on a potential function that aggregates a range of learning rates (which are essential tuning parameters). By choosing the right prior we construct efficient algorithms and show that they reap both benefits by proving the first bounds that are both second-order and incorporate quantiles.

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ID Code: 82489
Item Type: Other
Refereed: No
Additional Information: Preprint
Keywords: Online learning, prediction with expert advice, combinato rial prediction, easy data
Divisions: Current > QUT Faculties and Divisions > Science & Engineering Faculty
Past > Schools > Mathematical Sciences
Copyright Owner: Copyright 2015 [please consult the authors]
Deposited On: 12 Mar 2015 22:45
Last Modified: 30 May 2015 19:06

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