Open Access
November 2015 Adaptive-treed bandits
Adam D. Bull
Bernoulli 21(4): 2289-2307 (November 2015). DOI: 10.3150/14-BEJ644


We describe a novel algorithm for noisy global optimisation and continuum-armed bandits, with good convergence properties over any continuous reward function having finitely many polynomial maxima. Over such functions, our algorithm achieves square-root regret in bandits, and inverse-square-root error in optimisation, without prior information.

Our algorithm works by reducing these problems to tree-armed bandits, and we also provide new results in this setting. We show it is possible to adaptively combine multiple trees so as to minimise the regret, and also give near-matching lower bounds on the regret in terms of the zooming dimension.


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Adam D. Bull. "Adaptive-treed bandits." Bernoulli 21 (4) 2289 - 2307, November 2015.


Received: 1 February 2013; Revised: 1 February 2014; Published: November 2015
First available in Project Euclid: 5 August 2015

zbMATH: 1364.90269
MathSciNet: MR3378467
Digital Object Identifier: 10.3150/14-BEJ644

Keywords: bandits on taxonomies , continuum-armed bandits , noisy global optimisation , tree-armed bandits , zooming dimension

Rights: Copyright © 2015 Bernoulli Society for Mathematical Statistics and Probability

Vol.21 • No. 4 • November 2015
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