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On kernelized multi-armed bandits

Chowdhury, SR and Gopalan, A (2017) On kernelized multi-armed bandits. In: 34th International Conference on Machine Learning, ICML 2017, 6 - 11 August 2017, Sydney, pp. 1397-1422.

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Official URL: https://arxiv.org/abs/1704.00445


We consider the stochastic bandit problem with a continuous set of arms, with the expected reward function over the arms assumed to be fixed but unknown. We provide two new Gaussian process-based algorithms for continuous bandit optimization-Improved GP-UCB (IGP-UCB) and GP-Thomson sampling (GP-TS), and derive corresponding regret bounds. Specifically, the bounds hold when the expected reward function belongs to the reproducing kernel Hilbert space (RKHS) that naturally corresponds to a Gaussian process kernel used as input by the algorithms. Along the way, we derive a new self-normalized concentration inequality for vector-valued martingales of arbitrary, possibly infinite, dimension. Finally, experimental evaluation and comparisons to existing algorithms on synthetic and real-world environments are carried out that highlight the favorable gains of the proposed strategies in many cases.

Item Type: Conference Paper
Publication: 34th International Conference on Machine Learning, ICML 2017
Publisher: International Machine Learning Society (IMLS)
Additional Information: The copyright for this article belongs to the International Machine Learning Society (IMLS).
Keywords: Artificial intelligence; Gaussian distribution; Gaussian noise (electronic); Learning algorithms; Stochastic systems, Bandit problems; Concentration inequality; Experimental evaluation; Gaussian Processes; Multi armed bandit; Real world environments; Reproducing Kernel Hilbert spaces; Reward function, Learning systems
Department/Centre: Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited: 04 Aug 2022 09:55
Last Modified: 04 Aug 2022 09:55
URI: https://eprints.iisc.ac.in/id/eprint/74680

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