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On Kernelized Multi-armed Bandits
Sayak Ray Chowdhury · Aditya Gopalan

Mon Aug 07 01:30 AM -- 05:00 AM (PDT) @ Gallery #72

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 favourable gains of the proposed strategies in many cases.

Author Information

Sayak Ray Chowdhury (Indian Institute of Science)
Aditya Gopalan (Indian Institute of Science)

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