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Delayed Feedback in Kernel Bandits  Sattar Vakili
; Danyal Ahmed
; Alberto Bernacchia
; Ciara PikeBurke
;  Date: 
1 Feb 2023  Abstract:  Black box optimisation of an unknown function from expensive and noisy
evaluations is a ubiquitous problem in machine learning, academic research and
industrial production. An abstraction of the problem can be formulated as a
kernel based bandit problem (also known as Bayesian optimisation), where a
learner aims at optimising a kernelized function through sequential noisy
observations. The existing work predominantly assumes feedback is immediately
available; an assumption which fails in many real world situations, including
recommendation systems, clinical trials and hyperparameter tuning. We consider
a kernel bandit problem under stochastically delayed feedback, and propose an
algorithm with $ ilde{mathcal{O}}(sqrt{Gamma_k(T)T}+mathbb{E}[ au])$
regret, where $T$ is the number of time steps, $Gamma_k(T)$ is the maximum
information gain of the kernel with $T$ observations, and $ au$ is the delay
random variable. This represents a significant improvement over the state of
the art regret bound of
$ ilde{mathcal{O}}(Gamma_k(T)sqrt{T}+mathbb{E}[ au]Gamma_k(T))$ reported
in Verma et al. (2022). In particular, for very nonsmooth kernels, the
information gain grows almost linearly in time, trivializing the existing
results. We also validate our theoretical results with simulations.  Source:  arXiv, 2302.00392  Services:  Forum  Review  PDF  Favorites 


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