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24 June 2024
 
  » arxiv » 2302.00392

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Delayed Feedback in Kernel Bandits
Sattar Vakili ; Danyal Ahmed ; Alberto Bernacchia ; Ciara Pike-Burke ;
Date 1 Feb 2023
AbstractBlack 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 non-smooth 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
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