Finite-Time Analysis of Kernelised Contextual Bandits
This work addresses the challenge of efficient decision-making in contextual bandits with large action spaces, offering improved theoretical guarantees for practitioners in online learning and recommendation systems, though it is incremental as it builds on existing UCB methods.
The authors tackled the problem of online reward maximization over a large set of actions with contextual similarities by proposing KernelUCB, a kernelized UCB algorithm, and provided a cumulative regret bound that improves upon GP-UCB in the agnostic case and matches the lower bound for linear kernels.
We tackle the problem of online reward maximisation over a large finite set of actions described by their contexts. We focus on the case when the number of actions is too big to sample all of them even once. However we assume that we have access to the similarities between actions' contexts and that the expected reward is an arbitrary linear function of the contexts' images in the related reproducing kernel Hilbert space (RKHS). We propose KernelUCB, a kernelised UCB algorithm, and give a cumulative regret bound through a frequentist analysis. For contextual bandits, the related algorithm GP-UCB turns out to be a special case of our algorithm, and our finite-time analysis improves the regret bound of GP-UCB for the agnostic case, both in the terms of the kernel-dependent quantity and the RKHS norm of the reward function. Moreover, for the linear kernel, our regret bound matches the lower bound for contextual linear bandits.