  We present a new type of acquisition functions for online decision making in
multi-armed and contextual bandit problems with extreme payoffs. Specifically,
we model the payoff function as a Gaussian process and formulate a novel type
of upper confidence bound (UCB) acquisition function that guides exploration
towards the bandits that are deemed most relevant according to the variability
of the observed rewards. This is achieved by computing a tractable likelihood
ratio that quantifies the importance of the output relative to the inputs and
essentially acts as an \textit{attention mechanism} that promotes exploration
of extreme rewards. We demonstrate the benefits of the proposed methodology
across several synthetic benchmarks, as well as a realistic example involving
noisy sensor network data. Finally, we provide a JAX library for efficient
bandit optimization using Gaussian processes.
