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We present a new type of acquisition functions for online decision making inmulti-armed and contextual bandit problems with extreme payoffs. Specifically,we model the payoff function as a Gaussian process and formulate a novel typeof upper confidence bound (UCB) acquisition function that guides explorationtowards the bandits that are deemed most relevant according to the variabilityof the observed rewards. This is achieved by computing a tractable likelihoodratio that quantifies the importance of the output relative to the inputs andessentially acts as an \textit{attention mechanism} that promotes explorationof extreme rewards. We demonstrate the benefits of the proposed methodologyacross several synthetic benchmarks, as well as a realistic example involvingnoisy sensor network data. Finally, we provide a JAX library for efficientbandit optimization using Gaussian processes.

Output-Weighted Sampling for Multi-Armed Bandits with Extreme Payoffs