  Preferential Bayesian optimization (PBO) is a framework for optimizing a
decision maker's latent utility function using preference feedback. This work
introduces the expected utility of the best option (qEUBO) as a novel
acquisition function for PBO. When the decision maker's responses are
noise-free, we show that qEUBO is one-step Bayes optimal and thus equivalent to
the popular knowledge gradient acquisition function. We also show that qEUBO
enjoys an additive constant approximation guarantee to the one-step
Bayes-optimal policy when the decision maker's responses are corrupted by
noise. We provide an extensive evaluation of qEUBO and demonstrate that it
outperforms the state-of-the-art acquisition functions for PBO across many
settings. Finally, we show that, under sufficient regularity conditions,
qEUBO's Bayesian simple regret converges to zero at a rate $o(1/n)$ as the
number of queries, $n$, goes to infinity. In contrast, we show that simple
regret under qEI, a popular acquisition function for standard BO often used for
PBO, can fail to converge to zero. Enjoying superior performance, simple
computation, and a grounded decision-theoretic justification, qEUBO is a
promising acquisition function for PBO.
