This paper presents a novel approach to top-$k$ ranking Bayesian optimization
(top-$k$ ranking BO) which is a practical and significant generalization of
preferential BO to handle top-$k$ ranking and tie/indifference observations. We
first design a surrogate model that is not only capable of catering to the
above observations, but is also supported by a classic random utility model.
Another equally important contribution is the introduction of the first
information-theoretic acquisition function in BO with preferential observation
called multinomial predictive entropy search (MPES) which is flexible in
handling these observations and optimized for all inputs of a query jointly.
MPES possesses superior performance compared with existing acquisition
functions that select the inputs of a query one at a time greedily. We
empirically evaluate the performance of MPES using several synthetic benchmark
functions, CIFAR-$10$ dataset, and SUSHI preference dataset.

本文提出了一个新颖的基于 Bayesian 优化（top-k ranking BO）的算法，该算法能够处理 top-k ranking 和 tie/indifference observations，具有信息熵的预测搜索功能（MPES）。通过在多个综合基准数据集上的实验评估，MPES 的性能优于现有的贪心算法。

Top-k 排名贝叶斯优化

Top-$k$ Ranking Bayesian Optimization

The past decade has seen a significant interest in learning tractable
probabilistic representations. Arithmetic circuits (ACs) were among the first
proposed tractable representations, with some subsequent representations being
instances of ACs with weaker or stronger properties. In this paper, we provide
a formal basis under which variants on ACs can be compared, and where the
precise roles and semantics of their various properties can be made more
transparent. This allows us to place some recent developments on ACs in a
clearer perspective and to also derive new results for ACs. This includes an
exponential separation between ACs with and without determinism; completeness
and incompleteness results; and tractability results (or lack thereof) when
computing most probable explanations (MPEs).

本文提供了一种形式基础，可以在其中比较 AC 的变体，从而使它们的各种属性的作用和语义更加透明。本文还为 AC 提供了新的结果，包括具有和没有确定性的 AC 之间的指数分离；完备性和不完备性结果；以及计算最可能的解释时 (MPEs) 的可处理性结果（或缺乏处理性结果）。