This paper introduces CLEO, a novel preference elicitation algorithm capable of recommending complex configurable objects characterized by both discrete and continuous attributes and constraints defined over them. While existing preference elicitation techniques focus on searching for the best instance in a database of candidates, CLEO takes a constructive approach to recommendation through interactive optimization in a space of feasible configurations. The algorithm assumes minimal initial information, i.e., a set of catalog attributes, and defines decisional features as logic formulae combining Boolean and algebraic constraints over the attributes. The (unknown) utility of the decision maker is modeled as a weighted combination of features. CLEO iteratively alternates a preference elicitation step, where pairs of candidate configurations are selected based on the current utility model, and a refinement step where the utility is refined by incorporating the feedback received. The elicitation step leverages a Max-SMT solver to return optimal configurations according to the current utility model. The refinement step is implemented as learning to rank, and a sparsifying norm is used to favor the selection of few informative features in the combinatorial space of candidate decisional features.

A major feature of CLEO is that it can recommend optimal configurations in hybrid domains (i.e., including both Boolean and numeric attributes), thanks to the use of Max-SMT technology, while retaining uncertainty in the decision-maker's utility and noisy feedback. In so doing, it adapts the recently introduced learning modulo theory framework to the preference elicitation setting. The combinatorial formulation of the utility function coupled with the feature selection capabilities of 1-norm regularization allow to effectively deal with the uncertainty in the DM utility while retaining high expressiveness. Experimental results on complex recommendation tasks show the ability of CLEO to quickly identify optimal configurations, as well as its capacity to recover from suboptimal initial choices. Our empirical evaluation highlights how CLEO outperforms a state-of-the-art Bayesian preference elicitation algorithm when applied to a purely discrete task

本文介绍了CLEO，CLEO是一种新颖的偏好引发算法，能够推荐具有离散和连续属性以及在其上定义的约束的特征的复杂可配置对象。现有的偏好激发技术侧重于在候选人数据库中搜索最佳实例，而CLEO采取了建设性的措施在可行的配置空间中通过交互式优化进行推荐的方法。该算法假定最小的初始信息，即一组目录属性，并将决策特征定义为结合了属性上的布尔约束和代数约束的逻辑公式。决策者的（未知）效用被建模为特征的加权组合。CLEO迭代地交替一个偏好启发步骤和一个优化步骤，在该步骤中，基于当前实用新型选择一对候选配置，在优化步骤中，通过合并接收到的反馈来优化实用性。启发步骤利用Max-SMT求解器根据当前实用新型返回最佳配置。细化步骤是通过学习排名，

CLEO的主要特点是可以推荐最佳配置由于使用了Max-SMT技术，因此在混合域中（即包括布尔和数字属性），同时保留了决策者的效用和噪声反馈的不确定性。这样，它使最近引入的学习模理论框架适合于偏好启发设置。效用函数的组合公式与1-范数正则化的特征选择功能相结合，可以有效地处理DM效用中的不确定性，同时又能保持较高的表达能力。在复杂推荐任务上的实验结果表明，CLEO具有快速识别最佳配置的能力，以及从次优初始选择中恢复的能力。