Abstract Preference elicitation is an important component in many AI applications, including decision support and recommender systems. Such systems must assess user preferences, based on interactions with their users, and make recommendations using (possibly incomplete and imprecise) beliefs about those preferences. Mechanisms for explicit preference elicitation—asking users to answer direct queries about their preferences—can be of great value; but due to the cognitive and time cost imposed on users, it is important to minimize the number of queries by asking those that have high (expected) value of information. An alternative approach is to simply make recommendations and have users provide feedback (e.g., accept a recommendation or critique it in some way) and use this more indirect feedback to gradually improve the quality of the recommendations. Due to inherent uncertainty about a user's true preferences, often a set of recommendations is presented to the user at each stage. Conceptually, a set of recommendations can also be viewed as choice query, in which the user indicates which option is most preferred from that set. Because of the potential tension between making a good set recommendation and asking an informative choice query, we explore the connection between the two. We consider two different models of preference uncertainty and optimization: (a) a Bayesian framework in which a posterior over user utility functions is maintained, optimal recommendations are assessed using expected utility, and queries are assessed using expected value of information; and (b) a minimax-regret framework in which user utility uncertainty is strict (represented by a polytope), recommendations are made using the minimax-regret robustness criterion, and queries are assessed using worst-case regret reduction. We show that, somewhat surprisingly, in both cases, there is no tradeoff to be made between good recommendations and good queries: we prove that the optimal recommendation set of size k is also an optimal choice query of size k. We also examine the case where user responses to choice queries are error prone (using both constant and mixed multinomial logit noise models) showing the results are robust to this form of noise. In both frameworks, our theoretical results have practical consequences for the design of interactive recommenders. Our results also allow us to design efficient algorithms to compute optimal query/recommendation sets. We develop several such algorithms (both exact and approximate) for both settings and provide empirical validation of their performance.

中文翻译：

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关于最优推荐集和近视最优查询集的等价性

摘要 偏好获取是许多人工智能应用的重要组成部分，包括决策支持和推荐系统。此类系统必须根据与用户的交互来评估用户偏好，并使用（可能不完整和不精确的）关于这些偏好的信念做出推荐。明确的偏好引出机制——要求用户回答有关他们偏好的直接查询——可能具有重要价值；但由于强加给用户的认知和时间成本，重要的是通过询问那些具有高（预期）信息价值的人来最小化查询数量。另一种方法是简单地提出建议并让用户提供反馈（例如，接受建议或以某种方式对其进行批评）并使用这种更间接的反馈来逐步提高建议的质量。由于用户真实偏好的固有不确定性，通常在每个阶段向用户呈现一组推荐。从概念上讲，一组推荐也可以被视为选择查询，其中用户指示从该组中最喜欢哪个选项。由于提出好的集合推荐和询问信息丰富的选择查询之间存在潜在的紧张关系，我们探索了两者之间的联系。我们考虑了两种不同的偏好不确定性和优化模型：（a）贝叶斯框架，其中保持了用户效用函数的后验，使用预期效用评估了最佳推荐，使用信息的期望值评估查询；(b) 一个 minimax-regret 框架，其中用户效用不确定性是严格的（由多面体表示），使用 minimax-regret 稳健性标准提出建议，并使用最坏情况后悔减少来评估查询。我们表明，有点令人惊讶的是，在这两种情况下，好的推荐和好的查询之间没有权衡：我们证明了大小为 k 的最佳推荐集也是大小为 k 的最佳选择查询。我们还检查了用户对选择查询的响应容易出错的情况（使用常数和混合多项 logit 噪声模型），显示结果对这种形式的噪声是稳健的。在这两个框架中，我们的理论结果对交互式推荐器的设计具有实际意义。我们的结果还允许我们设计有效的算法来计算最佳查询/推荐集。我们为这两种设置开发了几种这样的算法（精确和近似），并对其性能提供经验验证。