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On the Equivalence of Optimal Recommendation Sets and Myopically Optimal Query Sets

Paolo Viappiani
Artificial Intelligence, vol. 286 (2020)


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.