Conversational Recommendation: Theoretical Model and Complexity Analysis

Recommender systems are software applications that help users find items of interest in situations of information overload in a personalized way, using knowledge about the needs and preferences of individual users. In conversational recommendation approaches, these needs and preferences are acquired by the system in an interactive, multi-turn dialog. A common approach in the literature to drive such dialogs is to incrementally ask users about their preferences regarding desired and undesired item features or regarding individual items. A central research goal in this context is efficiency, evaluated with respect to the number of required interactions until a satisfying item is found. This is usually accomplished by making inferences about the best next question to ask to the user. Today, research on dialog efficiency is almost entirely empirical, aiming to demonstrate, for example, that one strategy for selecting questions is better than another one in a given application. With this work, we complement empirical research with a theoretical, domain-independent model of conversational recommendation. This model, which is designed to cover a range of application scenarios, allows us to investigate the efficiency of conversational approaches in a formal way, in particular with respect to the computational complexity of devising optimal interaction strategies. Through such a theoretical analysis we show that finding an efficient conversational strategy is NP-hard, and in PSPACE in general, but for particular kinds of catalogs the upper bound lowers to POLYLOGSPACE. From a practical point of view, this result implies that catalog characteristics can strongly influence the efficiency of individual conversational strategies and should therefore be considered when designing new strategies. A preliminary empirical analysis on datasets derived from a real-world one aligns with our findings.