Sequential Diversification with Provable Guarantees

Diversification is a useful tool for exploring large collections of information items. It has been used to reduce redundancy and cover multiple perspectives in information-search settings. Diversification finds applications in many different domains, including presenting search results of information-retrieval systems and selecting suggestions for recommender systems. Interestingly, existing measures of diversity are defined over \emph{sets} of items, rather than evaluating \emph{sequences} of items. This design choice comes in contrast with commonly-used relevance measures, which are distinctly defined over sequences of items, taking into account the ranking of items. The importance of employing sequential measures is that information items are almost always presented in a sequential manner, and during their information-exploration activity users tend to prioritize items with higherranking. In this paper, we study the problem of \emph{maximizing sequential diversity}. This is a new measure of \emph{diversity}, which accounts for the \emph{ranking} of the items, and incorporates \emph{item relevance} and \emph{user behavior}. The overarching framework can be instantiated with different diversity measures, and here we consider the measures of \emph{sumdiversity} and \emph{coveragediversity}. The problem was recently proposed by Coppolillo et al.\citep{coppolillo2024relevance}, where they introduce empirical methods that work well in practice. Our paper is a theoretical treatment of the problem: we establish the problem hardness and present algorithms with constant approximation guarantees for both diversity measures we consider. Experimentally, we demonstrate that our methods are competitive against strong baselines.

💡 Research Summary

Introduction
Diversity is a cornerstone of modern information‑retrieval and recommender systems because it helps users encounter a broad set of perspectives. Most prior work treats diversification as a set‑selection problem: given a pool of items, choose a subset that maximizes a diversity function (e.g., coverage, pairwise distance). Ranking is either ignored or treated as a by‑product of a greedy construction. In practice, however, users consume results sequentially, paying more attention to items near the top of the list. This observation motivates the notion of sequential diversity: a diversity measure that explicitly depends on the order in which items are presented and on the probability that a user continues after each item.

Related Work
Traditional diversification methods (e.g., MMR, DPP, submodular coverage) assume that users examine all results equally. Some recent papers (Coppolillo et al., 2024; Kleinberg et al., 2014) introduced user‑behavior models with continuation probabilities, but they either lack theoretical guarantees or focus on a single diversity function. The present work builds on these ideas and provides a unified, provably‑approximate framework for two widely used diversity measures.

Model and Problem Definition

• Universe of items (U={1,\dots,n}).
• Each item (i) has a continuation probability (p_i\in