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Calibrated Recommendations for Users with Decaying Attention

Jon Kleinberg, Emily Ryu, Éva Tardos

TL;DR

The paper tackles calibrating recommendation lists under decaying user attention by introducing an overlap-based framework that quantifies how closely a list matches a user’s target genre distribution. It analyzes two genre models—discrete and distributional—and develops order-aware optimization methods: a $2/3$-approximation for the discrete-genre model via a novel ordered-submodular/bin-packing analysis, and a $(1-1/e)$-approximation for the distributional-genre model by transforming the problem into a laminar matroid constrained submodular optimization solvable by continuous greedy and pipage rounding. The key contributions are the MDR/SMDR overlap concepts, the extension of submodular guarantees to sequences with decaying attention, and the practical implication that near-optimal calibration can be achieved in ranking settings where ordering matters. Overall, the work provides the first nontrivial algorithmic guarantees for calibrated recommendations with decaying attention, bridging theory and ordering-aware recommender system design.

Abstract

Recommendation systems capable of providing diverse sets of results are a focus of increasing importance, with motivations ranging from fairness to novelty and other aspects of optimizing user experience. One form of diversity of recent interest is calibration, the notion that personalized recommendations should reflect the full distribution of a user's interests, rather than a single predominant category -- for instance, a user who mainly reads entertainment news but also wants to keep up with news on the environment and the economy would prefer to see a mixture of these genres, not solely entertainment news. Existing work has formulated calibration as a subset selection problem; this line of work observes that the formulation requires the unrealistic assumption that all recommended items receive equal consideration from the user, but leaves as an open question the more realistic setting in which user attention decays as they move down the list of results. In this paper, we consider calibration with decaying user attention under two different models. In both models, there is a set of underlying genres that items can belong to. In the first setting, where items are represented by fine-grained mixtures of genre percentages, we provide a $(1-1/e)$-approximation algorithm by extending techniques for constrained submodular optimization. In the second setting, where items are coarsely binned into a single genre each, we surpass the $(1-1/e)$ barrier imposed by submodular maximization and give a $2/3$-approximate greedy algorithm. Our work thus addresses the problem of capturing ordering effects due to decaying attention, allowing for the extension of near-optimal calibration from recommendation sets to recommendation lists.

Calibrated Recommendations for Users with Decaying Attention

TL;DR

The paper tackles calibrating recommendation lists under decaying user attention by introducing an overlap-based framework that quantifies how closely a list matches a user’s target genre distribution. It analyzes two genre models—discrete and distributional—and develops order-aware optimization methods: a -approximation for the discrete-genre model via a novel ordered-submodular/bin-packing analysis, and a -approximation for the distributional-genre model by transforming the problem into a laminar matroid constrained submodular optimization solvable by continuous greedy and pipage rounding. The key contributions are the MDR/SMDR overlap concepts, the extension of submodular guarantees to sequences with decaying attention, and the practical implication that near-optimal calibration can be achieved in ranking settings where ordering matters. Overall, the work provides the first nontrivial algorithmic guarantees for calibrated recommendations with decaying attention, bridging theory and ordering-aware recommender system design.

Abstract

Recommendation systems capable of providing diverse sets of results are a focus of increasing importance, with motivations ranging from fairness to novelty and other aspects of optimizing user experience. One form of diversity of recent interest is calibration, the notion that personalized recommendations should reflect the full distribution of a user's interests, rather than a single predominant category -- for instance, a user who mainly reads entertainment news but also wants to keep up with news on the environment and the economy would prefer to see a mixture of these genres, not solely entertainment news. Existing work has formulated calibration as a subset selection problem; this line of work observes that the formulation requires the unrealistic assumption that all recommended items receive equal consideration from the user, but leaves as an open question the more realistic setting in which user attention decays as they move down the list of results. In this paper, we consider calibration with decaying user attention under two different models. In both models, there is a set of underlying genres that items can belong to. In the first setting, where items are represented by fine-grained mixtures of genre percentages, we provide a -approximation algorithm by extending techniques for constrained submodular optimization. In the second setting, where items are coarsely binned into a single genre each, we surpass the barrier imposed by submodular maximization and give a -approximate greedy algorithm. Our work thus addresses the problem of capturing ordering effects due to decaying attention, allowing for the extension of near-optimal calibration from recommendation sets to recommendation lists.
Paper Structure (22 sections, 17 theorems, 77 equations, 2 figures, 2 tables)

This paper contains 22 sections, 17 theorems, 77 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Problem Statement and Overlap Measures
  4. Item Genres and Genre of Recommendation Lists
  5. Overlap Measures
  6. Constructing Families of Overlap Measures
  7. Monotone Diminishing Return (MDR) Overlap Measures
  8. Calibration in the Discrete Genre Model
  9. Ordered-submodular Functions and the Greedy Algorithm
  10. Improved Approximation for Calibration with Discrete Genres
  11. Calibration in the Distributional Genre Model
  12. Conclusion
  13. Survey of existing submodularity frameworks
  14. Deferred proofs
  15. Proofs and discussion from Section \ref{['sec:overlap_families']}
  16. ...and 7 more sections

Key Result

Theorem 4

Given any bounded monotone $f$-divergence $D_f$ with maximum value $d^* = \max_{(p,q)} D_f(p,q)$, the corresponding $D_f$-overlap measure $G_{D_f}(p,q) = d^* - D_f(p,q)$ is MDR.

Figures (2)

  • Figure 1: Change in $f(A_i||\bar{T}^{i+1})$ as we move $x$ weight from $g'$ to $g^*$.
  • Figure 2: Change in $f(A_i||\bar{T}^{i+1})$ as we move $x$ weight from $g'$ to $g^*$.

Theorems & Definitions (36)

  • Definition 1: Overlap measure
  • Definition 2: Distance-based overlap measure
  • Definition 3: (S)MDR overlap measure
  • Theorem 4
  • Theorem 5
  • Theorem 6
  • Theorem 7
  • Lemma 7
  • Theorem 8
  • proof
  • ...and 26 more