Fair Recommender Systems for Intersecting Groups

Christine Ling; Juba Ziani

cs.LGOct 29, 2026

Fair Recommender Systems for Intersecting Groups

Authors: Christine Ling, Juba Ziani

Organizations: Georgia Institute of Technology.

Abstract

Recommendation systems that optimize for the average user can fail to capture the preferences of diverse demographic groups. We consider a dynamic recommendation system, where arriving users can belong to different demographic groups. Importantly, these groups can intersect, and a user may belong to several groups. We first show that over time, any group-blind policy (which excludes all current-user group information) recommending $K \geq 1$ items incurs linear total regret under mild conditions. In turn, we introduce three group-aware algorithms based on the classical Upper Confidence Bound algorithm (UCB): i) Intersection-Fitting, which runs UCB on each intersection, but has a sublinear group- and intersection-level regret guarantee with an exponential dependence in the number of groups; and ii) two group-level heuristics, Inner-Outer UCB and Group-Item UCB which allocate different arms to different groups, and use a sleeping expert meta-learner to choose which active group's recommendation an intersection should inherit at any given time step. We provide experimental results on two datasets, Goodreads and BoardGameGeek, and highlight that our heuristics can be preferable to the intersection-fitting algorithm when intersection-level preferences are closely related to group-level preferences, but that intersection-fitting performs better when different intersections within a same group prefer different items.

Figures & tables

I_{j,t}=\hat{v}_{j,t}+V_{\max}\sqrt{\frac{2\ln\max\{2,t+1\}}{N_{j,t}}}

Algorithm 1 Group-Blind top-

K

UCB

I_{j,\iota_{P},t}=\hat{v}_{j,\iota_{P}}+V_{\max}\sqrt{\frac{2\ln\max\{2,\tau_{\iota_{P}}(t)\}}{N_{j,\iota_{P}}}}

Algorithm 2 Intersection-Fitting UCB

I_{j,k,t}=\hat{v}_{j,k}+V_{\max}\sqrt{\frac{2\ln\max\{2,t+1\}}{N_{j,k}}}

Algorithm 3 Inner–Outer UCB

I_{j,k,t}=\hat{v}_{j,k}+V_{\max}\sqrt{\frac{2\ln\max\{2,t+1\}}{N_{j,k}}}

Algorithm 4 Group–Item UCB

Panel of Figure 1 — Figure 1: Goodreads primary catalog ( $n=15$ ) at slate size $K=1$ . At the group level, Intersection-Fitting and both pooling heuristics (Group–Item UCB and Inner–Outer UCB) achieve comparable low cumulative regret. At the intersection level, common demographics (solid lines) and rare demographics (dotted lines) are plotted together. Across both traffic tiers, the pooling heuristics achieve strictly lower cumulative regret than exact Intersection-Fitting.

Panel of Figure 2 — Figure 2: Goodreads primary catalog ( $n=15$ ) at slate size $K=5$ . Group-Blind UCB incurs linear regret across all panels. Group–Item UCB achieves the lowest regret across groups and intersections, whereas Inner–Outer UCB’s cumulative regret exceeds Intersection-Fitting on common intersections.

Panel of Figure 3 — Figure 3: BoardGameGeek primary catalog ( $n=15$ ) at slate size $K=1$ . Intersection-Fitting achieves negative group-level regret by recommending intersection-specific slates that outperform the group’s best fixed slate. Both pooling heuristics (Group–item UCB and Inner–Outer UCB) result in higher cumulative regret than Intersection-Fitting across the groups and intersections.

Panel of Figure 4 — Figure 4: BoardGameGeek primary catalog ( $n=15$ ) at slate size $K=5$ . While the pooling heuristics also achieve negative group-level regret, Intersection-Fitting drives group regret to be more negative and achieves lower cumulative intersection regret across all displayed panels.

Appendix figures & tables10 assets

Supplementary material from the paper’s appendix.

Appendix

Panel of Figure 5 — Figure 5: Goodreads primary catalog ( $n=15$ ) at slate size $K=3$ . On rare intersections (dotted lines), Group–item UCB and Inner–Outer UCB achieve lower regret than Intersection-Fitting. On common intersections (solid lines), Group–item UCB maintains the lowest regret, while Inner–Outer UCB achieves comparable cumulative regret to Intersection-Fitting.

Panel of Figure 6 — Figure 6: BoardGameGeek primary catalog ( $n=15$ ) at slate size $K=3$ . Intersection-Fitting achieves the lowest cumulative regret at both the group and intersection levels. Group–Item UCB and Inner–Outer UCB have distinct regret trajectories that end strictly higher than Intersection-Fitting across the panels.

Panel of Figure 7 — Figure 7: Goodreads extended catalog ( $n=72$ ) at slate size $K=1$ . At this slate size, Group–Item UCB and Inner–Outer UCB are algorithmically equivalent. Both pooled heuristics efficiently leverage the inherited group structure to achieve strictly lower cumulative regret than Intersection-Fitting across both group and intersection levels.

Panel of Figure 8 — Figure 8: Goodreads extended catalog ( $n=72$ ) at slate size $K=3$ . Group–Item UCB achieves the lowest regret. Unlike the $15$ -item catalog where Inner–Outer UCB and Intersection-Fitting were comparable at $K=3$ , the expanded $72$ -item catalog separates Intersection-Fitting’s budget enough that Inner–Outer UCB establishes an advantage on common intersections.

Panel of Figure 9 — Figure 9: Goodreads extended catalog ( $n=72$ ) at slate size $K=5$ . This is a reversal of the dynamic observed in the $15$ -item catalog: the expanded action space penalizes Intersection-Fitting’s lack of data sharing more, allowing Inner–Outer UCB to maintain lower cumulative regret on common intersections. Group–Item UCB remains the most efficient policy.

Figure 10: BoardGameGeek extended catalog (

n=72

) at slate size

K=1

. Because the empirical intersections exhibit heterogeneous preferences that do not smoothly compose from their base themes, pooling data actively harms learning. Intersection-Fitting avoids this cross-group interference, driving group regret deeply negative and achieving the lowest cumulative intersection regret.

Figure 11: BoardGameGeek extended catalog (

n=72

) at slate size

K=3

. Intersection-Fitting consistently achieves the lowest cumulative regret across both evaluation levels. The skewed UCB-style indices caused by active-group updates prevent Inner–Outer UCB and Group–Item UCB from efficiently learning the optimal slates for atypical intersections.

Figure 12: BoardGameGeek extended catalog (

n=72

) at slate size

K=5

. Even at larger slate sizes within the expanded catalog, Intersection-Fitting remains the dominant policy. The structural penalty of pooling heterogeneous data persists, allowing exact, unbiased intersection-level learning to outpace both heuristics.

Catalog	$K$	Level	Algorithm	Avg Final $\|\text{Regret}\|$	Avg Std Dev	Relative Std
$n=15$	1	Group	Group-Blind	97,102.9	863.0	0.8888%
$n=15$	1	Group	Intersection-Fit	9,105.6	203.3	2.2331%
$n=15$	1	Group	Inner-Outer	5,616.8	166.0	2.9552%
$n=15$	1	Group	Group-Item	5,616.8	166.0	2.9552%
$n=15$	1	Intersection	Group-Blind	728.4	34.5	4.7325%
$n=15$	1	Intersection	Intersection-Fit	513.8	21.6	4.1955%

Appendix

Table 1: Robustness Analysis: Multi-Seed Variance in Goodreads (

T=200{,}000

)

Catalog	$K$	Level	Algorithm	Avg Final $\|\text{Regret}\|$	Avg Std Dev	Relative Std
$n=15$	1	Group	Group-Blind	79,064.8	1,080.5	1.3666%
$n=15$	1	Group	Intersection-Fit	72,146.8	532.8	0.7385%
$n=15$	1	Group	Inner-Outer	36,677.2	599.5	1.6345%
$n=15$	1	Group	Group-Item	36,677.2	599.5	1.6345%
$n=15$	1	Intersection	Group-Blind	89,014.4	1,234.1	1.3864%
$n=15$	1	Intersection	Intersection-Fit	36,947.7	481.4	1.3031%

Appendix

Table 2: Robustness Analysis: Multi-Seed Variance in BoardGameGeek (

T=10{,}000{,}000

)

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Data Science Research Centre, Tampere University, Tampere, Finland · Hellenic Mediterranean University & Archimedes/Athena RC, Greece

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Group recommender systems help users make collective choices but often lack transparency, leaving group members uncertain about why items are suggested. Existing explanation methods focus on individuals, offering limited support for groups where multiple preferences interact. In this work, we introduce and formalize the problem of finding counterfactual explanations for group recommendations. We introduce a comprehensive set of item- and explanation-level metrics that capture different aspects, such as relevance, popularity, explanation utility, interpretability, and fairness. We design five algorithms that employ techniques such as search-space pruning, greedy selection, early stopping, and incremental refinement to reduce computational cost and the number of recommender calls while producing high-quality explanations. The algorithms consider different trade-offs; for example, some prioritize computational efficiency at the expense of explanation quality, while others focus on improving explanation quality at a higher computational cost. Experiments on real-world datasets analyze these trade-offs in terms of explanation size, computational cost, utility, and fairness.

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