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This research advances the theoretical foundations of fair recommendation systems by modeling minimum-exposure constraints as a rounding problem within stochastic bandits. The authors introduce novel algorithms like BDQ-UCB and Beck-Fiala null-space rounding to handle both static and time-varying exposure floors, achieving optimal regret bounds that scale with nonmandatory budgets rather than total horizon length. These contributions are critical for building robust AI systems in regulated allocation scenarios where per-period fairness guarantees must be strictly enforced without performance degradation.
Discrepancy-Rounded Fair Bandits with Static and Time-Varying Exposure Floors
arXiv:2607.22935v1 Announce Type: new Abstract: Minimum-exposure constraints arise in recommendation, content curation, and regulated allocation when each provider, arm, or group must receive guaranteed exposure inside a period rather than only in aggregate. We study stochastic bandits with exact exposure floors and show that the right object is a rounding problem: a fractional fair schedule is realized as integral pulls, and the exposure error is exactly a discrepancy vector. The main contribution is a blockwise model with time-varying floors. BDQ-UCB satisfies every block floor deterministically and has fair regret governed by the nonmandatory budget $R$, not the horizon $T$, with high-probability regret $O(\sqrt{KR\log(KT)})$. A MOSS residual variant attains $O(\sqrt{KR})$, and a matching lower bound gives the minimax rate $\Theta(\sqrt{KR})$, even with positive mandatory exposure; a kl-UCB$^{++}$ residual rule adds instance-dependent optimality. The formulation becomes essential for overlapping group floors: per-arm rounding can violate a group constraint by $\Omega(s)$ in the group size, whereas Beck--Fiala null-space rounding meets every group floor within the block budget with violation below the arm degree $t$, and composes with UCB at the same $R$-parametrized regret. For learned group plans, we close disjoint systems at $\widetilde\Theta(\sqrt{KT})$, give a dual-ledger decomposition explaining why naive index rules fail under overlap, and prove a plan-sampling rule that is pathwise feasible under an initial cover-slack condition and attains a conditional $\widetilde O(\sqrt{KT})$ guarantee, leaving the condition-free overlap rate open. Experiments on synthetic floors, MovieLens-100k genre exposure, and deployment stress tests show exact feasibility without penalty tuning and regret competitive with tuned Lagrangian baselines.
Abstract:Minimum-exposure constraints arise in recommendation, content curation, and regulated allocation when each provider, arm, or group must receive guaranteed exposure inside a period rather than only in aggregate. We study stochastic bandits with exact exposure floors and show that the right object is a rounding problem: a fractional fair schedule is realized as integral pulls, and the exposure error is exactly a discrepancy vector. The main contribution is a blockwise model with time-varying floors. BDQ-UCB satisfies every block floor deterministically and has fair regret governed by the nonmandatory budget $R$, not the horizon $T$, with high-probability regret $O(\sqrt{KR\log(KT)})$. A MOSS residual variant attains $O(\sqrt{KR})$, and a matching lower bound gives the minimax rate $\Theta(\sqrt{KR})$, even with positive mandatory exposure; a kl-UCB$^{++}$ residual rule adds instance-dependent optimality. The formulation becomes essential for overlapping group floors: per-arm rounding can violate a group constraint by $\Omega(s)$ in the group size, whereas Beck--Fiala null-space rounding meets every group floor within the block budget with violation below the arm degree $t$, and composes with UCB at the same $R$-parametrized regret. For learned group plans, we close disjoint systems at $\widetilde\Theta(\sqrt{KT})$, give a dual-ledger decomposition explaining why naive index rules fail under overlap, and prove a plan-sampling rule that is pathwise feasible under an initial cover-slack condition and attains a conditional $\widetilde O(\sqrt{KT})$ guarantee, leaving the condition-free overlap rate open. Experiments on synthetic floors, MovieLens-100k genre exposure, and deployment stress tests show exact feasibility without penalty tuning and regret competitive with tuned Lagrangian baselines.
Machine Learning (cs.LG)
arXiv:2607.22935 [cs.LG]
(or arXiv:2607.22935v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2607.22935 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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