Discrepancy-Rounded Fair Bandits with Static and Time-Varying Exposure Floors

2026-07-24

AI Summary

This work addresses the challenge of enforcing strict per-round exposure lower bounds for providers or groups in online recommendation and allocation, rather than satisfying them only asymptotically. The authors formulate the stochastic bandit problem with exact exposure constraints as an integer rounding problem, using discrepancy vectors to characterize exposure errors, and introduce a block-wise model to handle time-varying lower bounds. Innovatively integrating fair bandits with discrepancy rounding theory, they design a deterministic algorithm that guarantees hard satisfaction of block-level constraints; for overlapping groups, feasibility is ensured via Beck–Fiala nullspace rounding. Combining BDQ-UCB, kl-UCB++ residual rules, and dual ledger decomposition, the method achieves a high-probability fair regret bound of $O(\sqrt{KR \log(KT)})$, with an optimal variant attaining the minimax rate $\Theta(\sqrt{KR})$. Experiments demonstrate that the approach satisfies constraints exactly without parameter tuning while matching the regret performance of 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 $Θ(\sqrt{KR})$, 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 $Ω(s)$ 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 $\widetildeΘ(\sqrt{KT})$, 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.

Problem

• fair bandits
• exposure floors
• discrepancy rounding
• group fairness
• stochastic bandits

Innovation

• discrepancy rounding
• fair bandits
• exposure floors
• blockwise scheduling
• overlapping groups