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

Ibne Farabi Shihab; Joyanta Jyoti Mondal; Anuj Sharma

cs.LGJul 24, 2026

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

Authors: Ibne Farabi Shihab, Joyanta Jyoti Mondal, Anuj Sharma

Organizations: Department of Computer Science, Iowa State University, USA · Department of Computer and Information Sciences, University of Delaware, USA · Department of Civil, Construction & Environmental Engineering, Iowa State University, USA

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.

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