Fair Continuous Resource Allocation with Learning of Impact
Blossom Metevier, Dennis Wei, Karthikeyan Natesan Ramamurthy, Philip Thomas
Recent works have studied fair resource allocation in social settings, where fairness is judged by the impact of allocation decisions rather than more traditional minimum or maximum thresholds on the allocations themselves. Our work significantly adds to this literature by developing continuous resource allocation strategies that adhere to  equality of impact, a generalization of equality of opportunity. We derive methods to maximize total welfare across groups subject to minimal violation of equality of impact, in settings where the outcomes of allocations are unknown but have a diminishing marginal effect. While focused on a two-group setting, our study addresses a broader class of welfare dynamics than explored in prior work. Our contributions are three-fold. First, we provide an algorithm designed for non-noisy continuous-resource environments that achieves sublinear fairness regret. Second, we propose a meta-algorithm for noisy settings building on the first contribution, and third, we empirically demonstrate that our approach consistently achieves fair, welfare-maximizing allocations.