We study fair allocation of constrained resources, where a market designer optimizes overall welfare while maintaining group fairness. In many large-scale settings, utilities are not known in advance, but are instead observed after realizing the allocation. We therefore estimate agent utilities using machine learning. Optimizing over estimates requires trading-off between mean utilities and their predictive variances. We discuss these trade-offs under two paradigms for preference modeling – in the stochastic optimization regime, the market designer has access to a probability distribution over utilities, and in the robust optimization regime they have access to an uncertainty set containing the true utilities with high probability. We discuss utilitarian and egalitarian welfare objectives, and we explore how to optimize for them under stochastic and robust paradigms. We demonstrate the efficacy of our approaches on three publicly available conference reviewer assignment datasets. The approaches presented enable scalable constrained resource allocation under uncertainty for many combinations of objectives and preference models.

We study mechanisms that allocate reviewers to papers in a fair and efficient manner. We model reviewer assignment as an instance of a fair allocation problem, presenting an extension of the classic round-robin mechanism, called Reviewer Round Robin (RRR). Round-robin mechanisms are a standard tool to ensure envy-free up to one item (EF1) allocations. However, fairness often comes at the cost of decreased efficiency. To overcome this challenge, we carefully select an approximately optimal round-robin order. Applying a relaxation of submodularity, γ-weak submodularity, we show that greedily inserting papers into an order yields a (1+γ²)-approximation to the maximum welfare attainable by our round-robin mechanism under any order. Our Greedy Reviewer Round Robin (GRRR) approach outputs highly efficient EF1 allocations for three real conference datasets, offering comparable performance to state-of-the-art paper assignment methods in fairness, efficiency, and runtime, while providing the only EF1 guarantee.

We consider the problem of utility maximization in online ranking applications while also satisfying a pre-defined fairness constraint. We consider batches of items which arrive over time, already ranked using an existing ranking model. We propose online post-processing for re-ranking these batches to enforce adherence to the pre-defined fairness constraint, while maximizing a specific notion of utility. To achieve this goal, we propose two deterministic re-ranking policies. In addition, we learn a re-ranking policy based on a novel variation of learning to search. Extensive experiments on real world and synthetic datasets demonstrate the effectiveness of our proposed policies both in terms of adherence to the fairness constraint and utility maximization. Furthermore, our analysis shows that the performance of the proposed policies depends on the original data distribution w.r.t the fairness constraint and the notion of utility.