Mohammad Reza Aminian

arXiv2026

Stationary Online Contention Resolution Schemes: Theory and Applications to Bayesian Online Resource Allocation

Motivated by problems in Bayesian reusable resource allocation, we introduce the concept of stationary online contention resolution schemes (S-OCRSs). OCRSs are a central tool used to solve non-reusable resource allocation problems. They convert solutions to fluid approximations of problems into feasible online policies while approximately preserving allocation probabilities. S-OCRSs depart from standard OCRSs in that they ensure that the probability of allocating any given set of resources is independent of the arrival order of requests. We show how S-OCRSs can be used to solve reusable resource allocation problems, and discuss a general 'maximum-entropy' approach to construct and analyze S-OCRSs. Our approach, using a unified method for a variety of feasibility constraints, obtains results that match the state-of-the-art for OCRSs, and even improves it for a bipartite matching feasibility constraint. Our results for reusable resource allocation also extend to the assortment optimization setting, and our policies can be implemented using prices.

cs.GT↗

arXiv2025

Markovian Search with Ex-Ante Constraints: Theory and Applications to Socially Aware Algorithmic Hiring

We develop an algorithmic framework to incorporate "ex-ante" constraints on outcomes (that hold only on average) into stateful sequential search with costly inspection. Our framework encompasses the classical Weitzman's Pandora's box [Weitzman, 1979] as well as its extensions to joint Markovian scheduling [Dumitriu et al., 2003; Gittins, 1979], modeling richer processes such as multistage search with multiple layers of inspection. Ex-ante constraints in search are particularly motivated by social considerations in algorithmic hiring, where they adjust outcome distributions to promote equity and access. Building on the optimality of index-based policies in the unconstrained problems, we show that optimal policies under a single ex-ante constraint (e.g., demographic parity) retain an index-based structure but require (i) dual-based adjustments of the indices and (ii) randomization between two such adjustments via a "tie-breaking rule," both easy to compute and economically interpretable. We then extend our results to handle multiple affine constraints by reduction to a variant of the exact Carathéodory problem and providing a polynomial-time algorithm to construct an optimal randomized dual-adjusted index-based policy that satisfies all constraints simultaneously. For general affine and convex constraints, we develop a primal-dual algorithm that randomizes over a polynomial number of dual-based adjustments, yielding a near-feasible, near-optimal policy. All these results rely on the key observation that a suitable relaxation of the Lagrange dual function for these constrained problems admits index-based policies akin to those in the unconstrained setting. Finally, through a numerical study, we investigate the implications of various socially aware ex-ante constraints on the utilitarian loss (price of fairness), and examine whether they achieve their intended socially desirable outcomes.

cs.DS↗