arXiv 11 Feb 2026 · Econometrics
arXiv:2602.10515 · PDF · DOI · OpenAlex · Extracted main text
Optimal transport is the problem of designing a joint distribution for two random variables with fixed marginals. In virtually the entire literature on this topic, the objective is to minimize expected cost. This paper is the first to study a variant in which the goal is to minimize a quantile of the cost, rather than the mean. For the semidiscrete setting, where one distribution is continuous and the other is discrete, we derive a complete characterization of the optimal transport plan and develop simulation-based methods to efficiently compute it. One particularly novel aspect of our approach is the efficient computation of a tie-breaking rule that preserves marginal distributions. In the context of geographical partitioning problems, the optimal plan is shown to produce a novel geometric structure.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Genevay, A. and Cuturi, M. and Peyré, G. and Bach, F (2016) Stochastic optimization for large-scale optimal transport | 0.843 | 3 | 3 | 100% |
| 2 | Carlsson, J. G. and Carlsson, E. and Devulapalli, R (2016) Shadow prices in territory division | 0.644 | 2 | 2 | 100% |
| 3 | Kushner, H. J. and Yin, G (2003) Stochastic approximation and recursive algorithms and applications (2nd ed.) | 0.644 | 2 | 2 | 100% |
| 4 | Boyd, S. and Vandenberghe, L (2004) Convex Optimization | 0.511 | 2 | 1 | 100% |
| 5 | Shapiro, A. and Dentcheva, D. and Ruszczynski, A (2021) Lectures on stochastic programming: modeling and theory | 0.511 | 2 | 1 | 100% |
| 6 | Villani, C (2021) Topics in optimal transportation | 0.511 | 2 | 1 | 100% |
| 7 | Aumann, R. J (1965) Integrals of set-valued functions | 0.405 | 1 | 1 | 100% |
| 8 | Aurenhammer, F (1991) Voronoi diagrams – a survey of a fundamental geometric data structure | 0.405 | 1 | 1 | 100% |
| 9 | Bach, F. and Moulines, E (2011) Non-asymptotic analysis of stochastic approximation algorithms for machine learning | 0.405 | 1 | 1 | 100% |
| 10 | Bach, F. and Moulines, E (2013) Non-strongly-convex smooth stochastic approximation with convergence rate O(1/n) | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 56 scored citations.