Multimarginal optimal transport (MOT) has gained increasing attention in recent years, notably due to its relevance in machine learning and statistics, where one seeks to jointly compare and align multiple probability distributions. This paper presents a unified and complete Kantorovich duality theory for MOT problem on general Polish product spaces with bounded continuous cost function. For marginal compact spaces, the duality identity is derived through a convex-analytic reformulation, that identifies the dual problem as a Fenchel-Rockafellar conjugate. We obtain dual attainment and show that optimal potentials may always be chosen in the class of $c$-conjugate families, thereby extending classical two-marginal conjugacy principle into a genuinely multimarginal setting. In non-compact setting, where direct compactness arguments are unavailable, we recover duality via a truncation-tightness procedure based on weak compactness of multimarginal transference plans and boundedness of the cost. We prove that the dual value is preserved under restriction to compact subsets and that admissible dual families can be regularized into uniformly bounded $c$-conjugate potentials. The argument relies on a refined use of $c$-splitting sets and their equivalence with multimarginal $c$-cyclical monotonicity. We then obtain dual attainment and exact primal-dual equality for MOT on arbitrary Polish spaces, together with a canonical representation of optimal dual potentials by $c$-conjugacy. These results provide a structural foundation for further developments in probabilistic and statistical analysis of MOT, including stability, differentiability, and asymptotic theory under marginal perturbations.

Column generation (CG) is a well-established method for solving large-scale linear programs. It involves iteratively optimizing a subproblem containing a subset of columns and using its dual solution to generate new columns with negative reduced costs. This process continues until the dual values converge to the optimal dual solution to the original problem. A natural phenomenon in CG is the heavy oscillation of the dual values during iterations, which can lead to a substantial slowdown in the convergence rate. Stabilization techniques are devised to accelerate the convergence of dual values by using information beyond the state of the current subproblem. However, there remains a significant gap in obtaining more accurate dual values at an earlier stage. To further narrow this gap, this paper introduces a novel approach consisting of 1) a machine learning approach for accurate prediction of optimal dual solutions and 2) an adaptive stabilization technique that effectively capitalizes on accurate predictions. On the graph coloring problem, we show that our method achieves a significantly improved convergence rate compared to traditional methods.

There are 27 million refugees around the world.22 The United Nations High Commissioner for Refugees (UNHCR) considers over 1.4 million to be in need of resettlement, that is, permanent relocation from a temporary country of asylum to a third country.21 Resettlement is mainly targeted at the most vulnerable of refugees, such as children at risk, survivors of violence and torture, and those with urgent medical needs. Dozens of countries around the world resettle refugees, but every year the number of refugees in need of resettlement far exceeds the number that is actually resettled. In 2019, for example, only around 63,000 refugees were resettled.21

The choice of the underlying probability measure is crucial in measuring risk or other objectives, but it presents a challenge for decision-makers (DMs) to find an expressive yet tractable reference measure. One simple option is to use the empirical measure on a sample dataset, but this choice is prone to model misspecification due to small sample sizes or blurred observations. Additionally, time-series data can pose further difficulties for modeling, creating another source of misspecification. This paper aims to provide a robust framework for risk evaluation with temporal data. Since Knight (1921) clarified the subtle difference between risk and model uncertainty (misspecification), several methodologies have been developed to incorporate robustness.

Data-driven analytics — in areas ranging from consumer marketing to public policy — often allow behavior prediction at the level of individuals rather than population segments , offering the opportunity to improve decisions that impact large populations. Modeling such (generalized) assignment problems as linear programs, we propose a general value-directed compression technique for solving such problems at scale. We dynamically segment the population into cells using a form of column generation, constructing groups of individuals who can provably be treated identically in the optimal solution. This compression allows problems, unsolvable using standard LP techniques, to be solved effectively. Indeed, once a compressed LP is constructed, problems can solved in milliseconds. We provide a theoretical analysis of themethods, outline the distributed implementation of the requisite data processing, and show how a single compressed LP can be used to solve multiple variants of the original LP near-optimally in real-time (e.g., tosupport scenario analysis). We also show how the method can be leveraged in integer programming models.  Experimental results on marketing contact optimization and political legislature problems validate the performance of our technique.