This study examines a resource-sharing problem involving multiple parties that agree to use a set of capacities together. We start with modeling the whole problem as a mathematical program, where all parties are required to exchange information to obtain the optimal objective function value. This information bears private data from each party in terms of coefficients used in the mathematical program. Moreover, the parties also consider the individual optimal solutions as private. In this setting, the concern for the parties is the privacy of their data and their optimal allocations. We propose a two-step approach to meet the privacy requirements of the parties. In the first step, we obtain a reformulated model that is amenable to a decomposition scheme. Although this scheme eliminates almost all data exchanges, it does not provide a formal privacy guarantee. In the second step, we provide this guarantee with a locally differentially private algorithm, which does not need a trusted aggregator, at the expense of deviating slightly from the optimality. We provide bounds on this deviation and discuss the consequences of these theoretical results. We also propose a novel modification to increase the efficiency of the algorithm in terms of reducing the theoretical optimality gap. The study ends with a numerical experiment on a planning problem that demonstrates an application of the proposed approach. As we work with a general linear optimization model, our analysis and discussion can be used in different application areas including production planning, logistics, and revenue management.

Recent work has shown a variety of ways in which machine learning can be used to accelerate the solution of constrained optimization problems. Increasing demand for real-time decision-making capabilities in applications such as artificial intelligence and optimal control has led to a variety of approaches, based on distinct strategies. This work proposes a novel approach to learning optimization, in which the underlying metric space of a proximal operator splitting algorithm is learned so as to maximize its convergence rate. While prior works in optimization theory have derived optimal metrics for limited classes of problems, the results do not extend to many practical problem forms including general Quadratic Programming (QP). This paper shows how differentiable optimization can enable the end-to-end learning of proximal metrics, enhancing the convergence of proximal algorithms for QP problems beyond what is possible based on known theory. Additionally, the results illustrate a strong connection between the learned proximal metrics and active constraints at the optima, leading to an interpretation in which the learning of proximal metrics can be viewed as a form of active set learning.

Problem definition: The recent advent of data-driven and end-to-end decision-making across different areas of operations management has led to an ever closer integration of prediction models from machine learning and optimization models from operations research. A key challenge in this context is the presence of estimation errors in the prediction models, which tend to be amplified by the subsequent optimization model -- a phenomenon that is often referred to as the Optimizer's Curse or the Error-Maximization Effect of Optimization.
Methodology/results: A contemporary approach to combat such estimation errors is offered by distributionally robust problem formulations that consider all data-generating distributions close to the empirical distribution derived from historical samples, where `closeness' is determined by the Wasserstein distance. While those techniques show significant promise in problems where all input features are continuous, they scale exponentially when binary and/or categorical features are present. In this talk, we demonstrate that such mixed-feature problems can indeed be solved in polynomial time. We present a practically efficient algorithm to solve mixed-feature problems, and we compare our method against alternative techniques both theoretically and empirically on standard benchmark instances.
Managerial implications: Data-driven operations management problems often involve prediction models with discrete features. We develop and analyze a methodology that faithfully accounts for the presence of discrete features, and we demonstrate that our approach can significantly outperform existing methods that are agnostic to the presence of discrete features, both theoretically and across standard benchmark instances.