A Pareto Dominance Principle for Data-Driven Optimization

Abstract

Our paper proposes an effective way to make decisions based on data for uncertain situations. In simple terms, a data-driven decision is just a choice we make by looking at the available data. We express this choice as the best one according to a model we create from the data. The quality of this decision is judged by how well it performs in situations not seen during training. We also consider how often it disappoints in those situations. The challenge is that we do not know the exact probability of generating the data. An ideal data-driven decision should work well for any possible probability. However, such ideal decisions are usually not possible. Therefore, we look for decisions that work well on unseen data, considering the chances of disappointment. We prove that such effective decisions exist under certain conditions, allowing for practical applications. This approach holds regardless of whether the original problem is simple or complex, and it works even when the data are not uniformly collected. Our study also uncovers how the characteristics of the data-generating process influence the optimal decision-making model.