Differentiation of Multi-objective Data-driven Decision Pipeline

Abstract: Real-world scenarios frequently involve multi-objective data-driven optimization problems, characterized by unknown problem coefficients and multiple conflicting objectives. Traditional two-stage methods independently apply a machine learning model to estimate problem coefficients, followed by invoking a solver to tackle the predicted optimization problem. The independent use of optimization solvers and prediction models may lead to suboptimal performance due to mismatches between their objectives. Recent efforts have focused on end-to-end training of predictive models that use decision loss derived from the downstream optimization problem. However, these methods have primarily focused on single-objective optimization problems, thus limiting their applicability. We aim to propose a multi-objective decision-focused approach to address this gap. In order to better align with the inherent properties of multi-objective optimization problems, we propose a set of novel loss functions. These loss functions are designed to capture the discrepancies between predicted and true decision problems, considering solution space, objective space, and decision quality, named landscape loss, Pareto set loss, and decision loss, respectively. Our experimental results demonstrate that our proposed method significantly outperforms traditional two-stage methods and most current decision-focused methods.