Differentiation of Multi-objective Data-driven Decision Pipeline

TL;DR

This work tackles data-driven multi-objective optimization with unknown coefficients by introducing MoDFL, a multi-objective decision-focused learning framework. MoDFL integrates three loss components—landscape loss based on $sRMMD$, Pareto set loss, and a decision loss—together with differentiable optimization mappings to enable end-to-end training. Empirical results on Web Advertisement Allocation and bipartite paper matching show MoDFL consistently outperforms two-stage methods and existing decision-focused baselines across multiple MO metrics including GD, MPFE, HAR, and average regret. The study demonstrates the value of aligning predictive models with downstream MO optimization and provides a scalable pathway for MO decision-focused learning in real-world data-driven systems.

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.

Figures (1)

• Figure 1: The pipeline of data-driven multi-objective problem