Differentiation of Multi-objective Data-driven Decision Pipeline

TL;DR

This paper introduces a novel multi-objective decision-focused learning approach with new loss functions, significantly improving performance over traditional methods in multi-objective data-driven optimization tasks.

Contribution

It proposes a set of innovative loss functions tailored for multi-objective problems, addressing the limitations of existing single-objective focused methods.

Findings

Proposed method outperforms traditional two-stage approaches.

New loss functions effectively capture decision discrepancies.

Significant performance improvements demonstrated in experiments.

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.