Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

End-to-End Learning for Fair Multiobjective Optimization Under Uncertainty

My H Dinh, James Kotary, Ferdinando Fioretto

TL;DR

The paper addresses end-to-end learning for decision problems where the objective is a nondifferentiable OWA, enabling fair and robust optimization under uncertainty. It develops differentiable OWA approximations (OWA-LP with Quadratic Smoothing and Moreau Envelope smoothing), nonparametric blackbox SPO+-style differentiation, and surrogate optimization mappings to enable gradient-based training. The experiments on robust portfolio optimization, multi-species Warcraft shortest path, and fair learning-to-rank demonstrate improved decision quality and fairness, with favorable scalability and runtime characteristics for the proposed methods. Overall, the work advances practical end-to-end learning for fair multiobjective optimization under uncertainty by bridging nondifferentiable OWA optimization with gradient-based training techniques.

Abstract

Many decision processes in artificial intelligence and operations research are modeled by parametric optimization problems whose defining parameters are unknown and must be inferred from observable data. The Predict-Then-Optimize (PtO) paradigm in machine learning aims to maximize downstream decision quality by training the parametric inference model end-to-end with the subsequent constrained optimization. This requires backpropagation through the optimization problem using approximation techniques specific to the problem's form, especially for nondifferentiable linear and mixed-integer programs. This paper extends the PtO methodology to optimization problems with nondifferentiable Ordered Weighted Averaging (OWA) objectives, known for their ability to ensure properties of fairness and robustness in decision models. Through a collection of training techniques and proposed application settings, it shows how optimization of OWA functions can be effectively integrated with parametric prediction for fair and robust optimization under uncertainty.

End-to-End Learning for Fair Multiobjective Optimization Under Uncertainty

TL;DR

The paper addresses end-to-end learning for decision problems where the objective is a nondifferentiable OWA, enabling fair and robust optimization under uncertainty. It develops differentiable OWA approximations (OWA-LP with Quadratic Smoothing and Moreau Envelope smoothing), nonparametric blackbox SPO+-style differentiation, and surrogate optimization mappings to enable gradient-based training. The experiments on robust portfolio optimization, multi-species Warcraft shortest path, and fair learning-to-rank demonstrate improved decision quality and fairness, with favorable scalability and runtime characteristics for the proposed methods. Overall, the work advances practical end-to-end learning for fair multiobjective optimization under uncertainty by bridging nondifferentiable OWA optimization with gradient-based training techniques.

Abstract

Many decision processes in artificial intelligence and operations research are modeled by parametric optimization problems whose defining parameters are unknown and must be inferred from observable data. The Predict-Then-Optimize (PtO) paradigm in machine learning aims to maximize downstream decision quality by training the parametric inference model end-to-end with the subsequent constrained optimization. This requires backpropagation through the optimization problem using approximation techniques specific to the problem's form, especially for nondifferentiable linear and mixed-integer programs. This paper extends the PtO methodology to optimization problems with nondifferentiable Ordered Weighted Averaging (OWA) objectives, known for their ability to ensure properties of fairness and robustness in decision models. Through a collection of training techniques and proposed application settings, it shows how optimization of OWA functions can be effectively integrated with parametric prediction for fair and robust optimization under uncertainty.
Paper Structure (37 sections, 33 equations, 10 figures, 3 tables, 1 algorithm)

This paper contains 37 sections, 33 equations, 10 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. OWA and its Optimization
  4. Predict-Then-Optimize Learning
  5. End-to-End Learning with Fair OWA Optimization
  6. Differentiable Approximate OWA Optimization
  7. OWA LP with Quadratic Smoothing
  8. Moreau Envelope Smoothing
  9. Blackbox Methods for Nonparametric OWA Objective
  10. Differentiable Surrogate Optimization Mappings
  11. Experiments
  12. Fair Multiobjective Predict-and-Optimize
  13. Evaluation.
  14. Baseline Models.
  15. Differentiable OWA Optimization: Robust Markowitz Portfolio Problem
  16. ...and 22 more sections

Figures (10)

  • Figure 1: Predict-Then-Optimize for OWA Optimization.
  • Figure 2: Percentage OWA regret (lower is better) on test set, on robust portfolio problem over $3$,$5$,$7$ scenarios.
  • Figure 3: Multi-species OWA path length regret on WSP.
  • Figure 4: Fairness-utility tradeoffs on MSLR. Left: binary group case, right: multi-group case
  • Figure 5: Average solving time of 2 smoothed OWA optimization models, on Robust Portfolio Optimization, over $1000$ input samples. Missing datapoints past $7$ scenarios are due to memory overflow as the QP model grows factorially.
  • ...and 5 more figures