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Distributionally Robust Resource Allocation with Trust-aided Parametric Information Fusion

Yanru Guo, Bo Zhou, Ruiwei Jiang, Xi, Yang, Siqian Shen

TL;DR

This paper dynamically update the trust parameter to simulate the decision maker’s trust change based on losses caused by mis-specified reference information, and shows an equivalent tractable linear programming reformulation of the distributionally robust optimization model and demonstrates the performance in a wildfire suppression application.

Abstract

Reference information plays an essential role for making decisions under uncertainty, yet may vary across multiple data sources. In this paper, we study resource allocation in stochastic dynamic environments, where we perform information fusion based on trust of different data sources, to design an ambiguity set for attaining distributionally robust resource allocation solutions. We dynamically update the trust parameter to simulate the decision maker's trust change based on losses caused by mis-specified reference information. We show an equivalent tractable linear programming reformulation of the distributionally robust optimization model and demonstrate the performance in a wildfire suppression application, where we use drone and satellite data to estimate the needs of resources in different regions. We demonstrate how our methods can improve trust and decision accuracy. The computational time grows linearly in the number of data sources and problem sizes.

Distributionally Robust Resource Allocation with Trust-aided Parametric Information Fusion

TL;DR

This paper dynamically update the trust parameter to simulate the decision maker’s trust change based on losses caused by mis-specified reference information, and shows an equivalent tractable linear programming reformulation of the distributionally robust optimization model and demonstrates the performance in a wildfire suppression application.

Abstract

Reference information plays an essential role for making decisions under uncertainty, yet may vary across multiple data sources. In this paper, we study resource allocation in stochastic dynamic environments, where we perform information fusion based on trust of different data sources, to design an ambiguity set for attaining distributionally robust resource allocation solutions. We dynamically update the trust parameter to simulate the decision maker's trust change based on losses caused by mis-specified reference information. We show an equivalent tractable linear programming reformulation of the distributionally robust optimization model and demonstrate the performance in a wildfire suppression application, where we use drone and satellite data to estimate the needs of resources in different regions. We demonstrate how our methods can improve trust and decision accuracy. The computational time grows linearly in the number of data sources and problem sizes.

Paper Structure

This paper contains 16 sections, 1 theorem, 16 equations, 5 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Models and Solution Approaches
  3. Problem Description and Notation
  4. SP and DRO Models
  5. Trust-Aided Parametric Data-fusion Ambiguity Set
  6. Tractable Reformulation of the DRO Model \ref{['eq:DRO']}
  7. Trust Update and Trust Selection
  8. Parametric Data-fusion Trust Update Procedures
  9. Numerical Studies
  10. Experimental Design
  11. Trust Update and Computational Results
  12. Sensitivity Analysis
  13. Varying Budget $B$
  14. Varying Sample Size $M$
  15. Computational Scalability Analysis
  16. ...and 1 more sections

Key Result

Theorem 1

If the uncertainty set $\Xi$ is convex and closed, and the loss function is additively separable with respect to $\xi$ and $\{-\ell_{jk}\}_{j \in J}$ is proper, convex, and lower semi-continuous for all $k \in [K]$mohajerin2018data, then eq:DRO is equivalent to eq:DRO-reformulation-1.

Figures (5)

  • Figure 1: Illustration of a parametric data-fusion trust-aided ambiguity set ($\mathbb{P}$: true demand distribution; $\mathbb{P}^{m}_{s}$: predicted distribution provided by the satellite; $\mathbb{P}^{m}_{d}$: predicted distribution provided by the drone; $\mathbb{P}^{m}_{e}$: empirical distribution; $\mathcal{P}$: ambiguity set)
  • Figure 2: Illustrating parametric data-fusion trust update based on losses
  • Figure 3: Trust update process with the baseline setting
  • Figure 4: Out-of-sample performances with different approaches ($B = 1000$)
  • Figure 5: Out-of-sample performances with different approaches ($B = 400$)

Theorems & Definitions (2)

  • Theorem 1
  • proof