Precedence-Aware Resource Allocation: Extending the AUTOC Framework to Multi-Level Treatments Open Access

Abstract

Many real world decision problems require allocating limited resources across individu-

als to maximize total benefit often through interventions that vary in intensity rather than

binary treat-or-not decisions. In these settings, higher-intensity treatments can require first

treating lower levels of treatment, inducing a precedence constraint that complicates allo-

cation under a fixed budget. While the causal inference literature has largely emphasized

accurate estimation of conditional average treatment effects (CATE), recent work has shown

that estimation accuracy alone does not guarantee effective resource allocation, motivating

ranking-based evaluation frameworks. The area under the targeting operating characteristic

(AUTOC) provides an effective way to evaluate prioritization rules across budget levels, but

existing formulations are limited to binary treatments. We introduce Multi-Level AUTOC

(ML-AUTOC), which is a generalization for AUTOC designed for multi-level treatment set-

tings with precedence. We also propose precedence-aware policies for mapping true marginal

treatment effects to feasible treatment assignments under fixed budget constraints. Our re-

sults show that in the multi-level treatment setting, maximizing realized treatment effects

may require re-allocation of treatments across individuals.

Table of Contents

Chapter 1: Introduction 1

1.1 Related Work: CATE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Related Work: AUTOC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Chapter 2: Problem Formulation 6

2.1 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2 Solutions via Dynamic Programming . . . . . . . . . . . . . . . . . . . . . . 7

Chapter 3: Methods 9

3.1 Scoring Functions, Rankings, and Allocation Policies . . . . . . . . . . . . . 9

3.2 Naive Policies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.3 Flattening the Multi-Level Allocation Problem . . . . . . . . . . . . . . . . . 12

3.4 Greedy and Optimal Policies . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.5 Formalizing ML-AUTOC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Chapter 4: Research Question 19

Chapter 5: Experiments and Results 20

5.1 Datasets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

5.2 RQ1: Strictly Increasing Marginal Benefit Dataset . . . . . . . . . . . . . . . 23

5.3 RQ1: Random Marginal Benefit Dataset . . . . . . . . . . . . . . . . . . . . 24

5.4 RQ1: Strictly Decreasing Marginal Benefit Dataset . . . . . . . . . . . . . . 26

5.5 RQ1: Heterogeneous Strictly Increasing Marginal Benefit Dataset . . . . . . 28

5.6 RQ2: PAO versus IFP and PAG . . . . . . . . . . . . . . . . . . . . . . . . . 30

Chapter 6: Discussion 31

6.1 Precedence-Aware Optimal versus Precedence-Aware Greedy . . . . . . . . . 31

6.2 Computational Complexity Analysis . . . . . . . . . . . . . . . . . . . . . . 32

6.3 When Does Flexibility Matter? . . . . . . . . . . . . . . . . . . . . . . . . . 36

6.4 Non-Nested Allocations In The Clinical Setting . . . . . . . . . . . . . . . . 37

6.5 On The Use Of Non-Synthetic Data . . . . . . . . . . . . . . . . . . . . . . . 38

Chapter 7: Conclusion 39

Chapter A: Appendix 44

A.1 Heterogeneous Treatment Costs . . . . . . . . . . . . . . . . . . . . . . . . . 44

A.2 PGP, IFP, LFP, and PAG Code Implementation . . . . . . . . . . . . . . . . 48

A.3 Dynamic Programming for PAO Implementation . . . . . . . . . . . . . . . . 50

A.4 Dataset Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

Chapter B: 56

B.1 Run Time Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

B.2 Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

About this Honors Thesis

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School	Emory College
Department	Computer Science
Degree	B.S.
Submission	Honors Thesis
Language	English
Research Field	Computer Science
Keyword	Optimization Greedy algorithms Resource Allocation Operations Research Dynamic Programming
Committee Chair / Thesis Advisor	Shengpu Tang, Emory University
Committee Members	Michelangelo Grigni, Emory University Ruoxuan Xiong, Emory University

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