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Machine Learning-Powered Course Allocation

Ermis Soumalias, Behnoosh Zamanlooy, Jakob Weissteiner, Sven Seuken

TL;DR

This work tackles the course allocation problem under indivisible seats without money by improving the prevailing CM mechanism with ML-powered preference elicitation (MLCM). Each student maintains a per-user MVNN utility model trained on initial GUI reports and optionally refined via online pairwise comparisons (CQs) generated by OBIS, allowing rapid, personalized corrections to reporting mistakes. The approach preserves CM's structure while enabling significant welfare gains: simulations show average utility gains of 7-11% and minimum utility gains of 17-29% with as few as 10 CQs, and results are robust to environment shifts and user behavior. Practically, MLCM supports optional participation, scales to many courses, and offers a compatible variant (MLCM-Projected) for easy piloting alongside existing CM deployments, suggesting a feasible path to higher efficiency and fairness in real-world course allocations.

Abstract

We study the course allocation problem, where universities assign course schedules to students. The current state-of-the-art mechanism, Course Match, has one major shortcoming: students make significant mistakes when reporting their preferences, which negatively affects welfare and fairness. To address this issue, we introduce a new mechanism, Machine Learning-powered Course Match (MLCM). At the core of MLCM is a machine learning-powered preference elicitation module that iteratively asks personalized pairwise comparison queries to alleviate students' reporting mistakes. Extensive computational experiments, grounded in real-world data, demonstrate that MLCM, with only ten comparison queries, significantly increases both average and minimum student utility by 7%-11% and 17%-29%, respectively. Finally, we highlight MLCM's robustness to changes in the environment and show how our design minimizes the risk of upgrading to MLCM while making the upgrade process simple for universities and seamless for their students.

Machine Learning-Powered Course Allocation

TL;DR

This work tackles the course allocation problem under indivisible seats without money by improving the prevailing CM mechanism with ML-powered preference elicitation (MLCM). Each student maintains a per-user MVNN utility model trained on initial GUI reports and optionally refined via online pairwise comparisons (CQs) generated by OBIS, allowing rapid, personalized corrections to reporting mistakes. The approach preserves CM's structure while enabling significant welfare gains: simulations show average utility gains of 7-11% and minimum utility gains of 17-29% with as few as 10 CQs, and results are robust to environment shifts and user behavior. Practically, MLCM supports optional participation, scales to many courses, and offers a compatible variant (MLCM-Projected) for easy piloting alongside existing CM deployments, suggesting a feasible path to higher efficiency and fairness in real-world course allocations.

Abstract

We study the course allocation problem, where universities assign course schedules to students. The current state-of-the-art mechanism, Course Match, has one major shortcoming: students make significant mistakes when reporting their preferences, which negatively affects welfare and fairness. To address this issue, we introduce a new mechanism, Machine Learning-powered Course Match (MLCM). At the core of MLCM is a machine learning-powered preference elicitation module that iteratively asks personalized pairwise comparison queries to alleviate students' reporting mistakes. Extensive computational experiments, grounded in real-world data, demonstrate that MLCM, with only ten comparison queries, significantly increases both average and minimum student utility by 7%-11% and 17%-29%, respectively. Finally, we highlight MLCM's robustness to changes in the environment and show how our design minimizes the risk of upgrading to MLCM while making the upgrade process simple for universities and seamless for their students.
Paper Structure (79 sections, 4 theorems, 17 equations, 28 figures, 38 tables, 4 algorithms)

This paper contains 79 sections, 4 theorems, 17 equations, 28 figures, 38 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Course Match
  3. Preference Elicitation Shortcomings of Course Match
  4. Machine Learning-powered Preference Elicitation
  5. Overview of Contributions
  6. Related Work
  7. Course Allocation
  8. Machine Learning-based Preference Elicitation
  9. Preliminaries
  10. Formal Model
  11. Approximate Competitive Equilibrium from Equal Incomes (A-CEEI)
  12. Course Match (CM)
  13. Stage 1:
  14. Stage 2:
  15. Stage 3:
  16. ...and 64 more sections

Key Result

Proposition 1

Let $l$ be the current length of the student's sorted list of schedules $S$ at the start of an iteration of binary insertion sort. Then, in the worst case, the average number of additional schedule pairs for which the student's preference relation can be inferred is $\frac{l}{ \lceil \log_2 (l + 1)

Figures (28)

  • Figure 1: Schematic overview of CM and MLCM
  • Figure 2: A latent space with 30 courses.
  • Figure 3: CM language reporting mistakes robustness experiment for a supply ratio of 1.25 and 9 popular courses. Shown are average results in % over 100 runs including 95% CI.
  • Figure 4: Comparison of different query generation algorithms with respect to the ordinal dataset size they induce and how often the students' answers agree with the ML predictions for the generated CQs. Shown are averages over 300 students.
  • Figure 5: MIP solution time as a function of the number of courses. Shown are averages over 100 students and 20 price vectors and 95% CIs.
  • ...and 23 more figures

Theorems & Definitions (14)

  • Proposition 1
  • Example 1: Correcting reporting mistakes
  • Remark 1
  • Remark EC.1
  • Lemma EC.1
  • Example EC.1: Inferring Missing Base Values
  • Definition EC.1: $\varepsilon$-approximation of a utility function
  • Definition EC.2: Envy $\varepsilon$-bounded by a single good
  • Definition EC.3: $l$-maximin share, budish2011aceei
  • Definition EC.4: $(l,\varepsilon)$-maximin share
  • ...and 4 more