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A Learning-Based Hybrid Decision Framework for Matching Systems with User Departure Detection

Ruiqi Zhou, Donghao Zhu, Houcai Shen

TL;DR

A learning-based Hybrid framework that adaptively combines immediate and delayed matching is proposed that can substantially reduce waiting times and congestion while sacrificing only a limited amount of matching efficiency.

Abstract

In matching markets such as kidney exchanges and freight exchanges, delayed matching has been shown to improve overall market efficiency. The benefits of delay are highly sensitive to participants' sojourn times and departure behavior, and delaying matches can impose significant costs, including longer waiting times and increased market congestion. These competing effects make fixed matching policies inherently inflexible in dynamic environments. We propose a learning-based Hybrid framework that adaptively combines immediate and delayed matching. The framework continuously collects data on user departures over time, estimates the underlying departure distribution via regression, and determines whether to delay matching in the subsequent period based on a decision threshold that governs the system's tolerance for matching efficiency loss. The proposed framework can substantially reduce waiting times and congestion while sacrificing only a limited amount of matching efficiency. By dynamically adjusting its matching strategy, the Hybrid framework enables system performance to flexibly interpolate between purely greedy and purely patient policies, offering a robust and adaptive alternative to static matching mechanisms.

A Learning-Based Hybrid Decision Framework for Matching Systems with User Departure Detection

TL;DR

A learning-based Hybrid framework that adaptively combines immediate and delayed matching is proposed that can substantially reduce waiting times and congestion while sacrificing only a limited amount of matching efficiency.

Abstract

In matching markets such as kidney exchanges and freight exchanges, delayed matching has been shown to improve overall market efficiency. The benefits of delay are highly sensitive to participants' sojourn times and departure behavior, and delaying matches can impose significant costs, including longer waiting times and increased market congestion. These competing effects make fixed matching policies inherently inflexible in dynamic environments. We propose a learning-based Hybrid framework that adaptively combines immediate and delayed matching. The framework continuously collects data on user departures over time, estimates the underlying departure distribution via regression, and determines whether to delay matching in the subsequent period based on a decision threshold that governs the system's tolerance for matching efficiency loss. The proposed framework can substantially reduce waiting times and congestion while sacrificing only a limited amount of matching efficiency. By dynamically adjusting its matching strategy, the Hybrid framework enables system performance to flexibly interpolate between purely greedy and purely patient policies, offering a robust and adaptive alternative to static matching mechanisms.
Paper Structure (21 sections, 2 theorems, 3 equations, 7 figures, 1 algorithm)

This paper contains 21 sections, 2 theorems, 3 equations, 7 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Framework
  4. The Operational Platform
  5. The Decision Support Analyst Module
  6. The Feedback Module
  7. Model and Methodology
  8. Matching Model Setting and Policies
  9. $\mathsf{Greedy}$ policy.
  10. $\mathsf{Patient}$ policy.
  11. $\mathsf{Hybrid}$ framework.
  12. System Performance Metrics
  13. Statistical Learning Model
  14. Policy Decision Model
  15. Heuristic Algorithm for $\mathsf{Hybrid}$
  16. ...and 6 more sections

Key Result

theorem thmcountertheorem

The following proposition rephrases Theorems 4.10 and 4.12 in baumler2022superiority using our notation. For any departure-time distribution with finite mean, the loss of any admissible policy is bounded below by an exponential rate, i.e., $\Omega(e^{-d})$. The $\mathsf{Patient}$ policy achieves los

Figures (7)

  • Figure 1: Decision framework: a kidney exchange example.
  • Figure 2: A data-driven adaptive matching system.
  • Figure 3: Heatmap of $\mathsf{Greedy}$ vs. $\mathsf{Patient}$ policy gap across Log-normal parameters ($\mu$, $\sigma$). Solid lines trace actual contours for loss tolerance threshold $\tau\in\{1\%, 10\%, 15\%\}$.; dashed lines show framework-fitted decision thresholds.
  • Figure 4: Performance of the $\mathsf{Hybrid}$ framework (under varying thresholds $\tau$) versus static policies as $d$ varies. Fixed parameters include $w=0.3$, $\lambda=100$, $T_0=50$, and $T=100$. Results are averaged over $k=10$ independent runs.
  • Figure 5: Performance of the $\mathsf{Hybrid}$ framework (under varying window sizes $w$) versus static policies as $d$ varies. Fixed parameters include $\tau=10\%$, $\lambda=100$, $T_0=50$, $T=100$, and $k=10$.
  • ...and 2 more figures

Theorems & Definitions (3)

  • definition thmcounterdefinition
  • theorem thmcountertheorem: Theoretical limits and policy behavior
  • theorem thmcountertheorem: Asymptotic waiting time of $\mathsf{Greedy}$ policy