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PateGail: A Privacy-Preserving Mobility Trajectory Generator with Imitation Learning

Huandong Wang, Changzheng Gao, Yuchen Wu, Depeng Jin, Lina Yao, Yong Li

TL;DR

PateGail tackles the privacy risks of collecting real mobility trajectories by proposing a privacy-preserving imitation-learning framework that trains a mobility trajectory generator on decentralized device data. It leverages generative adversarial imitation learning (GAIL) with per-user discriminators and a private aggregation mechanism inspired by PATE to produce a DP-protected reward signal, guiding a global transformer-based policy to generate realistic trajectories. The approach introduces a reward dynamics compensation to stabilize learning across heterogeneous users and provides theoretical guarantees that the aggregated rewards maximize a lower bound on the discounted returns. Empirically, PateGail achieves close alignment with real trajectories across multiple statistics, outperforms state-of-the-art baselines, and demonstrates practical utility in mobility prediction and location recommendation, while offering DP guarantees and publicly releasing code and data.

Abstract

Generating human mobility trajectories is of great importance to solve the lack of large-scale trajectory data in numerous applications, which is caused by privacy concerns. However, existing mobility trajectory generation methods still require real-world human trajectories centrally collected as the training data, where there exists an inescapable risk of privacy leakage. To overcome this limitation, in this paper, we propose PateGail, a privacy-preserving imitation learning model to generate mobility trajectories, which utilizes the powerful generative adversary imitation learning model to simulate the decision-making process of humans. Further, in order to protect user privacy, we train this model collectively based on decentralized mobility data stored in user devices, where personal discriminators are trained locally to distinguish and reward the real and generated human trajectories. In the training process, only the generated trajectories and their rewards obtained based on personal discriminators are shared between the server and devices, whose privacy is further preserved by our proposed perturbation mechanisms with theoretical proof to satisfy differential privacy. Further, to better model the human decision-making process, we propose a novel aggregation mechanism of the rewards obtained from personal discriminators. We theoretically prove that under the reward obtained based on the aggregation mechanism, our proposed model maximizes the lower bound of the discounted total rewards of users. Extensive experiments show that the trajectories generated by our model are able to resemble real-world trajectories in terms of five key statistical metrics, outperforming state-of-the-art algorithms by over 48.03%. Furthermore, we demonstrate that the synthetic trajectories are able to efficiently support practical applications, including mobility prediction and location recommendation.

PateGail: A Privacy-Preserving Mobility Trajectory Generator with Imitation Learning

TL;DR

PateGail tackles the privacy risks of collecting real mobility trajectories by proposing a privacy-preserving imitation-learning framework that trains a mobility trajectory generator on decentralized device data. It leverages generative adversarial imitation learning (GAIL) with per-user discriminators and a private aggregation mechanism inspired by PATE to produce a DP-protected reward signal, guiding a global transformer-based policy to generate realistic trajectories. The approach introduces a reward dynamics compensation to stabilize learning across heterogeneous users and provides theoretical guarantees that the aggregated rewards maximize a lower bound on the discounted returns. Empirically, PateGail achieves close alignment with real trajectories across multiple statistics, outperforms state-of-the-art baselines, and demonstrates practical utility in mobility prediction and location recommendation, while offering DP guarantees and publicly releasing code and data.

Abstract

Generating human mobility trajectories is of great importance to solve the lack of large-scale trajectory data in numerous applications, which is caused by privacy concerns. However, existing mobility trajectory generation methods still require real-world human trajectories centrally collected as the training data, where there exists an inescapable risk of privacy leakage. To overcome this limitation, in this paper, we propose PateGail, a privacy-preserving imitation learning model to generate mobility trajectories, which utilizes the powerful generative adversary imitation learning model to simulate the decision-making process of humans. Further, in order to protect user privacy, we train this model collectively based on decentralized mobility data stored in user devices, where personal discriminators are trained locally to distinguish and reward the real and generated human trajectories. In the training process, only the generated trajectories and their rewards obtained based on personal discriminators are shared between the server and devices, whose privacy is further preserved by our proposed perturbation mechanisms with theoretical proof to satisfy differential privacy. Further, to better model the human decision-making process, we propose a novel aggregation mechanism of the rewards obtained from personal discriminators. We theoretically prove that under the reward obtained based on the aggregation mechanism, our proposed model maximizes the lower bound of the discounted total rewards of users. Extensive experiments show that the trajectories generated by our model are able to resemble real-world trajectories in terms of five key statistical metrics, outperforming state-of-the-art algorithms by over 48.03%. Furthermore, we demonstrate that the synthetic trajectories are able to efficiently support practical applications, including mobility prediction and location recommendation.
Paper Structure (21 sections, 7 theorems, 12 equations, 7 figures, 2 tables)

This paper contains 21 sections, 7 theorems, 12 equations, 7 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Mathematical Model and System Overview
  3. Mathematical Model
  4. System Overview
  5. Method
  6. Policy Function
  7. Reward Function
  8. Model Training
  9. Privacy Analysis
  10. Experiments
  11. Datasets
  12. Experimental Settings
  13. Statistical Evaluation Results
  14. Practical Demonstrations
  15. Privacy Risk Analysis
  16. ...and 6 more sections

Key Result

Theorem 1

Denote the discounted total reward based on the policy function $\pi$ and reward function $R$ as $\boldsymbol{J}(\pi,R)=\sum_{i}\gamma^{i}R(s_i,a_i)$, where $a_i\sim\pi(\cdot|s_i)$ and $s_{i+1}\sim P(\cdot|s_i,a_i)$. Let $R_u$ denote the personal reward function of user $u$, i.e., $R_u=D_{\phi_u}$.

Figures (7)

  • Figure 1: Illustration of (a) existing trajectory generator and our proposed (b) federated trajectory generator.
  • Figure 2: The framework of our system.
  • Figure 3: Visualization of the distribution of the selected statistical metrics on the ISP dataset.
  • Figure 4: Performance of the individual mobility prediction based on trajectory data augmented by different models.
  • Figure 5: Location recommendation on different datasets.
  • ...and 2 more figures

Theorems & Definitions (9)

  • Definition 1: Privacy-Preserving Federated Mobility Trajectory Generation Problem
  • Theorem 1
  • Definition 2: $(\epsilon,\delta)$-differential privacy
  • Theorem 2
  • Theorem 3
  • Theorem 1
  • Theorem 2
  • Lemma 1: Composition Theorem for Differential Privacy
  • Theorem 3