Length-Aware Adversarial Training for Variable-Length Trajectories: Digital Twins for Mall Shopper Paths

TL;DR

This paper introduces length-aware sampling for training generative models of variable-length trajectories, improving distribution matching and stability in modeling shopper paths and other sequential data.

Contribution

It proposes a simple batching strategy called length-aware sampling (LAS) that enhances training stability and distribution matching for variable-length sequence models.

Findings

LAS improves distribution matching of derived variables.

LAS outperforms random sampling on multiple datasets.

The method provides theoretical guarantees for distribution-level accuracy.

Abstract

We study generative modeling of \emph{variable-length trajectories} -- sequences of visited locations/items with associated timestamps -- for downstream simulation and counterfactual analysis. A recurring practical issue is that standard mini-batch training can be unstable when trajectory lengths are highly heterogeneous, which in turn degrades \emph{distribution matching} for trajectory-derived statistics. We propose \textbf{length-aware sampling (LAS)}, a simple batching strategy that groups trajectories by length and samples batches from a single length bucket, reducing within-batch length heterogeneity (and making updates more consistent) without changing the model class. We integrate LAS into a conditional trajectory GAN with auxiliary time-alignment losses and provide (i) a distribution-level guarantee for derived variables under mild boundedness assumptions, and (ii) an IPM/Wasserstein mechanism explaining why LAS improves distribution matching by removing length-only shortcut critics and targeting within-bucket discrepancies. Empirically, LAS consistently improves matching of derived-variable distributions on a multi-mall dataset of shopper trajectories and on diverse public sequence datasets (GPS, education, e-commerce, and movies), outperforming random sampling across dataset-specific metrics.