Length-Aware Adversarial Training for Variable-Length Trajectories: Digital Twins for Mall Shopper Paths
This addresses a practical issue in simulation and counterfactual analysis for domain-specific applications like shopper paths, but it is incremental as it modifies batching without changing the model class.
The paper tackles the problem of unstable training in generative modeling of variable-length trajectories due to heterogeneous lengths, proposing length-aware sampling (LAS) to improve distribution matching. The result shows consistent improvements in matching derived-variable distributions across multiple datasets, outperforming random sampling.
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.