NeurIPS 2026

Temporal Gradient Inversion for Private Trajectory Reconstruction in Embodied Reinforcement Learning

Sudip Bhujel¹, Shanghao Shi², Ruiquan Huang¹, Ning Zhang², Yang Xiao¹

¹University of Kentucky²Washington University in St. Louis

Abstract

Distributed learning in embodied reinforcement-learning agents offers a degree of privacy by retaining raw sensor data on-device and transmitting only policy gradients to the server. Yet temporal structure can amplify this leakage beyond single-frame attacks. We introduce Temporal Reconstruction Attack on Consecutive Encodings (TRACE), an amortized temporal gradient-inversion attack that autoregressively reconstructs the sequence of private observation-action trajectories from per-step policy-learning gradients.

The attack exploits two structural signals ignored by prior single-frame methods: (i) cross-time correlation between successive embodied gradients, which we formalize via a conditional mutual-information bound, and (ii) closed-form action recovery from policy-head gradient structure, which we prove exact when standard entropy regularization is sufficiently small. On held-out embodied scenes, TRACE reaches 18.8 dB PSNR with near-perfect action recovery at 3–4.5 ms per reconstructed frame, dominating the learning-based baseline across all reconstruction metrics and exceeding optimization attacks while running orders of magnitude faster. Further evaluation demonstrates TRACE's broader applicability across recurrent, residual, and compact transformer victim architectures, multi-modal inputs, and larger discrete action spaces. Defense experiments suggest that protecting temporal gradient streams may require sequence-aware privacy mechanisms.

Trajectory leakage

An embodied agent shares per-step policy gradients with a server; TRACE inverts the gradient stream back into the private observation-action trajectory. — Per-step policy gradients are not a private channel. Consecutive gradients are correlated in time, and TRACE turns that correlation into a full reconstruction of what the agent saw and did.

At a glance

Amortized and autoregressive: A trained inverter conditions on the previous reconstruction and the current gradient to emit the next observation and action. No per-sample optimization, so a frame takes milliseconds rather than minutes.
Two structural signals: Cross-time correlation between successive gradients, bounded via conditional mutual information, and closed-form action recovery from the policy head, proven exact when entropy regularization is small.
Beyond the base setting: Holds up across recurrent, residual, and compact transformer victims, multi-modal inputs, larger discrete action spaces, and aggregated gradients.
What it means for defenses: Per-step perturbation is not enough. Protecting a gradient stream calls for sequence-aware privacy mechanisms.

Attack pipeline

TRACE pipeline: a gradient encoder compresses each gradient to a latent, an image encoder embeds prior observations, a causal temporal transformer contextualizes the interleaved sequence, and a residual decoder reconstructs the observation and predicts the action. — Gradient encoder, image encoder, causal temporal transformer, and a residual decoder that reconstructs the observation and predicts the action at every step.

Citation

@misc{bhujel2026trace,
  title         = {Temporal Gradient Inversion for Private Trajectory Reconstruction in Embodied Reinforcement Learning},
  author        = {Sudip Bhujel and Shanghao Shi and Ruiquan Huang and Ning Zhang and Yang Xiao},
  year          = {2026},
  eprint        = {2609.30258},
  archivePrefix = {arXiv},
  primaryClass  = {cs.LG},
  url           = {https://arxiv.org/abs/2609.30258}
}