Driving · 2026-10-09

Residual Modeling Closes the Regression and Generative Policy Gap in Robot Learning

Yuchen Zhou, Jiacheng You, Weikang Wan, Weijun Dong, Yang Gao, Jiayuan Mao

AI-assisted summary based on the paper. Consult the linked source for methods and limitations. Benchmark numbers appear after editor verification.

TL;DR

The authors analyze why action regression (MSE-Policies) underperforms generative policies in robot imitation: demonstration action residuals are input-dependent and heavy-tailed, and MSE gradients concentrate on large-residual samples. They propose HT-Policies, which use heteroscedastic Student-t residual modeling with learned input-dependent scales and single-pass inference. Across simulations and real robots, HT-Policies are competitive with generative baselines and faster in training/inference.

Why it matters

The paper gives a statistical explanation for the “regression vs generative” gap in robot learning from demonstrations, linking residual distribution mismatch to optimization behavior. It introduces an efficient direct-regression alternative (HT-Policies) that explicitly models input-dependent scales and heavy tails, and can reuse pretrained flow-matching backbones, aiming for competitive success with better efficiency.

Method

Analyze action-prediction residuals and gradients for MSE-Policies vs flow-matching/diffusion policies, showing heavy-tailed residuals and different gradient concentration patterns.
Introduce HT-Policies: heteroscedastic Student-t action regression with learned input-dependent residual scales; predict action chunks in a single feed-forward pass.
Reuse pretrained flow-matching networks by setting the action input to zero and timestep to the pure-noise endpoint, adding a scale prediction head and fine-tuning with the HT loss.

Abstract (from arXiv)

Learning from demonstration has enabled impressive robot behaviors. A common choice for policy learning is to use diffusion or flow matching (Flow-Policies), which often outperforms direct action regression trained with mean squared error (MSE-Policies). This gap is commonly attributed to multimodal demonstrations. We revisit this gap from the perspective of statistical modeling: how action-prediction residuals shape policy optimization. Our analysis of real-world robot demonstration data reveals substantial state-dependent variation in residual scales and heavier-than-Gaussian tails. While both MSE-Policies and Flow-Policies exhibit heavy-tailed action residuals, their training gradients behave differently: MSE allocates more gradient magnitude to observations with large action residuals, which hurts optimization. Motivated by these findings, we introduce heteroscedastic Student-t action regression (HT-Policies), which learns input-dependent residual scales and reduces the influence of heavy tails. HT-Policies predict action chunks with a single feed-forward pass and can reuse pretrained flow-matching-based policy networks as the backbone. Across four simulation benchmarks and real-robot evaluations, HT-Policies achieves success rates competitive with generative policy baselines, both when trained from scratch and from pretrained vision-language-action and world-action models, despite being faster in training and inference. Together, these findings shed light on the practical advantages of generative objectives in robot learning from demonstrations and offer an efficient direct-regression alternative for a range of architectures and tasks. Project page: https://the-labone.github.io/regression-policy-project/

Publication record

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First public release: 2026-10-08 · Indexed by Pub-AI: 2026-10-09 UTC

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