Driving · 2026-10-09
Higher-Order Action Supervision Makes A Strong Policy Class
Peng Cheng, Yunxian Hou, Zhi Zhou, Qian Zhang, Chang Huang, Xianyuan Zhan
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 argue control instability and poor robustness in offline learning come from supervising only 0th-order actions (action labels) and ignoring higher-order action dynamics/temporal consistency. They propose a plug-and-play loss that adds first-order (time-derivative) action supervision to off-the-shelf policy models (deterministic, stochastic, or flow) without structural changes, with theoretical guarantees (IL) and improved performance/robustness on OGBench and D4RL.
Why it matters
If learned policies produce noisy, temporally inconsistent actions, real-world systems can experience instability, jitter, and increased mechanical wear. The paper proposes a way to enforce first-order temporal consistency directly on the original policy model, aiming to improve control robustness and out-of-distribution generalization in low-data offline regimes.
Method
- Propose simultaneous 0th- and 1st-order action supervision by leveraging the time-derivative property of the policy model: π̇(s)=∇sπ(s)⋅ṡ.
- Provide practical loss instantiations for deterministic, stochastic, and generative flow-matching policies, each regressing a derived policy derivative signal to dataset-derived action derivatives.
- Use the resulting enhanced policy class as a lightweight plug-and-play module compatible with offline RL frameworks; supported by theoretical error bounds for imitation learning under assumptions.
Abstract (from arXiv)
Modern data-driven decision-making methods, such as imitation learning (IL) and reinforcement learning (RL), have achieved great success in solving many complex tasks. However, these methods often suffer from serious control instability and robustness issues when applied in real-world applications such as robotics and autonomous driving, posing notable challenges for their practical deployment. We argue that this instability issue stems largely from their limitations in solely supervising and optimizing zeroth-order actions (i.e., the action labels), failing to account for higher-order action dynamics and temporal consistency. In this paper, we show that simultaneously supervising both zeroth- and first-order actions can dramatically enhance policies' performance and control robustness. To achieve this, we introduce a novel and elegant loss scheme supported by formal theoretical guarantees that can equip any off-the-shelf policy model (e.g., deterministic, stochastic, or flow policies) with the capability for higher-order action supervision, without requiring any structural modifications. Moreover, our proposed method can serve as a lightweight plug-and-play module that seamlessly integrates with a broad spectrum of existing offline RL frameworks. Extensive evaluations on OGBench and D4RL demonstrate that our approach yields substantial performance and robustness improvements across a wide range of continuous control environments. Notably, our method can also enhance policies' out-of-distribution (OOD) generalization capability in the challenging low-data regime, making it an ideal tool in tackling many real-world control problems.
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Publication record
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First public release: 2026-10-08 · Indexed by Pub-AI: 2026-10-09 UTC
Higher-Order Action Supervision Makes A Strong Policy Class
Preprint posted: 2026-10-08 · Original record ↗
- arxiv
- 2610.11175
Explicit source versions (1)
- v2 · 2026-10-09
- Preprint available
Source date: 2026-10-08 · First detected: 2026-10-25 UTC · Historical baseline
Source evidence (1)
- Official evidence ↗ · atom:published (official metadata)
- Explicit source version detected · v2
Source date: 2026-10-09 · First detected: 2026-10-25 UTC · Historical baseline
Source evidence (1)
- Official evidence ↗ · atom:id explicit version (official metadata)
Abstract · arxiv
Modern data-driven decision-making methods, such as imitation learning (IL) and reinforcement learning (RL), have achieved great success in solving many complex tasks. However, these methods often suffer from serious control instability and robustness issues when applied in real-world applications such as robotics and autonomous driving, posing notable challenges for their practical deployment. We argue that this instability issue stems largely from their limitations in solely supervising and optimizing zeroth-order actions (i.e., the action labels), failing to account for higher-order action dynamics and temporal consistency. In this paper, we show that simultaneously supervising both zeroth- and first-order actions can dramatically enhance policies' performance and control robustness. To achieve this, we introduce a novel and elegant loss scheme supported by formal theoretical guarantees that can equip any off-the-shelf policy model (e.g., deterministic, stochastic, or flow policies) with the capability for higher-order action supervision, without requiring any structural modifications. Moreover, our proposed method can serve as a lightweight plug-and-play module that seamlessly integrates with a broad spectrum of existing offline RL frameworks. Extensive evaluations on OGBench and D4RL demonstrate that our approach yields substantial performance and robustness improvements across a wide range of continuous control environments. Notably, our method can also enhance policies' out-of-distribution (OOD) generalization capability in the challenging low-data regime, making it an ideal tool in tackling many real-world control problems.