# 一种面向运动学习的基于 Zonotope 的 Soft Actor-Critic 几何方法

> 原文链接：https://robotics.hellobike.com/papers/2026-10-08-2610-12113
> 频道：papers | 更新日期：2026-10-08 | 标签：arxiv, cs.RO
> 核心摘要：GeZo-SAC通过critic侧Zonotope几何宽度与分歧自适应悲观性，并在四个MuJoCo-v5运动基准上验证。

# 一种面向运动学习的基于 Zonotope 的 Soft Actor-Critic 几何方法

::: v-pre
> 原文链接：[A Geometric Approach to Soft Actor-Critic with Zonotopes for Locomotion Learning](https://arxiv.org/abs/2610.12113)（arXiv 2610.12113 · 发布日期：2026-10-08）

**A Geometric Approach to Soft Actor-Critic with Zonotopes for Locomotion Learning**

GeZo-SAC通过critic侧Zonotope几何宽度与分歧自适应悲观性，并在四个MuJoCo-v5运动基准上验证。

## 核心要点

- 现有离策略actor-critic统一取双critic最小值，未区分critic分歧情形。
- 每个critic同时预测标量值和Zonotope生成元，用采样方向探测几何宽度。
- 几何宽度作为悲观偏移，分歧经log-sum-exp聚合并调节critic组合方式。
- 在四个MuJoCo-v5任务对比六种基线，Ant/Hopper回报最高且动作努力较低。

**验证范围与局限**：验证范围为四个MuJoCo-v5运动仿真基准，摘要未提及真机实验。

## 英文摘要 (Abstract)

Off-policy actor--critic methods control overestimation bias by taking the minimum of two critics. This uses the same aggregation rule everywhere, regardless of how the critics disagree. We propose \textbf{GeZo-SAC}, which uses auxiliary geometric representations to adapt critic pessimism to the state and action. Alongside its scalar value, each critic predicts a set of generators defining a zonotope. Probing this zonotope along sampled directions provides a geometric width, "subtracted from each critic value as a pessimistic offset, and a measure of disagreement between the two critics, aggregated with log-sum-exp. This disagreement controls how the critics are combined, moving from a width-weighted average toward the usual minimum as disagreement increases. At inference, the deployed policy is an unmodified SAC actor, since the generators are used only on the critic side during training.Across four MuJoCo-v5 locomotion benchmarks and six off-policy baselines, GeZo-SAC achieves the highest mean return on Ant-v5 and Hopper-v5 and remains competitive with other methods on the remaining tasks. Our analysis further shows that GeZo-SAC achieves the lowest average actuator work and action effort per metre among the evaluated methods, while maintaining near-zero measured overestimation frequency across all four environments.

作者：Panagiotis Roditis, Panagiotis Paraskevas Filntisis, Petros Maragos
:::

## 原始参考来源 (Sources)

- [arXiv 2610.12113：A Geometric Approach to Soft Actor-Critic with Zonotopes for Locomotion Learning](https://arxiv.org/abs/2610.12113)