外观
论文arXiv 2610.2301012 天前
什么构成混合离散-连续规划的好符号？
原文链接：What Makes a Good Symbol for Hybrid Discrete-Continuous Planning?（arXiv 2610.23010 · 发布日期：2026-10-16）
What Makes a Good Symbol for Hybrid Discrete-Continuous Planning?
本文从推理算法视角定义有用符号，并在仿真与真实机器人任务中验证其可降低求解成本且保持解质量。
核心要点
- 问题动机：现有方法多依赖人工定义符号或语言监督符号，缺少对符号计算有用性的追问。
- 方法：提出 solver-sufficient symbolization，并为有限时域分段仿射系统设计反例引导的符号发明算法。
- 扩展：将原则用于由一般神经网络能量函数参数化的优化目标，从连续优化景观中诱导符号。
- 实验结果：在仿真和真实机器人任务中，所得符号降低求解成本、保持解质量，并提升可解释性和可操控性。
验证范围与局限：验证范围为仿真和真实机器人任务，摘要未说明具体任务类型或机器人数量。
英文摘要 (Abstract)
The physical world has continuous state and action spaces, yet robot planning often benefits from hybrid discrete-continuous formulations that explicitly expose combinatorial structure, such as contact modes or discrete primitive actions. Existing methods typically rely on human-defined symbol sets or symbols derived from language supervision, without asking what makes a symbol computationally useful. In this paper, we take an inference-algorithm--centric view to define usefulness: a good symbol should expose the discrete commitments that simplify solving the original planning problem. We first introduce the concept of solver-sufficient symbolization by studying finite-horizon piecewise-affine systems, for which solver sufficiency can be precisely characterized, and develop a counterexample-guided algorithm for symbol invention. We then extend this principle to invent symbols for optimization objectives parameterized by general neural networks as energy functions, showing that solver-sufficient symbols can nevertheless be induced from their continuous optimization landscapes. Experiments on simulated and real-robot tasks show that the resulting symbols reduce solving cost while preserving solution quality, while also improving interpretability and steerability. Furthermore, our theoretical and algorithmic insights help explain why certain human-defined symbols are computationally useful.
作者：Yiyuan Pan, Changliu Liu, Jiayuan Mao
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