发表机构
Army Engineering University of PLA (Shijiazhuang Campus)（中国人民解放军陆军工程大学（石家庄校区））
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出拓扑必然性作为跨具身子目标，通过同调从轨迹提取不可跳过阶段，无需重训即可迁移至新执行器，显著提升多路线任务性能。
AI 中文摘要
长视野目标条件强化学习将控制委托给一个高层模块，该模块提出子目标，但现有的子目标是价值函数或潜在动作的隐式副产品，与产生它们的执行器绑定。我们研究了一个不同的对象：一个由路线条件化的、每个成功执行器都必须经过的不可避免阶段的有序序列，它可以从离线轨迹中恢复，且不属于任何特定执行器。其定义属性是拓扑性的：一个不可跳过的阶段是一个分离集，任何可容许路径都必须穿过它；自由空间中的环强制进行路线选择。我们通过同调在维度0和1上，从成功轨迹构建的传输加权载体中读取这两点，产生一个具有壳级证书的可枚举门集；这些经过认证的门就是我们所说的拓扑必然性。经过认证的门以递归拓扑门层次结构进入决策循环。在固定、同构的自由空间下，该对象在执行器替换后依然存在：在PointMaze数据上冻结的门无需重新训练即可迁移到Ant和Humanoid，在统一接口下达到最高的Humanoid总分（96.1），在多路线任务上比具有地图特权的参考高出+36.0（p=1.4e-5）；该规划器在PointMaze上达到饱和（100±0），并在AntMaze（giant +22.9）和Kitchen（+15.8/+12.6）上匹配或超过最强基线。
英文摘要
Long-horizon goal-conditioned reinforcement learning delegates control to a high-level module that proposes subgoals, but existing subgoals are implicit byproducts of value functions or latent actions, tied to the executor that produced them. We study a different object: a route-conditioned order of unavoidable stages that every successful executor must traverse, recoverable from offline trajectories and belonging to none of them. Its defining properties are topological: an unskippable stage is a separating set that every admissible path must cross, and a loop in free space forces a route choice. We read the two by homology in dimensions 0 and 1 over a transport-weighted carrier built from successful trajectories, yielding an enumerable gate set with shell-level certificates; the certified gates are what we call topological necessities. Certified gates enter the decision loop as a recursive topological gate hierarchy. Under a fixed, isomorphic free space, the object survives executor replacement: gates frozen on PointMaze data transfer without retraining to Ant and Humanoid, attaining the highest Humanoid aggregate under a unified interface (96.1), with +36.0 over a map-privileged reference on the multi-route task (p=1.4e-5); the planner saturates PointMaze (100+/-0) and matches or exceeds the strongest baselines on AntMaze (giant +22.9) and Kitchen (+15.8/+12.6).
Comments60 pages total (9-page main text + appendices), 16 figures. Code and data: https://osf.io/wak7u/overview?view_only=70a3d17f63114468a43b2d7a918e47db
