Topology-Aware State Abstraction with Tangle Cores for Markov Decision Processes
For reinforcement learning researchers, this provides a principled topology-aware abstraction method that handles overlapping regions, addressing a limitation of hard-partition approaches.
The paper introduces tangle-core abstraction, an overlapping state-abstraction framework for MDPs that uses graph tangles to represent shared interface states (e.g., doors, hubs). It provides theoretical guarantees and demonstrates favorable compression-return tradeoffs against baselines in bottlenecked domains, while also identifying a failure regime where transition topology is uninformative.
State abstraction in reinforcement learning is usually formulated as a partition of states based on reward and transition similarity. This excludes a common structural pattern in navigation, graph, and hierarchical decision problems: interface states such as doors, hubs, and bottlenecks naturally participate in more than one region. We introduce \emph{tangle-core abstraction}, an overlapping state-abstraction framework based on graph tangles of empirical transition graphs. The method constructs abstract states from consistently oriented low-order separations and represents shared interfaces through a membership kernel rather than a hard partition. We give value-preservation guarantees for the induced overlapping abstract MDP under an explicit action-consistency condition, identify an interior-homogeneity/boundary-leakage error decomposition, and prove a quantitative interface-overlap result showing when hard partitions incur an avoidable boundary error. Empirically, tangle-core abstractions achieve favorable compression--return tradeoffs against reward-aware, learned, topological-map, and graph-partitioning baselines across bottlenecked tabular domains, procedurally generated mazes, and MiniGrid representations. We also identify a clear failure regime in which transition topology is uninformative, where tangles predictably offer little benefit. These results position graph tangles as an effective topology-aware abstraction prior for decision problems with shared interface structure.