Stochastic Reset Pathfinding: Path-Level Regret for Cascading Bandits over Graph Paths

2026-07-16

AI Summary

This work addresses the problem of path selection in a directed graph with unknown edge success probabilities, where traversal failure on any edge resets the agent to the source. The authors model this as a combinatorial cascading bandit and leverage the global reset property to prove that an optimal policy is necessarily open-loop. They propose two algorithms, PathUCB and PathTS, built upon a Log-Dijkstra framework. Introducing, for the first time, path-level regret bounds, they decompose suboptimal path regret via a path complexity measure \( C(\pi) \), yielding tighter and more informative guarantees than traditional edge-level bounds on structured graphs. Theoretical analysis establishes a regret bound for PathUCB, while experiments demonstrate that PathTS achieves superior empirical performance on quantum networks and hierarchical DAGs, though its convergence limitations are exposed under adversarial instances.

Abstract

We introduce Stochastic Reset Pathfinding (SRP), an episodic learning problem on a known directed graph with unknown stationary edge success probabilities. In each episode, the agent commits to a source-to-goal path, and any edge failure during execution resets it to the source. SRP captures settings such as entanglement distribution in quantum repeater networks, payment routing on the Lightning Network, and delivery in unreliable mesh networks. We show that the global-reset structure makes the optimal policy open-loop, placing SRP within the combinatorial cascading bandit (CCB) framework. We propose a Log-Dijkstra meta-algorithm with UCB (PathUCB) and Thompson Sampling (PathTS) instantiations. Our main technical result is a path-level regret bound for PathUCB that decomposes regret over suboptimal paths via a per-path complexity C(pi) combining each edge's prefix and suffix reliability. The bound is complementary to the edge-level CCB bound and more informative on structured graphs with polynomially many source-to-goal paths. Experiments on quantum-network, layered-DAG, grid-world, and Erdos-Renyi domains support the theory and show that PathTS typically achieves the best empirical performance among the algorithms tested. We then exhibit an adversarial instance on which PathTS fails to converge, consistent with a known exponential obstruction for combinatorial Thompson Sampling on multiplicative-reward problems. We recommend PathTS as the practical default while cautioning that adversarial instances exist.

Problem

• Stochastic Reset Pathfinding
• Cascading Bandits
• Graph Paths
• Regret Minimization
• Edge Success Probabilities

Innovation

• Stochastic Reset Pathfinding
• Combinatorial Cascading Bandits
• Path-Level Regret
• Log-Dijkstra
• Thompson Sampling