Stochastic Reset Pathfinding: Path-Level Regret for Cascading Bandits over Graph Paths
Machine Learning
Summary
The authors study a problem where an agent tries to find a path from start to finish in a network, but if any part of the chosen path fails, the agent is sent back to the start. They show that the best way to solve this is to pick a fixed path without changing it mid-way, and they connect this to a known mathematical problem called combinatorial cascading bandits. They create new algorithms to learn the best path over time and prove some math about how well one of these algorithms performs. Their tests show one algorithm usually works best, but they also find special cases where it does not work well, so they advise caution when using it.
Authors
Guni Sharon, Wei Zhang
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.