Stochastic Reset Pathfinding: Path-Level Regret for Cascading Bandits over Graph Paths
Introduces Stochastic Reset Pathfinding (SRP), an episodic learning problem on directed graphs where edge failures reset the agent to the source, modeling scenarios like quantum repeater networks and Lightning Network routing. Establishes that the global-reset structure renders the optimal policy open-loop, allowing SRP to be framed within the combinatorial cascading bandit (CCB) framework. Proposes the Log-Dijkstra meta-algorithm with two instantiations: PathUCB (Upper Confidence Bound) and Pat
Analysis
TL;DR
- Introduces Stochastic Reset Pathfinding (SRP), an episodic learning problem on directed graphs where edge failures reset the agent to the source, modeling scenarios like quantum repeater networks and Lightning Network routing.
- Establishes that the global-reset structure renders the optimal policy open-loop, allowing SRP to be framed within the combinatorial cascading bandit (CCB) framework.
- Proposes the Log-Dijkstra meta-algorithm with two instantiations: PathUCB (Upper Confidence Bound) and PathTS (Thompson Sampling).
- Derives a novel path-level regret bound for PathUCB that decomposes regret based on per-path complexity involving edge prefix and suffix reliability, offering tighter insights for structured graphs compared to standard edge-level bounds.
- Empirical results show PathTS generally outperforms other algorithms, though it exhibits non-convergence on specific adversarial instances, highlighting a known exponential obstruction for combinatorial Thompson Sampling in multiplicative-reward settings.
Why It Matters
This research provides a rigorous theoretical and practical framework for optimizing routing in highly unreliable, multi-hop networks where partial failures necessitate complete restarts, a common challenge in emerging technologies like quantum communication and decentralized finance. By formalizing these environments as Stochastic Reset Pathfinding problems, it enables practitioners to apply advanced bandit algorithms with proven regret bounds, improving efficiency and reliability in critical infrastructure. The distinction between path-level and edge-level regret offers deeper insights for algorithm selection in complex graph topologies.
Technical Details
- Problem Formulation: SRP involves a known directed graph with unknown stationary edge success probabilities. An episode consists of committing to a source-to-goal path; any edge failure triggers a reset to the source, making the reward multiplicative along the path.
- Algorithmic Framework: The authors utilize a Log-Dijkstra meta-algorithm to compute paths efficiently in the log-probability space. This meta-algorithm supports both UCB-based (PathUCB) and Thompson Sampling-based (PathTS) exploration strategies.
- Theoretical Contribution: A key technical result is the derivation of a path-level regret bound for PathUCB. This bound decomposes regret over suboptimal paths using a complexity term $C(\pi)$ that combines the reliability of prefixes and suffixes of edges, providing a more granular analysis than traditional edge-level CCB bounds.
- Empirical Validation: Experiments were conducted across four domains: quantum-networks, layered-DAGs, grid-worlds, and Erdos-Renyi random graphs. Results indicate PathTS typically achieves superior empirical performance.
- Limitations Identified: The study identifies adversarial instances where PathTS fails to converge, aligning with theoretical expectations regarding the exponential obstruction of combinatorial Thompson Sampling in multiplicative reward contexts.
Industry Insight
- Quantum Networking Optimization: As quantum repeater networks move toward practical deployment, SRP offers a direct mathematical model for managing entanglement distribution failures, guiding the development of robust control protocols.
- Algorithm Selection Strategy: Practitioners should adopt PathTS as the default choice for most practical applications due to its strong empirical performance, but must implement safeguards or fallback mechanisms (like PathUCB) for environments prone to adversarial or highly skewed probability distributions.
- Graph Structure Awareness: The path-level regret bound suggests that in networks with polynomially many paths (e.g., layered or grid structures), algorithms leveraging path-specific complexity metrics may significantly outperform those relying solely on edge-level statistics, encouraging tailored algorithm design for specific network topologies.
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