Solving Stochastic Orienteering Problems with Chance Constraints Using a GNN Powered Monte Carlo Tree Search

2024-09-06

arXiv.org

AI Summary

This paper addresses the Stochastic Orienteering Problem with Chance Constraints (SOP-CC): maximizing collected rewards under stochastic travel costs and a deterministic budget, while strictly bounding the probability of budget violation below a given threshold. We propose an online, anytime Monte Carlo Tree Search (MCTS) framework that, for the first time, integrates Message-Passing Graph Neural Networks (MPNNs) into the rollout phase to jointly model action utility and path failure probability—enabling efficient, robust real-time decision-making. This design accelerates search convergence and supports cross-distribution generalization. Experiments demonstrate controlled reward loss on challenging instances and strong generalization to unseen scenarios. Our approach establishes a novel paradigm for sequential chance-constrained optimization under uncertainty.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Sampling/Simulation-based Search
• Planning, Routing, and Scheduling: Planning under Uncertainty

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Research challenges in human and human-AI computation
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Leveraging the power of a graph neural network (GNN) with message passing, we present a Monte Carlo Tree Search (MCTS) method to solve stochastic orienteering problems with chance constraints. While adhering to an assigned travel budget the algorithm seeks to maximize collected reward while incurring stochastic travel costs. In this context, the acceptable probability of exceeding the assigned budget is expressed as a chance constraint. Our MCTS solution is an online and anytime algorithm alternating planning and execution that determines the next vertex to visit by continuously monitoring the remaining travel budget. The novelty of our work is that the rollout phase in the MCTS framework is implemented using a message passing GNN, predicting both the utility and failure probability of each available action. This allows to enormously expedite the search process. Our experimental evaluation shows that with the proposed method and architecture we manage to efficiently solve complex problem instances while incurring in moderate losses in terms of collected reward. Moreover, we demonstrate how the approach is capable of generalizing beyond the characteristics of the training dataset. The paper's website, open-source code, and supplementary documentation can be found at ucmercedrobotics.github.io/gnn-sop.

Problem

• Solving stochastic orienteering with chance-constrained travel budget
• Maximizing collected reward under stochastic travel costs
• Using GNN-powered MCTS for online planning and execution

Innovation

• GNN-powered MCTS for stochastic orienteering
• Message passing GNN predicts utility and failure
• Online anytime algorithm with chance constraints