Planning spatial networks with Monte Carlo tree search

We tackle the problem of goal-directed graph construction: given a starting graph, finding a set of edges whose addition maximally improves a global objective function. This problem emerges in many transportation and infrastructure networks that are of critical importance to society. We identify two significant shortcomings of present reinforcement learning methods: their exclusive focus on topology to the detriment of spatial characteristics (which are known to influence the growth and density of links), as well as the rapid growth in the action spaces and costs of model training. Our formulation as a deterministic Markov decision process allows us to adopt the Monte Carlo tree search framework, an artificial intelligence decision-time planning method. We propose improvements over the standard upper confidence bounds for trees (UCT) algorithm for this family of problems that addresses their single-agent nature, the trade-off between the cost of edges and their contribution to the objective, and an action space linear in the number of nodes. Our approach yields substantial improvements over UCT for increasing the efficiency and attack resilience of synthetic networks and real-world Internet backbone and metro systems, while using a wall clock time budget similar to other search-based algorithms. We also demonstrate that our approach scales to significantly larger networks than previous reinforcement learning methods, since it does not require training a model.