Optimizing the spatial layout of urban service facilities under benefit uncertainty: a Bayesian-guided hierarchical reinforcement learning framework

Abstract

Spatial layout optimization of urban service facilities aims to maximize system-wide locational benefits through rational facility placement. However, due to pronounced spatial heterogeneity and nonlinear interactions among urban environmental features, locational benefits vary significantly across regions and are subject to varying degrees of uncertainty, making the optimization objective difficult to quantify and causing the spatial layout outcomes to fall short of real-world requirements. To address this issue, we propose a Bayesian-guided hierarchical reinforcement learning framework that learns locational benefits from historical data and incorporates benefit uncertainty into the spatial layout optimization process, enabling layout schemes to simultaneously maximize locational benefits while adapting to spatial heterogeneity. Specifically, we first develop a Bayesian neural network to characterize the nonlinear mapping between geospatial factors and locational benefits, which yields probabilistic benefit estimates with explicit uncertainty quantification for each candidate site. These estimates are then integrated into the optimization pipeline via a hierarchical multi-agent deep reinforcement learning model that generates region-specific location decisions under globally coordinated optimization. Experiments in Shenzhen, China demonstrate that our method outperforms mainstream benchmark methods, delivering over 10% higher total benefits and superior out-of-sample robustness. This work presents a novel and actionable uncertainty-aware spatial optimization framework for smart city development.