PID-Controlled Constrained RL for Hub-based Joint Pricing, Dispatching, and Routing with Service Guarantees

Abstract

Joint optimization of pricing, dispatching, and routing is critical for hub-based mobility services but challenging due to complex decision couplings and strict service guarantees, such as Order Response Rate (ORR). Conventional constrained reinforcement learning often struggles in this mixed continuous--combinatorial action space, suffering from oscillatory behavior in Lagrangian dual variables and unstable constraint satisfaction. To address this, we propose PID-SACA, a unified framework that integrates an entropy-regularized actor--critic policy for continuous pricing and dispatching assisted by an embedded routing solver for execution-aware feedback. Crucially, we adapt the PID control mechanism to the Lagrangian dual update process. This approach leverages proportional, integral, and derivative feedback to dampen oscillations caused by stochastic gradient variance, ensuring robust long-term constraint enforcement. We provide theoretical analysis on the boundedness of dual variables, and experiments on publicly available large-scale mobility datasets demonstrate that PID-SACA significantly outperforms baselines, achieving high revenue with stable service compliance. Code: https://github.com/jerry0375/PID-SACA