Closed-Loop Optimal Freeway Ramp Metering Using Continuous State Space Reinforcement Learning with Function Approximation

In recent years, Reinforcement Learning (RL), an Artificial Intelligence based learning method, has gained some interest among researchers in solving control systems problems. Although RL methods have been applied to different transportation problems such as ramp metering and traffic signal control, RL in its conventional form, with discrete state space representation, lacks learning efficiency and becomes intractable when applied to medium and large-scale transportation control problems. Continuous state space representation in RL problems implies direct representation of the problem’s continuous variables using function approximation techniques that has the potential to addresses some of the challenges associated with employing RL in large transportation networks. Function approximation methods, when properly designed, have the potential to result in 1) faster learning, 2) better performance, and 3) easier design/set up for RL control systems. In this paper, three function approximation techniques: k-nearest neighbor weighted average, multi-layer perception neural network, and linear model tree are developed and compared against the conventional table-based RL as a benchmark. The four approaches are applied to a ramp metering case study in the city of Toronto. The approaches are tested on a microsimulation model and compared using the following criteria: learning speed, design effort, computational requirements, and network performance. It is concluded that, for RL problems, the linear model tree method provides the best function approximation with minimal design effort given the noisy measurements in traffic control applications with more than 10 times faster leaning speed over the conventional table-based RL methods.