  This article develops a deep reinforcement learning (Deep-RL) framework for
dynamic pricing on managed lanes with multiple access locations and
heterogeneity in travelers' value of time, origin, and destination. This
framework relaxes assumptions in the literature by considering multiple origins
and destinations, multiple access locations to the managed lane, en route
diversion of travelers, partial observability of the sensor readings, and
stochastic demand and observations. The problem is formulated as a partially
observable Markov decision process (POMDP) and policy gradient methods are used
to determine tolls as a function of real-time observations. Tolls are modeled
as continuous and stochastic variables, and are determined using a feedforward
neural network. The method is compared against a feedback control method used
for dynamic pricing. We show that Deep-RL is effective in learning toll
policies for maximizing revenue, minimizing total system travel time, and other
joint weighted objectives, when tested on real-world transportation networks.
The Deep-RL toll policies outperform the feedback control heuristic for the
revenue maximization objective by generating revenues up to 9.5% higher than
the heuristic and for the objective minimizing total system travel time (TSTT)
by generating TSTT up to 10.4% lower than the heuristic. We also propose reward
shaping methods for the POMDP to overcome the undesired behavior of toll
policies, like the jam-and-harvest behavior of revenue-maximizing policies.
Additionally, we test transferability of the algorithm trained on one set of
inputs for new input distributions and offer recommendations on real-time
implementations of Deep-RL algorithms. The source code for our experiments is
available online at https://github.com/venktesh22/ExpressLanes_Deep-RL
