Using deep reinforcement learning, we derive novel control policies for autonomous vehicles to improve the throughput of a bottleneck modeled after the San Francisco-Oakland Bay Bridge. Using Flow, a new library for applying deep reinforcement learning to traffic micro-simulators, we consider the problem of improving the throughput of a traffic benchmark: a two-stage bottleneck where four lanes reduce to two and then reduce to one. We first characterize the inflow-outflow curve of this bottleneck without any control. We introduce an inflow of autonomous vehicles with the intent of improving the congestion through Lagrangian control. To handle the varying number of autonomous vehicles in the system we derive a per-lane variable speed limits parametrization of the controller. We demonstrate that a 10% penetration rate of controlled autonomous vehicles can improve the throughput of the bottleneck by 200 vehicles per hour: a 25% improvement at high inflows. Finally, we compare the performance of our control policies to feedback ramp metering and show that the AV controller provides comparable performance to ramp metering without the need to build new ramp metering infrastructure. Illustrative videos of the results can be found at https://sites.google.com/view/itsc-lagrangian-avs/home and code and tutorials can be found at https://github.com/flow-project/flow.