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Expert Level control of Ramp Metering based on Multi-task Deep Reinforcement Learning

Francois Belletti, Daniel Haziza, Gabriel Gomes, Alexandre M. Bayen

arXiv:1701.08832v1cs.AI

TL;DR

Traffic control needs adaptable methods because infrastructure changes are costly and model-based controllers require calibration. The paper uses neural RL to control discretized PDEs without an explicit model and introduces MWR for scalable multi-agent specialization. Across traffic-control settings, the approach demonstrates robust PDE control and ramp-metering performance comparable to expert-designed parametric methods.

  • Problem

    Traffic control needs adaptable use of existing infrastructure, while discretized nonlinear PDEs and scalable multi-agent control are difficult to handle without known dynamics or model calibration.

  • Method

    The paper uses neural policy-gradient RL for non-parametric control of discretized PDEs and introduces MWR to share multi-agent experience while preserving local specialization.

  • Results

    The approach robustly controls traffic PDEs under stochastic parameter variation and achieves ramp-metering performance comparable to the parametric ALINEA method.

  • Takeaways & Limitations

    Neural RL can control discretized macroscopic traffic equations without an explicit dynamics model, while MWR supports adaptive control across large cyberphysical systems.

Abstract

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This article shows how the recent breakthroughs in Reinforcement Learning (RL) that have enabled robots to learn to play arcade video games, walk or assemble colored bricks, can be used to perform other tasks that are currently at the core of engineering cyberphysical systems. We present the first use of RL for the control of systems modeled by discretized non-linear Partial Differential Equations (PDEs) and devise a novel algorithm to use non-parametric control techniques for large multi-agent systems. We show how neural network based RL enables the control of discretized PDEs whose parameters are unknown, random, and time-varying. We introduce an algorithm of Mutual Weight Regularization (MWR) which alleviates the curse of dimensionality of multi-agent control schemes by sharing experience between agents while giving each agent the opportunity to specialize its action policy so as to tailor it to the local parameters of the part of the system it is located in.

94720, USA

The paper targets traffic congestion by replacing costly, infrequent infrastructure changes with model-free RL control of traffic systems. It introduces PDE control and MWR for scalable multi-agent ramp metering, achieving performance comparable to expert-designed parametric control.

  • Motivation: Traffic control is motivated by congestion costs and the expense of changing network infrastructure, making dynamic use of existing roads attractive.The paper frames traffic-flow control as an alternative that adapts existing infrastructure to demand without repeated network reconstruction.
  • Contributions: RL provides robust, non-parametric control of discretized PDEs, including traffic models with non-smooth finite-difference schemes.The framework is presented as the first use of RL for control of PDEs discretized by finite differencing.
  • Contributions: The approach controls traffic PDEs at boundaries and within the domain across scenarios, including training with stochastic variations in model parameters.The authors assess robustness after an extremely noisy training phase and use a Godunov-based simulator alongside BeATS for benchmarking.
  • Contributions: MWR shares experience across agents while allowing local policy specialization, addressing scalability in multi-agent traffic control.Applied to ramp metering, MWR avoids the curse of dimensionality with respect to the number of agents.
  • Ramp metering: For ramp metering, the RL policy achieves control comparable to ALINEA, a model-dependent state-of-the-art method calibrated by a traffic engineer.The paper positions this result as matching pre-existing parametric solutions while avoiding assumed model parameters and calibration.

II. MODELS AND METHODOLOGY

The paper models highway traffic with a fundamental-diagram PDE and evaluates reinforcement-learning control through progressively more realistic traffic simulators. The experiments move from a Godunov discretization proof of concept to the BeATS cell-transmission model, where the learned policy achieves performance comparable to ALINEA without requiring its parametric model.

  • The traffic PDE’s fundamental diagram maps uniform vehicle density to flow, with a critical density maximizing flow and congestion reducing flow beyond that point.
  • The control formulation avoids explicitly constructing unknown PDE transition probabilities by learning from simulation trials with policy-gradient algorithms.
  • The experimental method first tests neural-network RL control on a coarse Godunov discretization across different situations and objectives.This step provides a proof of concept for controlling discretized PDEs with policy-gradient methods.
  • In the more realistic BeATS cell-transmission simulator, the learned policy reaches performance comparable to ALINEA while using a non-parametric approach.The second step changes the control tasks to reflect production traffic-management needs.

III. CONTROLLING CYBERPHYSICAL SYSTEMS WITH NEURAL NETWORKS TRAINED BY REINFORCEMENT LEARNING

The paper formulates non-parametric PDE control as a finite-horizon discounted Markov decision process and trains a stochastic neural policy from sampled trajectories. This formulation accommodates unknown, non-differentiable, and time-varying system dynamics while optimizing practitioner-defined rewards.

  • Reinforcement learning represents discretized traffic control as a finite-horizon discounted MDP whose actions specify freeway inflow through a weak boundary condition.
  • The policy seeks to maximize expected discounted reward, with the reward function defined by the practitioner’s control objective.
  • A stochastic policy maps system observations to action distributions, allowing policy gradients even when system dynamics are unknown, discontinuous, or non-differentiable.
  • The discretized PDE solution is computed with a Godunov scheme under a Courant-Friedrichs-Lewy resolution condition.
  • The actuator uses a neural network to determine parameters of a stochastic action policy from observations of the system state.

C. Neural Networks

The control policies are neural networks whose layers transform observations into action-policy outputs, with architecture chosen to match the data and control setting. Continuous-control training methods include policy-gradient and non-gradient alternatives, with TNPG and TRPO outperforming others when regime changes occur in the reported experiments.

  • Neural Networks: A neural network stacks layers that transform an input vector into an output vector through interconnected artificial neurons.
  • Neural Networks: For continuous control, the paper considers policy-gradient and non-gradient training approaches, including REINFORCE, TNPG, TRPO, PPO, and the cross-entropy method.
  • Neural Networks: Back-propagation trains neural networks through stochastic gradient descent on a non-convex function.
  • Neural Networks: The policy network uses a stochastic output distribution whose parameters are determined from observations, supporting non-parametric action selection.
  • Neural Networks: TNPG and TRPO outperform other methods when stochastic boundary-condition regime changes occur, whereas all approaches perform conveniently when those patterns are sufficiently stationary.

1) REINFORCE:

The REINFORCE procedure trains a stochastic neural policy by estimating policy gradients from sampled trajectories and ascending the resulting objective. The architecture processes spatial highway observations with convolutional layers while sharing parameters across ramp policies.

  • 1) REINFORCE:: REINFORCE estimates the policy gradient across multiple simulated trajectories and updates network parameters by gradient ascent.
  • 1) REINFORCE:: The policy network receives environment observations and outputs an action probability distribution parameterized by its weights.
  • 1) REINFORCE:: Sharing parameters across on-ramp policies gives agents the same policy, while Mutual Weight Regularization is introduced to support experience sharing with specialization.
  • 1) REINFORCE:: The observation is an n × 3 spatial array containing vehicle density, off-ramp presence, and on-ramp queue information.
  • 1) REINFORCE:: Three convolutional layers extract spatially local features before a final layer selects how many vehicles may enter through the ramp.

3) Sharing information while allowing specialization among agents: the Mutual Weight Regularization algorithm:

Mutual Weight Regularization shares learning across ramp agents while preserving agent-specific adaptations for local highway conditions. It interpolates between fully independent and fully shared policies through a regularized parameterization.

  • 3) Sharing information while allowing specialization among agents: the Mutual Weight Regularization algorithm:: The convolutional representation computes spatially invariant local features for each controllable on-ramp before producing agent actions.The network uses m features per cell and identifies each agent with the features at its associated highway cells.
  • 3) Sharing information while allowing specialization among agents: the Mutual Weight Regularization algorithm:: Fully shared parameters impose one identical policy on every on-ramp, which cannot represent local differences such as lane counts or speed limits.The supplied text identifies reduced lanes and different speed limits as examples of local highway specificity.
  • 3) Sharing information while allowing specialization among agents: the Mutual Weight Regularization algorithm:: Dedicated parameters give each on-ramp flexibility but increase parameter count, prevent shared learning, and fail to converge to a good policy.This is the independent-policy extreme that MWR is designed to avoid.
  • 3) Sharing information while allowing specialization among agents: the Mutual Weight Regularization algorithm:: Mutual Weight Regularization shares experience between agents while allowing local policy specialization, mitigating scaling difficulties in multi-agent control.The method is positioned between fully shared policies and independent policies, combining shared learning with agent-specific modifications.
  • 3) Sharing information while allowing specialization among agents: the Mutual Weight Regularization algorithm:: MWR adds a regularization term to the global gradient, with α controlling the strength of mutual information shared between agents.α = 0 corresponds to independent policies, whereas α = ∞ corresponds to shared weights across on-ramps.

IV. EXPERIMENTAL RESULTS

The initial experiments test whether one RL training procedure can robustly control discretized traffic PDEs across substantially different tasks. They use a simple Godunov discretization of the LWR PDE.

  • IV. EXPERIMENTAL RESULTS: One training procedure converges to successful policies for two very different traffic-control tasks using a simple Godunov discretization of the LWR PDE.These experiments are presented as evidence that RL can control discretized PDEs robustly and generically.

1) Highway outflow control:

The experiments apply RL to highway outflow and interior-density control under stochastic traffic dynamics, accidents, and multiple entry points. The learned policies track prescribed objectives, while PPO performs best among the compared training methods in the accident setting.

  • 1) Highway outflow control:: The boundary-control action is a positive scalar specifying how many vehicles may enter the highway per time unit, while the reward targets a prescribed downstream outflow pattern.The policy receives only the current time step as its state observation together with the rollout reward.
  • 1) Highway outflow control:: The policy converges to a control scheme that replicates the objective density despite non-differentiability, non-smoothness, nonlinearity, accidents, and random input queues.PPO, TRPO, and REINFORCE are reported as reliable in this instance, with PPO converging faster to a reward plateau.
  • 1) Highway outflow control:: With ramps distributed along the freeway, TRPO learns to reproduce a target interior density despite the higher-dimensional action space, whereas TNPG fails to converge efficiently.The experiment uses reward shaping based on the L2 distance between observed and target density.
  • 1) Highway outflow control:: The real-world benchmark uses a calibrated BeATS simulation of a 20-mile section of California’s 210 Eastbound freeway and compares RL, ALINEA, and no metering.The benchmark includes NoRM, NoMWR, MWR, and ALINEA as control strategies.
  • 1) Highway outflow control:: PPO outperforms TNPG, VPG, and TRPO for downstream-boundary control under accidents.The comparison is presented in Fig. 6, where TNPG performs poorly and VPG and TRPO show mediocre performance.

1) Reinforcement Learning problem:

The BeATS RL formulation controls 29 on-ramp rates at 32-second intervals using a structured observation of freeway conditions. Stochastic actions and shared learning are used to support a generic policy across the highway.

  • 1) Reinforcement Learning problem:: Each action is a 29-dimensional vector of ramp-metering rates, and the reward is total outflow during the preceding 32 seconds.The 29 entries correspond to the on-ramps along the simulated highway section.
  • 1) Reinforcement Learning problem:: The benchmark table reports that RL provides non-parametric control with performance similar to ALINEA, while MWR improves that performance.The comparison aggregates scores over the congested period.
  • 1) Reinforcement Learning problem:: Gaussian action noise and shared learning across 29 on-ramps are used to encourage a generic policy and prevent overfitting.The applied metering rates are sampled around the neural-network output.

2) Numerical results:

MWR-based reinforcement learning improves traffic-control performance and nearly matches ALINEA while learning adaptive control without model calibration.

  • MWR significantly outperforms regular parameter sharing and nearly reaches the performance of the reference ALINEA controller on aggregate traffic measures.The comparison uses Total Vehicle Miles and Total Vehicle Hour.
  • The approach provides adaptive control without model calibration and allows agents to specialize while sharing experience across the system.
  • RL methods, especially MWR, implicitly learn the expert-calibrated optimal speed that ALINEA maintains above.
  • Ramp-metering methods reduce the number of vehicles during congestion peaks, while MWR maintains vehicle counts at a level similar to ALINEA.
  • MWR reproduces 96% of ALINEA’s performance improvement over no ramp-metering, compared with 80% for regular RL training.

APPENDIX A GODUNOV DISCRETIZATION SCHEME

The appendix formulates traffic dynamics and boundary conditions through weak solutions and approximates them with the non-differentiable Godunov discretization scheme.

  • The traffic PDE is formulated in the weak sense because its solutions contain discontinuities.
  • The flux function defines the system dynamics and is domain-specific; in transportation engineering, it is also called the fundamental diagram.
  • Entropy conditions provide uniqueness and continuous dependence on initial data, while weak-solution definitions alone do not guarantee admissibility.
  • The Godunov scheme recursively computes an approximate weak solution for the Dirichlet problem using a piecewise Godunov flux.
  • Godunov is second-order accurate in space but non-differentiable, and its parameterized flux makes uncertainty assessment difficult for nonlinear, non-smooth schemes.
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