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Train DQN Agent to Balance Cart-Pole System

This example shows how to train a deep Q-learning network (DQN) agent to balance a cart-pole system modeled in MATLAB®.

For more information on DQN agents, see Deep Q-Network (DQN) Agents. For an example that trains a DQN agent in Simulink®, see Train DQN Agent to Swing Up and Balance Pendulum.

Cart-Pole MATLAB Environment

The reinforcement learning environment for this example is a pole attached to an unactuated joint on a cart, which moves along a frictionless track. The training goal is to make the pole stand upright without falling over.

For this environment:

  • The upward balanced pole position is 0 radians, and the downward hanging position is pi radians.

  • The pole starts upright with an initial angle between –0.05 and 0.05 radians.

  • The force action signal from the agent to the environment is either –10 or 10 N.

  • The observations from the environment are the position and velocity of the cart, the pole angle, and the pole angle derivative.

  • The episode terminates if the pole is more than 12 degrees from vertical or if the cart moves more than 2.4 m from the original position.

  • A reward of +1 is provided for every time step that the pole remains upright. A penalty of –5 is applied when the pole falls.

For more information on this model, see Load Predefined Control System Environments.

Create Environment Interface

Create a predefined environment interface for the system.

env = rlPredefinedEnv("CartPole-Discrete")
env = 
  CartPoleDiscreteAction with properties:

                  Gravity: 9.8000
                 MassCart: 1
                 MassPole: 0.1000
                   Length: 0.5000
                 MaxForce: 10
                       Ts: 0.0200
    ThetaThresholdRadians: 0.2094
               XThreshold: 2.4000
      RewardForNotFalling: 1
        PenaltyForFalling: -5
                    State: [4x1 double]

The interface has a discrete action space where the agent can apply one of two possible force values to the cart, –10 or 10 N.

Get the observation and action specification information.

obsInfo = getObservationInfo(env)
obsInfo = 
  rlNumericSpec with properties:

     LowerLimit: -Inf
     UpperLimit: Inf
           Name: "CartPole States"
    Description: "x, dx, theta, dtheta"
      Dimension: [4 1]
       DataType: "double"

actInfo = getActionInfo(env)
actInfo = 
  rlFiniteSetSpec with properties:

       Elements: [-10 10]
           Name: "CartPole Action"
    Description: [0x0 string]
      Dimension: [1 1]
       DataType: "double"

Fix the random generator seed for reproducibility.


Create DQN Agent

DQN agents can use vector Q-value functions critics, which are generally more efficient than comparable single-output critics. A vector Q-value function critic has observations as inputs and state-action values as outputs. Each output element represents the expected cumulative long-term reward for taking the corresponding discrete action from the state indicated by the observation inputs. For more information on creating value-functions, see Create Policies and Value Functions.

To approximate the Q-value function within the critic, use a neural network with one input channel (the 4-dimensional observed state vector) and one output channel with two elements (one for the 10 N action, another for the –10 N action). Define the network as an array of layer objects, and get the dimension of the observation space and the number of possible actions from the environment specification objects.

net = [

Convert to dlnetwork and display the number of weights.

net = dlnetwork(net);
   Initialized: true

   Number of learnables: 142

      1   'input'   4 features

View the network configuration.


Figure contains an axes object. The axes object contains an object of type graphplot.

Create the critic approximator using net and the environment specifications. For more information, see rlVectorQValueFunction.

critic = rlVectorQValueFunction(net,obsInfo,actInfo);

Check the critic with a random observation input.

ans = 2x1 single column vector


Create the DQN agent using critic. For more information, see rlDQNAgent.

agent = rlDQNAgent(critic);

Check the agent with a random observation input.

ans = 1x1 cell array

Specify the DQN agent options, including training options for the critic. Alternatively, you can use rlDQNAgentOptions and rlOptimizerOptions objects.

agent.AgentOptions.UseDoubleDQN = false;
agent.AgentOptions.TargetSmoothFactor = 1;
agent.AgentOptions.TargetUpdateFrequency = 4;
agent.AgentOptions.ExperienceBufferLength = 1e5;
agent.AgentOptions.MiniBatchSize = 256;
agent.AgentOptions.CriticOptimizerOptions.LearnRate = 1e-3;
agent.AgentOptions.CriticOptimizerOptions.GradientThreshold = 1;

Train Agent

To train the agent, first specify the training options. For this example, use the following options:

  • Run one training session containing at most 1000 episodes, with each episode lasting at most 500 time steps.

  • Display the training progress in the Episode Manager dialog box (set the Plots option) and disable the command line display (set the Verbose option to false).

  • Stop training when the agent receives an moving average cumulative reward greater than 480. At this point, the agent can balance the cart-pole system in the upright position.

For more information, see rlTrainingOptions.

trainOpts = rlTrainingOptions(...
    MaxEpisodes=1000, ...
    MaxStepsPerEpisode=500, ...
    Verbose=false, ...

You can visualize the cart-pole system by using the plot function during training or simulation.


Figure Cart Pole Visualizer contains an axes object. The axes object contains 6 objects of type line, polygon.

Train the agent using the train function. Training this agent is a computationally intensive process that takes several minutes to complete. To save time while running this example, load a pretrained agent by setting doTraining to false. To train the agent yourself, set doTraining to true.

doTraining = false;
if doTraining
    % Train the agent.
    trainingStats = train(agent,env,trainOpts);
    % Load the pretrained agent for the example.

Simulate DQN Agent

To validate the performance of the trained agent, simulate it within the cart-pole environment. For more information on agent simulation, see rlSimulationOptions and sim. The agent can balance the cart-pole even when the simulation time increases to 500 steps.

simOptions = rlSimulationOptions(MaxSteps=500);
experience = sim(env,agent,simOptions);

Figure Cart Pole Visualizer contains an axes object. The axes object contains 6 objects of type line, polygon.

totalReward = sum(experience.Reward)
totalReward = 500

See Also




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