Train AC Agent to Balance Discrete Cart-Pole System

This example shows how to train an actor-critic (AC) agent to balance a cart-pole system modeled in MATLAB®.

For more information on AC agents, see Actor-Critic (AC) Agent. For an example showing how to train an AC agent using parallel computing, see Train AC Agent to Balance Discrete Cart-Pole System Using Parallel Computing.

Fix Random Number Stream for Reproducibility

The example code might involve computation of random numbers at various stages. Fixing the random number stream at the beginning of various sections in the example code preserves the random number sequence in the section every time you run it, and increases the likelihood of reproducing the results. For more information, see Results Reproducibility.

Fix the random number stream with seed 0 and random number algorithm Mersenne Twister. For more information on controlling the seed used for random number generation, see rng.

previousRngState = rng(0,"twister");

The output previousRngState is a structure that contains information about the previous state of the stream. You will restore the state at the end of the example.

Discrete Action Space 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 pendulum stand upright.

For this environment:

• The balanced, upright pendulum position is 0 radians, and the downward hanging pendulum position is pi radians.

• The pendulum starts upright with an initial angle between –0.05 and 0.05 rad.

• 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 pendulum angle (clockwise-positive), and the pendulum 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 pendulum falls.

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

Create Environment Object

Create a predefined environment object for the pendulum.

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: [4×1 double]

env.PenaltyForFalling = -10;

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

Obtain the observation and action information from the environment object.

obsInfo = getObservationInfo(env);
actInfo = getActionInfo(env);

Create AC Agent with Custom Networks

An AC agent approximates the discounted cumulative long-term reward using a value-function critic. A value-function critic must accept an observation as input and return a single scalar (the estimated discounted cumulative long-term reward) as output.

To approximate the value function within the critic, use a neural network. 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. For more information on creating a deep neural network value function representation, see Create Policies and Value Functions.

criticNet = [
    featureInputLayer(obsInfo.Dimension(1))
    fullyConnectedLayer(32)
    reluLayer
    fullyConnectedLayer(1)
    ];

Convert to dlnetwork and display the number of weights.

criticNet = dlnetwork(criticNet);
summary(criticNet)

   Initialized: true

   Number of learnables: 193

   Inputs:
      1   'input'   4 features

Create the critic approximator object using criticNet, and the observation specification. For more information, see rlValueFunction.

critic = rlValueFunction(criticNet,obsInfo);

Check the critic with a random observation input.

getValue(critic,{rand(obsInfo.Dimension)})

ans = single

-0.3590

An AC agent decides which action to take using a stochastic policy, which for discrete action spaces is approximated by a discrete categorical actor. This actor must take the observation signal as input and return a probability for each action.

To approximate the policy function within the actor, use a deep neural network. 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.

actorNet = [
    featureInputLayer(obsInfo.Dimension(1))
    fullyConnectedLayer(32)
    reluLayer
    fullyConnectedLayer(numel(actInfo.Elements))
    softmaxLayer
    ];

Convert to dlnetwork and display the number of weights.

actorNet = dlnetwork(actorNet);
summary(actorNet)

   Initialized: true

   Number of learnables: 226

   Inputs:
      1   'input'   4 features

Create the actor approximator object using actorNet and the observation and action specifications. For more information, see rlDiscreteCategoricalActor.

actor = rlDiscreteCategoricalActor(actorNet,obsInfo,actInfo);

To return the probability distribution of the possible actions as a function of a random observation, and given the current network weights, use evaluate.

prb = evaluate(actor,{rand(obsInfo.Dimension)})

prb = 1×1 cell array
    {2×1 single}

prb{1}

ans = 2×1 single column vector

    0.4414
    0.5586

Create the agent using the actor and critic. For more information, see rlACAgent.

agent = rlACAgent(actor,critic);

Check the agent with a random observation input.

getAction(agent,{rand(obsInfo.Dimension)})

ans = 1×1 cell array
    {[-10]}

Specify agent options, including training options for the actor and critic, using dot notation. Alternatively, you can use rlACAgentOptions and rlOptimizerOptions objects before creating the agent.

agent.AgentOptions.EntropyLossWeight = 0.01;

agent.AgentOptions.ActorOptimizerOptions.LearnRate = 1e-2;
agent.AgentOptions.ActorOptimizerOptions.GradientThreshold = 1;
agent.AgentOptions.CriticOptimizerOptions.LearnRate = 1e-2;
agent.AgentOptions.CriticOptimizerOptions.GradientThreshold = 1;

Train Agent

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

• Run each training episode for a maximum of 1000 episodes, with each episode lasting at most 500 time steps.

• Display the training progress in the Reinforcement Learning Training Monitor 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 average cumulative reward greater than 480 over 10 consecutive episodes. At this point, the agent can balance the pendulum in the upright position.

For more information on training options, see rlTrainingOptions.

trainOpts = rlTrainingOptions(...
    MaxEpisodes=1000,...
    MaxStepsPerEpisode=500,...
    Verbose=false,...
    Plots="training-progress",...
    StopTrainingCriteria="AverageReward",...
    StopTrainingValue=480,...
    ScoreAveragingWindowLength=10);

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

plot(env)

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);
else
    % Load the pretrained agent for the example.
    load("MATLABCartpoleAC.mat","agent");
end

Simulate AC 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.

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

totalReward = sum(experience.Reward)

totalReward = 
500

Restore the random number stream using the information stored in previousRngState.

rng(previousRngState);