Train PG Agent with Custom Networks to Control Discrete Double Integrator

Fix Random Seed Generator to Improve Reproducibility

The example code may involve computation of random numbers at various stages such as initialization of the agent, creation of the actor and critic, resetting the environment during simulations, generating observations (for stochastic environments), generating exploration actions, and sampling min-batches of experiences for learning. Fixing the random number stream preserves the sequence of the random numbers every time you run the code and improves reproducibility of results. You will fix the random number stream at various locations in the example.

Fix the random number stream with the seed 0 and random number algorithm Mersenne twister. For more information on 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 Double Integrator MATLAB Environment

The reinforcement learning environment for this example is a second-order double integrator system with a gain and a discrete action space. The training goal is to control the position of a mass in the second-order system by applying a force input.

For this environment:

Here:

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

Create Environment Object

Create a predefined environment interface for the pendulum.

env = rlPredefinedEnv("DoubleIntegrator-Discrete")

env = 
  DoubleIntegratorDiscreteAction with properties:

             Gain: 1
               Ts: 0.1000
      MaxDistance: 5
    GoalThreshold: 0.0100
                Q: [2x2 double]
                R: 0.0100
         MaxForce: 2
            State: [2x1 double]

Obtain the observation and action information from the environment interface.

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

Create Actor With Custom Network

The actor network of the PG agent are initialized randomly. Fix the random number stream.

rng(0, "twister");

For policy gradient agents, the actor executes 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 within the actor, use a neural network. Define the network as an array of layer objects with one input (the observation) and one output (the action), 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.

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

Convert to dlnetwork and display the number of weights.

actorNet = dlnetwork(actorNet);
summary(actorNet)

   Initialized: true

   Number of learnables: 9

   Inputs:
      1   'input'   2 features

Create the actor representation using the neural network and the environment specification objects. 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 = 1x1 cell array
    {3x1 single}

prb{1}

ans = 3x1 single column vector

    0.4994
    0.3770
    0.1235

Create Baseline With Custom Network

The baseline network of the PG agent are initialized randomly. Fix the random number stream.

rng(0, "twister");

The PG Agent algorithm, (also known as REINFORCE) returns can be compared to a baseline that depends on the state. Using a basellline can reduce the variance of the expected value of the update and thus improve the speed of learning. A possible choice for the baseline is an estimate of the state value function [1].

A value-function approximator object must accept an observation as input and return a single scalar (the estimated discounted cumulative long-term reward) as output. Use a neural network as approximation model. 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.

baselineNet = [
    featureInputLayer(obsInfo.Dimension(1))
    fullyConnectedLayer(8)
    reluLayer
    fullyConnectedLayer(1)
    ];

Convert to dlnetwork and display the number of weights.

baselineNet = dlnetwork(baselineNet);

Create the baseline value function approximator baselineNet, and the observation specification. For more information, see rlValueFunction.

baseline = rlValueFunction(baselineNet,obsInfo);

Check the baseline with a random observation input.

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

ans = single

1.5300

Configure Agent Options and Create Agent

Specify options for the actor. For more information, see rlOptimizerOptions. Alternatively, you can change agent (including actor and critic) options using dot notation after the agent is created.

actorOpts = rlOptimizerOptions( ...
    LearnRate=5e-3, ...
    GradientThreshold=1);

Specify some options for the baseline.

baselineOpts = rlOptimizerOptions( ...
    LearnRate=5e-3, ...
    GradientThreshold=1);

Specify the PG agent options using rlPGAgentOptions and set the UseBaseline option set to true.

agentOpts = rlPGAgentOptions(...
    UseBaseline=true, ...
    ActorOptimizerOptions=actorOpts, ...
    CriticOptimizerOptions=baselineOpts);

Create the agent using the specified actor representation, baseline representation, and agent options. For more information, see rlPGAgent.

agent = rlPGAgent(actor,baseline,agentOpts);

Check the agent with a random observation input.

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

ans = 1x1 cell array
    {[0]}

Configure Training Options

Set up an evaluator object to evaluate the agent five times without exploration every 50 episodes.

evl = rlEvaluator(NumEpisodes=5,EvaluationFrequency=50);

Configure the training options. For this example, use the following options.

For more information, see rlTrainingOptions.

trainOpts = rlTrainingOptions(...
    MaxEpisodes=1000, ...
    MaxStepsPerEpisode=200, ...
    Verbose=false, ...
    Plots="training-progress",...
    StopTrainingCriteria="EvaluationStatistic",...
    StopTrainingValue=-40);

Train Agent

Fix the random number stream.

rng(0, "twister");

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,Evaluator=evl);
else
    % Load the pretrained parameters for the example.
    load("DoubleIntegPGBaseline.mat");
end

Simulate Agent

Fix the random number stream.

rng(0, "twister");

You can visualize the double integrator system using the plot function during training or simulation.

plot(env)

To validate the performance of the trained agent, simulate it within the double integrator 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 = 
-63.8540

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

rng(previousRngState)

References

[1] Sutton, Richard S., and Andrew G. Barto. Reinforcement Learning: An Introduction. Second edition. Adaptive Computation and Machine Learning Series. Cambridge, MA: The MIT Press, 2018.