Create an observation specification object (or alternatively use getObservationInfo to extract the specification object from an environment). For this example, define the observation space as a continuous four-dimensional space, so that a single observation is a column vector containing four doubles.

obsInfo = rlNumericSpec([4 1]);

Create an action specification object (or alternatively use getActionInfo to extract the specification object from an environment). For this example, define the action space as consisting of three values, -10, 0, and 10.

actInfo = rlFiniteSetSpec([-10 0 10]);

Create a deep neural network approximator for the actor. The input of the network (here called state) must accept a four-element vector (the observation vector just defined by obsInfo), and its output (here called actionProb) must be a three-element vector. Each element of the output vector must be between 0 and 1 since it represents the probability of executing each of the three possible actions (as defined by actInfo). Using softmax as the output layer enforces this requirement.

net = [  featureInputLayer(4,'Normalization','none','Name','state')
         fullyConnectedLayer(3,'Name','fc')
         softmaxLayer('Name','actionProb')  ];

Create the actor with rlStochasticActorRepresentation, using the network, the observations and action specification objects, as well as the names of the network input layer.

actor = rlStochasticActorRepresentation(net,obsInfo,actInfo,'Observation','state')

actor = 
  rlStochasticActorRepresentation with properties:

         ActionInfo: [1x1 rl.util.rlFiniteSetSpec]
    ObservationInfo: [1x1 rl.util.rlNumericSpec]
            Options: [1x1 rl.option.rlRepresentationOptions]

To validate your actor, use getAction to return a random action from the observation vector [1 1 1 1], using the current network weights.

act = getAction(actor,{[1 1 1 1]}); 
act{1}

ans = 10

You can now use the actor to create a suitable agent, such as an rlACAgent, or rlPGAgent agent.

Create an observation specification object (or alternatively use getObservationInfo to extract the specification object from an environment). For this example, define the observation space as a continuous six-dimensional space, so that a single observation is a column vector containing 6 doubles.

obsInfo = rlNumericSpec([6 1]);

Create an action specification object (or alternatively use getActionInfo to extract the specification object from an environment). For this example, define the action space as a continuous two-dimensional space, so that a single action is a column vector containing 2 doubles both between -10 and 10.

actInfo = rlNumericSpec([2 1],'LowerLimit',-10,'UpperLimit',10);

Create a deep neural network approximator for the actor. The observation input (here called myobs) must accept a six-dimensional vector (the observation vector just defined by obsInfo). The output (here called myact) must be a four-dimensional vector (twice the number of dimensions defined by actInfo). The elements of the output vector represent, in sequence, all the means and all the standard deviations of every action.

The fact that standard deviations must be non-negative while mean values must fall within the output range means that the network must have two separate paths. The first path is for the mean values, and any output nonlinearity must be scaled so that it can produce values in the output range. The second path is for the standard deviations, and you can use a softplus or relu layer to enforce non-negativity.

% input path layers (6 by 1 input and a 2 by 1 output)
inPath = [ imageInputLayer([6 1 1], 'Normalization','none','Name','myobs') 
           fullyConnectedLayer(2,'Name','infc') ]; % 2 by 1 output

% path layers for mean value (2 by 1 input and 2 by 1 output)
% using scalingLayer to scale the range
meanPath = [ tanhLayer('Name','tanh'); % output range: (-1,1)
             scalingLayer('Name','scale','Scale',actInfo.UpperLimit) ]; % output range: (-10,10)

% path layers for standard deviations (2 by 1 input and output)
% using softplus layer to make it non negative
sdevPath =  softplusLayer('Name', 'splus');

% conctatenate two inputs (along dimension #3) to form a single (4 by 1) output layer
outLayer = concatenationLayer(3,2,'Name','mean&sdev');

% add layers to network object
net = layerGraph(inPath);
net = addLayers(net,meanPath);
net = addLayers(net,sdevPath);
net = addLayers(net,outLayer);

% connect layers: the mean value path output MUST be connected to the FIRST input of the concatenationLayer
net = connectLayers(net,'infc','tanh/in');              % connect output of inPath to meanPath input
net = connectLayers(net,'infc','splus/in');             % connect output of inPath to sdevPath input
net = connectLayers(net,'scale','mean&sdev/in1');       % connect output of meanPath to gaussPars input #1
net = connectLayers(net,'splus','mean&sdev/in2');       % connect output of sdevPath to gaussPars input #2

% plot network
plot(net)

Set some training options for the actor.

actorOpts = rlRepresentationOptions('LearnRate',8e-3,'GradientThreshold',1);

Create the actor with rlStochasticActorRepresentation, using the network, the observations and action specification objects, the names of the network input layer and the options object.

actor = rlStochasticActorRepresentation(net, obsInfo, actInfo, 'Observation','myobs',actorOpts)

actor = 
  rlStochasticActorRepresentation with properties:

         ActionInfo: [1x1 rl.util.rlNumericSpec]
    ObservationInfo: [1x1 rl.util.rlNumericSpec]
            Options: [1x1 rl.option.rlRepresentationOptions]

To check your actor, use getAction to return a random action from the observation vector ones(6,1), using the current network weights.

act = getAction(actor,{ones(6,1)}); 
act{1}

ans = 2x1 single column vector

   -0.0763
    9.6860

You can now use the actor to create a suitable agent (such as an rlACAgent, rlPGAgent, or rlPPOAgent agent).

Create an observation specification object (or alternatively use getObservationInfo to extract the specification object from an environment). For this example, define the observation space as a continuous four-dimensional space, so that a single observation is a column vector containing 2 doubles.

obsInfo = rlNumericSpec([2 1]);

The stochastic actor based on a custom basis function does not support continuous action spaces. Therefore, create a discrete action space specification object (or alternatively use getActionInfo to extract the specification object from an environment with a discrete action space). For this example, define the action space as a finite set consisting of 3 possible values (named 7, 5, and 3 in this case).

actInfo = rlFiniteSetSpec([7 5 3]);

Create a custom basis function. Each element is a function of the observations defined by obsInfo.

myBasisFcn = @(myobs) [myobs(2)^2; myobs(1); exp(myobs(2)); abs(myobs(1))]

myBasisFcn = function_handle with value:
    @(myobs)[myobs(2)^2;myobs(1);exp(myobs(2));abs(myobs(1))]

The output of the actor is the action, among the ones defined in actInfo, corresponding to the element of softmax(W'*myBasisFcn(myobs)) which has the highest value. W is a weight matrix, containing the learnable parameters, which must have as many rows as the length of the basis function output, and as many columns as the number of possible actions.

Define an initial parameter matrix.

W0 = rand(4,3);

Create the actor. The first argument is a two-element cell containing both the handle to the custom function and the initial parameter matrix. The second and third arguments are, respectively, the observation and action specification objects.

actor = rlStochasticActorRepresentation({myBasisFcn,W0},obsInfo,actInfo)

actor = 
  rlStochasticActorRepresentation with properties:

         ActionInfo: [1x1 rl.util.rlFiniteSetSpec]
    ObservationInfo: [1x1 rl.util.rlNumericSpec]
            Options: [1x1 rl.option.rlRepresentationOptions]

To check your actor use the getAction function to return one of the three possible actions, depending on a given random observation and on the current parameter matrix.

v = getAction(actor,{rand(2,1)})

v = 1x1 cell array
    {[3]}

You can now use the actor (along with an critic) to create a suitable discrete action space agent.

For this example, you create a stochastic actor with a discrete action space using a recurrent neural network. You can also use a recurrent neural network for a continuous stochastic actor using the same method.

Create an environment and obtain observation and action information.

env = rlPredefinedEnv('CartPole-Discrete');
obsInfo = getObservationInfo(env);
actInfo = getActionInfo(env);
numObs = obsInfo.Dimension(1);
numDiscreteAct = numel(actInfo.Elements);

Create a recurrent deep neural network for the actor. To create a recurrent neural network, use a sequenceInputLayer as the input layer and include at least one lstmLayer.

actorNetwork = [
    sequenceInputLayer(numObs,'Normalization','none','Name','state')
    fullyConnectedLayer(8,'Name','fc')
    reluLayer('Name','relu')
    lstmLayer(8,'OutputMode','sequence','Name','lstm')
    fullyConnectedLayer(numDiscreteAct,'Name','output')
    softmaxLayer('Name','actionProb')];

Create a stochastic actor representation for the network.

actorOptions = rlRepresentationOptions('LearnRate',1e-3,'GradientThreshold',1);
actor = rlStochasticActorRepresentation(actorNetwork,obsInfo,actInfo,...
    'Observation','state', actorOptions);