rlDiscreteCategoricalActor

Stochastic categorical actor with a discrete action space for reinforcement learning agents

Since R2022a

Description

This object implements a function approximator to be used as a stochastic actor within a reinforcement learning agent with a discrete action space. A discrete categorical actor takes an environment observation as input and returns as output a random action sampled from a categorical (also known as Multinoulli) probability distribution, thereby implementing a parametrized stochastic policy. After you create an rlDiscreteCategoricalActor object, use it to create a suitable agent, such as rlACAgent or rlPGAgent. For more information on creating actors and critics, see Create Policies and Value Functions.

Creation

Syntax

actor = rlDiscreteCategoricalActor(net,observationInfo,actionInfo)

actor = rlDiscreteCategoricalActor({basisFcn,W0},observationInfo,actionInfo)

actor = rlDiscreteCategoricalActor(___,Name=Value)

Description

actor = rlDiscreteCategoricalActor(net,observationInfo,actionInfo) creates a stochastic actor with a discrete action space, using the deep neural network net as underlying approximation model. For this actor, actionInfo must specify a discrete action space. The network input layers are automatically associated with the environment observation channels according to the dimension specifications in observationInfo. The network must have a single output layer with as many elements as the number of possible discrete actions, as specified in actionInfo. This function sets the ObservationInfo and ActionInfo properties of actor to the inputs observationInfo and actionInfo, respectively.

actor = rlDiscreteCategoricalActor({basisFcn,W0},observationInfo,actionInfo) creates a discrete space stochastic actor using a custom basis function as underlying approximation model. The first input argument is a two-element cell array whose first element is the handle basisFcn to a custom basis function and whose second element is the initial weight matrix W0. This function sets the ObservationInfo and ActionInfo properties of actor to the inputs observationInfo and actionInfo, respectively.

actor = rlDiscreteCategoricalActor(___,Name=Value) specifies names of the observation input layers (for network-based approximators) or sets the UseDevice property using one or more name-value arguments. Specifying the input layer names allows you explicitly associate the layers of your network approximator with specific environment channels. For all types of approximators, you can specify the device where computations for actor are executed, for example UseDevice="gpu".

Input Arguments

net — Deep neural network

array of Layer objects | layerGraph object | DAGNetwork object | SeriesNetwork object | dlNetwork object (preferred)

Deep neural network used as the underlying approximator within the actor, specified as one of the following:

• Array of Layer objects

• layerGraph object

• DAGNetwork object

• SeriesNetwork object

• dlnetwork object

Note

Among the different network representation options, dlnetwork is preferred, since it has built-in validation checks and supports automatic differentiation. If you pass another network object as an input argument, it is internally converted to a dlnetwork object. However, best practice is to convert other representations to dlnetwork explicitly before using it to create a critic or an actor for a reinforcement learning agent. You can do so using dlnet=dlnetwork(net), where net is any Deep Learning Toolbox™ neural network object. The resulting dlnet is the dlnetwork object that you use for your critic or actor. This practice allows a greater level of insight and control for cases in which the conversion is not straightforward and might require additional specifications.

The network must have as many input layers as the number of environment observation channels (with each input layer receiving input from an observation channel), and a single output layer with as many elements as the number of possible discrete actions. Since the actor must return the probability of executing each possible action, the software automatically adds a softmaxLayer as a final output layer if you do not specify it explicitly. When computing the action, the actor then randomly samples the distribution to return an action.

rlDiscreteCategoricalActor objects support recurrent deep neural networks. For an example, see Create Discrete Categorical Actor from Deep Recurrent Neural Network.

The learnable parameters of the actor are the weights of the deep neural network. For a list of deep neural network layers, see List of Deep Learning Layers. For more information on creating deep neural networks for reinforcement learning, see Create Policies and Value Functions.

basisFcn — Custom basis function

function handle

Custom basis function, specified as a function handle to a user-defined MATLAB function. The user defined function can either be an anonymous function or a function on the MATLAB path. The number of the action to be taken based on the current observation, which is the output of the actor, is randomly sampled from a categorical distribution with probabilities p = softmax(W'*B), where W is a weight matrix containing the learnable parameters and B is the column vector returned by the custom basis function. Each element of p represents the probability of executing the corresponding action from the observed state.

Your basis function must have the following signature.

B = myBasisFunction(obs1,obs2,...,obsN)

Here, obs1 to obsN are inputs in the same order and with the same data type and dimensions as the environment observation channels defined in observationInfo.

Example: @(obs1,obs2,obs3) [obs3(2)*obs1(1)^2; abs(obs2(5)+obs3(1))]

W0 — Initial value of the basis function weights

matrix

Initial value of the basis function weights W, specified as a matrix having as many rows as the length of the vector returned by the basis function and as many columns as the dimension of the action space.

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Example: UseDevice="gpu"

ObservationInputNames — Network input layers names corresponding to the environment observation channels

string array | cell array of strings | cell array of character vectors

Network input layers names corresponding to the environment observation channels, specified as a string array or a cell array of strings or character vectors. The function assigns, in sequential order, each environment observation channel specified in observationInfo to each layer whose name is specified in the array assigned to this argument. Therefore, the specified network input layers, ordered as indicated in this argument, must have the same data type and dimensions as the observation channels, as ordered in observationInfo.

This name-value argument is supported only when the approximation model is a deep neural network.

Example: ObservationInputNames={"obsInLyr1_airspeed","obsInLyr2_altitude"}

Properties

ObservationInfo — Observation specifications

rlFiniteSetSpec object | rlNumericSpec object | array

Observation specifications, specified as an rlFiniteSetSpec or rlNumericSpec object or an array containing a mix of such objects. Each element in the array defines the properties of an environment observation channel, such as its dimensions, data type, and name.

When you create the approximator object, the constructor function sets the ObservationInfo property to the input argument observationInfo.

You can extract observationInfo from an existing environment, function approximator, or agent using getObservationInfo. You can also construct the specifications manually using rlFiniteSetSpec or rlNumericSpec.

Example: [rlNumericSpec([2 1]) rlFiniteSetSpec([3,5,7])]

ActionInfo — Action specifications

rlFiniteSetSpec object

Action specifications, specified as an rlNumericSpec object. This object defines the properties of the environment action channel, such as its dimensions, data type, and name.

Note

Only one action channel is allowed.

When you create the approximator object, the constructor function sets the ActionInfo property to the input argument actionInfo.

You can extract ActionInfo from an existing environment, approximator object, or agent using getActionInfo. You can also construct the specification manually using rlFiniteSetSpec.

Example: rlNumericSpec([2 1])

Normalization — Normalization method

"none" (default) | string array

Normalization method, returned as an array in which each element (one for each input channel defined in the observationInfo and actionInfo properties, in that order) is one of the following values:

• "none" — Do not normalize the input of the function approximator object.

• "rescale-zero-one" — Normalize the input by rescaling it to the interval between 0 and 1. The normalized input Y is (U–Min)./(UpperLimit–LowerLimit), where U is the nonnormalized input. Note that nonnormalized input values lower than LowerLimit result in normalized values lower than 0. Similarly, nonnormalized input values higher than UpperLimit result in normalized values higher than 1. Here, UpperLimit and LowerLimit are the corresponding properties defined in the specification object of the input channel.

• "rescale-symmetric" — Normalize the input by rescaling it to the interval between –1 and 1. The normalized input Y is 2(U–LowerLimit)./(UpperLimit–LowerLimit) – 1, where U is the nonnormalized input. Note that nonnormalized input values lower than LowerLimit result in normalized values lower than –1. Similarly, nonnormalized input values higher than UpperLimit result in normalized values higher than 1. Here, UpperLimit and LowerLimit are the corresponding properties defined in the specification object of the input channel.

Note

When you specify the Normalization property of rlAgentInitializationOptions, normalization is applied only to the approximator input channels corresponding to rlNumericSpec specification objects in which both the UpperLimit and LowerLimit properties are defined. After you create the agent, you can use setNormalizer to assign normalizers that use any normalization method. For more information on normalizer objects, see rlNormalizer.

Example: "rescale-symmetric"

UseDevice — Computation device used for training and simulation

"cpu" (default) | "gpu"

Computation device used to perform operations such as gradient computation, parameter update and prediction during training and simulation, specified as either "cpu" or "gpu".

The "gpu" option requires both Parallel Computing Toolbox™ software and a CUDA^® enabled NVIDIA^® GPU. For more information on supported GPUs see GPU Computing Requirements (Parallel Computing Toolbox).

You can use gpuDevice (Parallel Computing Toolbox) to query or select a local GPU device to be used with MATLAB^®.

Note

Training or simulating an agent on a GPU involves device-specific numerical round-off errors. These errors can produce different results compared to performing the same operations using a CPU.

To speed up training by using parallel processing over multiple cores, you do not need to use this argument. Instead, when training your agent, use an rlTrainingOptions object in which the UseParallel option is set to true. For more information about training using multicore processors and GPUs for training, see Train Agents Using Parallel Computing and GPUs.

Example: "gpu"

Learnables — Learnable parameters of the approximator object

cell array of dlarray objects

Learnable parameters of the approximation object, specified as a cell array of dlarray objects. This property contains the learnable parameters of the approximation model used by the approximator object.

Example: {dlarray(rand(256,4)),dlarray(rand(256,1))}

State — State of the approximator object

cell array of dlarray objects

State of the approximation object, specified as a cell array of dlarray objects. For dlnetwork-based models, this property contains the Value column of the State property table of the dlnetwork model. The elements of the cell array are the state of the recurrent neural network used in the approximator (if any), as well as the state for the batch normalization layer (if used).

For model types that are not based on a dlnetwork object, this property is an empty cell array, since these model types do not support states.

Example: {dlarray(rand(256,1)),dlarray(rand(256,1))}

Object Functions

rlACAgent	Actor-critic (AC) reinforcement learning agent
rlPGAgent	Policy gradient (PG) reinforcement learning agent
rlPPOAgent	Proximal policy optimization (PPO) reinforcement learning agent
getAction	Obtain action from agent, actor, or policy object given environment observations
evaluate	Evaluate function approximator object given observation (or observation-action) input data
gradient	(Not recommended) Evaluate gradient of function approximator object given observation and action input data
accelerate	(Not recommended) Option to accelerate computation of gradient for approximator object based on neural network
getLearnableParameters	Obtain learnable parameter values from agent, function approximator, or policy object
setLearnableParameters	Set learnable parameter values of agent, function approximator, or policy object
setModel	Set approximation model in function approximator object
getModel	Get approximation model from function approximator object

Examples

Create Discrete Categorical Actor from Deep Neural Network

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 there is a single observation channel that carries 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 actions, labeled -10, 0, and 10.

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

A discrete categorical actor implements a parametrized stochastic policy for a discrete action space. This actor takes an observation as input and returns as output a random action sampled (among the finite number of possible actions) from a categorical probability distribution.

To model the probability distribution within the actor, use a neural network with one input layer (which receives the content of the environment observation channel, as specified by obsInfo) and one output layer.

The output layer must return a vector of probabilities of taking each possible action, as specified by actInfo. Therefore, each element of the output vector must be between 0 and 1. Using softmax as the output layer enforces this requirement (the software automatically adds a softmaxLayer as a final output layer if you do not specify it explicitly).

Note that prod(obsInfo.Dimension) returns the total number of dimensions of the observation space regardless of whether the observation space is arranged as a column vector, row vector, or matrix, while numel(actInfo.Dimension) returns the number of elements of the discrete action space.

Define the network as an array of layer objects.

net = [  
    featureInputLayer(prod(obsInfo.Dimension))
    fullyConnectedLayer(16)
    reluLayer
    fullyConnectedLayer(16)
    reluLayer
    fullyConnectedLayer(numel(actInfo.Elements))
    ];

Convert the network to a dlnetwork object and display the number of learnable parameters.

net = dlnetwork(net);
summary(net)

   Initialized: true

   Number of learnables: 403

   Inputs:
      1   'input'   4 features

Create the actor with rlDiscreteCategoricalActor, using the network, the observations and action specification objects. When the network has multiple input layers, they are automatically associated with the environment observation channels according to the dimension specifications in obsInfo.

actor = rlDiscreteCategoricalActor(net,obsInfo,actInfo);

To check your actor, use getAction to return an action from a random observation vector, given the current network weights.

act = getAction(actor,{rand(obsInfo.Dimension)}); 
act

act = 1x1 cell array
    {[-10]}

To return the probability distribution of the actions, given an observation, use evaluate.

prb = evaluate(actor,{rand(obsInfo.Dimension)});
prb{1}

ans = 3x1 single column vector

    0.3736
    0.1875
    0.4389

You can now use the actor (along with a critic) to create an agent for the environment described by the given observation specification object. Examples of agents that can work with a continuous observation space, a discrete action space, and use a discrete categorical actor, are rlACAgent, rlPGAgent, rlPPOAgent, and rlTRPOAgent.

For more information on creating approximator objects such as actors and critics, see Create Policies and Value Functions.

Create Discrete Categorical Actor from Deep Neural Network Specifying Input Layer Name

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 there is a single observation channel that carries 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 actions, labeled -10, 0, and 10.

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

A discrete categorical actor implements a parametrized stochastic policy for a discrete action space. This actor takes an observation as input and returns as output a random action sampled (among the finite number of possible actions) from a categorical probability distribution.

To model the probability distribution within the actor, use a neural network with one input layer (which receives the content of the environment observation channel, as specified by obsInfo) and one output layer. The output layer must return a vector of probabilities for each possible action, as specified by actInfo. Therefore, each element of the output vector must be between 0 and 1. Using softmax as the output layer enforces this requirement (the software automatically adds a softmaxLayer as a final output layer if you do not specify it explicitly).

Note that prod(obsInfo.Dimension) returns the total number of dimensions of the observation space regardless of whether the observation space is arranged as a column vector, row vector, or matrix, while numel(actInfo.Dimension) returns the number of elements of the discrete action space.

Define the network as an array of layer objects. Specify a name for the input layer, so you can later explicitly associate it with the observation channel.

net = [  
    featureInputLayer( ...
        prod(obsInfo.Dimension), ...
        Name="netObsIn")
    fullyConnectedLayer(32)
    reluLayer
    fullyConnectedLayer(numel(actInfo.Elements))
    softmaxLayer(Name="actionProb")
    ];

Convert the network to a dlnetwork object and display the number of learnable parameters (weights).

net = dlnetwork(net);
summary(net)

   Initialized: true

   Number of learnables: 259

   Inputs:
      1   'netObsIn'   4 features

Create the actor with rlDiscreteCategoricalActor, using the network, the observations and action specification objects, and the name of the network input layer.

actor = rlDiscreteCategoricalActor(net, ...
    obsInfo,actInfo,...
    Observation="netObsIn");

To validate your actor, use getAction to return an action from a random observation, given the current network weights.

act = getAction(actor,{rand(obsInfo.Dimension)}); 
act{1}

ans = -10

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

    0.3038
    0.2658
    0.4304

You can now use the actor (along with a critic) to create an agent for the environment described by the given observation specification object. Examples of agents that can work with a continuous observation space, a discrete action space, and use a discrete categorical actor, are rlACAgent, rlPGAgent, rlPPOAgent, and rlTRPOAgent.

For more information on creating approximator objects such as actors and critics, see Create Policies and Value Functions.

Create Discrete Categorical Actor from Custom Basis Function

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 consisting of two channels, the first carrying a two-dimensional vector in a continuous space, the second carrying a two dimensional vector that can assume only three values, -[1 2], [0 1], and [1 3]. Therefore a single observation consists of two two-dimensional vectors, one continuous, the other discrete.

obsInfo = [rlNumericSpec([2 1]) rlFiniteSetSpec({-[1 2],[0 1],[1 3]})];

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 three possible actions, labeled 7, 5, and 3.

actInfo = rlFiniteSetSpec([7 5 3]);

A discrete categorical actor implements a parametrized stochastic policy for a discrete action space. To model the parametrized probability distribution within the actor, use a custom basis function with two inputs (which receive the content of the environment observation channels, as specified by obsInfo).

Create a function that returns a vector of four elements, depending on a given observation.

myBasisFcn = @(obsC,obsD) [obsC(1)^2-obsD(2)^2; 
                           obsC(2)^2-obsD(1)^2;  
                           exp(obsC(2))+abs(obsD(1)); 
                           exp(obsC(1))+abs(obsD(2))];

The actor samples the action randomly, according to the probability distribution softmax(W'*myBasisFcn(obsC,obsD)). Here, W is a weight matrix, containing the learnable parameters, which must have as many rows as the length of the basis function output (for this example, four), and as many columns as the number of possible actions (for this example, three).

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 = rlDiscreteCategoricalActor({myBasisFcn,W0},obsInfo,actInfo);

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

getAction(actor,{rand(2,1),[1 1]})

ans = 1x1 cell array
    {[3]}

Note that the discrete set constraint is not enforced.

getAction(actor,{rand(2,1),[0.5 -0.7]})

ans = 1x1 cell array
    {[3]}

To return the probability of each action as a function of a random observation (and given the current weights), use evaluate.

prb = evaluate(actor, ...
    {rand(obsInfo(1).Dimension), ...
     rand(obsInfo(2).Dimension)})

prb = 1x1 cell array
    {3x1 single}

prb{1}

ans = 3x1 single column vector

    0.3434
    0.2074
    0.4492

You can now use the actor (along with a critic) to create an agent for the environment described by the given observation specification object. Examples of agents that can work with a mixed observation space, a discrete action space, and use a discrete categorical actor, are rlACAgent, rlPGAgent, and rlPPOAgent. rlTRPOAgent does not support actors or critics that use custom basis functions.

For more information on creating approximator objects such as actors and critics, see Create Policies and Value Functions.

Create Discrete Categorical Actor from Deep Recurrent Neural Network

This example shows you how to create a stochastic actor with a discrete action space using a recurrent neural network.

For this example, use the same environment used in Train PG Agent to Balance Cart-Pole System. Load the environment and obtain the observation and action specifications.

env = rlPredefinedEnv("CartPole-Discrete");
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: [0×0 string]
      Dimension: [1 1]
       DataType: "double"

A discrete categorical actor implements a parametrized stochastic policy for a discrete action space. This actor takes an observation as input and returns as output a random action sampled (among the finite number of possible actions) from a categorical probability distribution.

To model the probability distribution within the actor, use a neural network with one input layer (which receives the content of the environment observation channel, as specified by obsInfo) and one output layer.

The output layer must return a vector of probabilities of taking each possible action, as specified by actInfo. Therefore, each element of the output vector must be between 0 and 1. Using softmax as the output layer enforces this requirement (the software automatically adds a softmaxLayer as a final output layer if you do not specify it explicitly).

Note that prod(obsInfo.Dimension) returns the total number of dimensions of the observation space regardless of whether the observation space is arranged as a column vector, row vector, or matrix, while numel(actInfo.Dimension) returns the number of elements of the discrete action space.

Define the network as an array of layer objects. To create a recurrent network, use a sequenceInputLayer as the input layer and include at least one lstmLayer.

net = [
    sequenceInputLayer( ...
        prod(obsInfo.Dimension), ...
        Name="netObsIn")
    fullyConnectedLayer(8)
    reluLayer
    lstmLayer(8)
    fullyConnectedLayer( ...
    numel(actInfo.Elements)) 
    ];

Convert the network to a dlnetwork object and display the number of learnable parameters (weights).

net = dlnetwork(net);
summary(net)

   Initialized: true

   Number of learnables: 602

   Inputs:
      1   'netObsIn'   Sequence input with 4 dimensions

Create a discrete categorical actor using the network, the environment specifications, and the name of the network input layer to be associated with the observation channel.

actor = rlDiscreteCategoricalActor(net, ...
    obsInfo,actInfo,...
    Observation="netObsIn");

To check your actor use getAction to return one of the two possible actions, depending on a given random observation and on the current network weights.

act = getAction(actor,{rand(obsInfo.Dimension)});
act{1}

ans = -10

To return the probability of each of the two possible action, use evaluate. Note that the type of the returned numbers is single, not double.

prb = evaluate(actor,{rand(obsInfo.Dimension)});
prb{1}

ans = 2×1 single column vector

    0.4549
    0.5451

You can use dot notation to extract and set the current state of the recurrent neural network in the actor.

actor.State

ans=2×1 cell array
    {8×1 dlarray}
    {8×1 dlarray}

actor.State = {
      dlarray(-0.1*rand(8,1))
      dlarray(0.1*rand(8,1)) 
      };

To evaluate the actor using sequential observations, use the sequence length (time) dimension. For example, obtain actions for 5 independent sequences each one consisting of 9 sequential observations.

[action,state] = getAction(actor, ...
    {rand([obsInfo.Dimension 5 9])});

Display the action corresponding to the seventh element of the observation sequence in the fourth sequence.

action = action{1};
action(1,1,4,7)

ans = 10

Display the updated state of the recurrent neural network.

state

state=2×1 cell array
    {8×5 single}
    {8×5 single}

You can now use the actor (along with a critic) to create an agent for the environment described by the given observation specification object. Examples of agents that can work with a continuous observation space, a discrete action space, and use a discrete categorical actor, are rlACAgent, rlPGAgent, and rlPPOAgent. rlTRPOAgent does not support actors or critics with recurrent neural networks.

For more information on input and output format for recurrent neural networks, see the Algorithms section of lstmLayer. For more information on creating approximator objects such as actors and critics, see Create Policies and Value Functions.

Version History

Introduced in R2022a