rlValueFunction

Value function approximator object for reinforcement learning agents

Since R2022a

Description

This object implements a value function approximator object that you can use as a critic for a reinforcement learning agent. A value function is a mapping from an environment observation to the value of a policy. Specifically, its output is a scalar that represents the expected discounted cumulative long-term reward when an agent starts from the state corresponding to the given observation and executes actions according to a given policy afterwards. After you create an rlValueFunction critic, use it to create an agent such as an rlACAgent, rlPGAgent, or rlPPOAgent agent. For an example of this workflow, see Create Actor and Critic Representations. For more information on creating value functions, see Create Policies and Value Functions.

Creation

Syntax

critic = rlValueFunction(net,observationInfo)

critic = rlValueFunction(net,ObservationInputNames=netObsNames)

critic = rlValueFunction(tab,observationInfo)

critic = rlValueFunction({basisFcn,W0},observationInfo)

critic = rlValueFunction(___,UseDevice=useDevice)

Description

critic = rlValueFunction(net,observationInfo) creates the value-function object critic using the deep neural network net as approximation model, and sets the ObservationInfo property of critic to the observationInfo input argument. The network input layers are automatically associated with the environment observation channels according to the dimension specifications in observationInfo.

critic = rlValueFunction(net,ObservationInputNames=netObsNames) specifies the network input layer names to be associated with the environment observation channels. The function assigns, in sequential order, each environment observation channel specified in observationInfo to the layer specified by the corresponding name in the string array netObsNames. Therefore, the network input layers, ordered as the names in netObsNames, must have the same data type and dimensions as the observation channels, as ordered in observationInfo.

critic = rlValueFunction(tab,observationInfo) creates the value function object critic with a discrete observation space, from the table tab, which is an rlTable object containing a column array with as many elements as the number of possible observations. The function sets the ObservationInfo property of critic to the observationInfo input argument, which in this case must be a scalar rlFiniteSetSpec object.

critic = rlValueFunction({basisFcn,W0},observationInfo) creates the value function object critic using a custom basis function as underlying approximator. 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 vector W0. The function sets the ObservationInfo property of critic to the observationInfo input argument.

critic = rlValueFunction(___,UseDevice=useDevice) specifies the device used to perform computations for the critic object, and sets the UseDevice property of critic to the useDevice input argument. You can use this syntax with any of the previous input-argument combinations.

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 critic, 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 returning a scalar value.

rlValueFunction objects support recurrent deep neural networks.

The learnable parameters of the critic 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.

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

string array | 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 character vectors. When you use this argument after 'ObservationInputNames', the function assigns, in sequential order, each environment observation channel specified in observationInfo to each network input layer specified by the corresponding name in the string array netObsNames. Therefore, the network input layers, ordered as the names in netObsNames, must have the same data type and dimensions as the observation channels, as ordered in observationInfo.

Example: {"NetInput1_airspeed","NetInput2_altitude"}

tab — Value table

rlTable object

Value table, specified as an rlTable object containing a column vector with length equal to the number of possible observations from the environment. Each element is the predicted discounted cumulative long-term reward when the agent starts from the given observation and takes the best possible action. The elements of this vector are the learnable parameters of the representation.

basisFcn — Custom basis function

function handle

Custom basis function, specified as a function handle to a user-defined function. The user defined function can either be an anonymous function or a function on the MATLAB path. The output of the critic is the scalar c = W'*B, where W is a weight vector containing the learnable parameters and B is the column vector returned by the custom basis function.

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.

For an example on how to use a basis function to create a value function critic with a mixed continuous and discrete observation space, see Create Mixed Observation Space Value Function Critic from Custom Basis Function.

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

W0 — Initial value of basis function weights

column vector

Initial value of the basis function weights W, specified as a column vector having the same length as the vector returned by the basis function.

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.

rlValueFucntion sets the ObservationInfo property of critic to the input argument observationInfo.

You can extract ObservationInfo from an existing environment or agent using getObservationInfo. You can also construct the specifications manually.

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"

Object Functions

rlACAgent	Actor-critic (AC) reinforcement learning agent
rlPGAgent	Policy gradient (PG) reinforcement learning agent
rlPPOAgent	Proximal policy optimization (PPO) reinforcement learning agent
getValue	Obtain estimated value from a critic given environment observations and actions
evaluate	Evaluate function approximator object given observation (or observation-action) input data
gradient	Evaluate gradient of function approximator object given observation and action input data
accelerate	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 function approximation model for actor or critic
getModel	Get function approximator model from actor or critic

Examples

Create Value Function Critic 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]);

A value-function critic takes the current observation as input and returns a single scalar as output (the estimated discounted cumulative long-term reward for following the policy from the state corresponding to the current observation).

To model the parametrized value function within the critic, use a neural network with one input layer (which returns the content of the observation channel, as specified by obsInfo) and one output layer (returning the scalar value). Note that prod(obsInfo.Dimension) returns the total number of dimensions of the observation space regardless of whether the observation space is a column vector, row vector, or matrix.

Define the network as an array of layer objects.

net = [ 
    featureInputLayer(prod(obsInfo.Dimension));
    fullyConnectedLayer(10);
    reluLayer;
    fullyConnectedLayer(1)
    ];

Convert the network to a dlnetwork object.

dlnet = dlnetwork(net);

You can plot the network using plot and display its main characteristics, like the number of weights, using summary.

plot(dlnet)

summary(dlnet)

   Initialized: true

   Number of learnables: 61

   Inputs:
      1   'input'   4 features

Create the critic using the network and the observation specification object.

critic = rlValueFunction(dlnet,obsInfo)

critic = 
  rlValueFunction with properties:

    ObservationInfo: [1x1 rl.util.rlNumericSpec]
          UseDevice: "cpu"

To check your critic, use getValue to return the value of a random observation, using the current network weights.

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

v = single
    0.5196

You can now use the critic (along with an actor) 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, and use a value function critic, 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 Actor and Critic

Create an actor and a critic that you can use to define a reinforcement learning agent such as an Actor-Critic (AC) agent. For this example, create actor and critic for an agent that can be trained against the cart-pole environment described in Train AC Agent to Balance Cart-Pole System.

First, create the environment. Then, extract the observation and action specifications from the environment. You need these specifications to define the agent and critic.

env = rlPredefinedEnv("CartPole-Discrete");
obsInfo = getObservationInfo(env);
actInfo = getActionInfo(env);

A value-function critic takes the current observation as input and returns a single scalar as output (the estimated discounted cumulative long-term reward for following the policy from the state corresponding to the current observation).

To model the parametrized value function within the critic, use a neural network with one input layer (receiving the content of the observation channel, as specified by obsInfo) and one output layer (returning the scalar value).

Define the network as an array of layer objects, and get the dimension of the observation space from the environment specification objects. Name the network input layer criticNetInput.

CriticNet = [
    featureInputLayer(prod(obsInfo.Dimension));
    fullyConnectedLayer(10);
    reluLayer;
    fullyConnectedLayer(10);
    reluLayer;
    fullyConnectedLayer(1)];

Convert the network to a dlnetwork object.

CriticNet = dlnetwork(CriticNet);

To display the network main characteristics, use summary.

summary(CriticNet)

   Initialized: true

   Number of learnables: 171

   Inputs:
      1   'input'   4 features

Create the critic using CriticNet and the environment specification object. Set the observation name to observation, which is the name of the criticNetwork input layer.

critic = rlValueFunction(CriticNet,obsInfo)

critic = 
  rlValueFunction with properties:

    ObservationInfo: [1x1 rl.util.rlNumericSpec]
          UseDevice: "cpu"

Check your critic using getValue to return the value of a random observation, given the current network weights.

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

v = single
    -0.3229

AC agents use a parametrized stochastic policy, which for discrete action spaces is implemented by a discrete categorical actor.

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 parametrized policy 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.

You can obtain the number of actions from the actInfo specification. Name the network output actorNetOutput.

actorNet = [
    featureInputLayer(prod(obsInfo.Dimension))
    fullyConnectedLayer(10);
    reluLayer;
    fullyConnectedLayer(10);
    reluLayer;
    fullyConnectedLayer(numel(actInfo.Elements)) ];

Convert the network to a dlnetwork object.

actorNet = dlnetwork(actorNet);

To display the network main characteristics, use summary.

summary(actorNet)

   Initialized: true

   Number of learnables: 182

   Inputs:
      1   'input'   4 features

Create the actor using rlDiscreteCategoricalActor together with the observation and action specifications.

actor = rlDiscreteCategoricalActor(actorNet,obsInfo,actInfo)

actor = 
  rlDiscreteCategoricalActor with properties:

       Distribution: [1x1 rl.distribution.rlDiscreteGaussianDistribution]
    ObservationInfo: [1x1 rl.util.rlNumericSpec]
         ActionInfo: [1x1 rl.util.rlFiniteSetSpec]
          UseDevice: "cpu"

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

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

a = 1x1 cell array
    {[-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
    {2x1 single}

prb{1}

ans = 2x1 single column vector

    0.5917
    0.4083

Specify the optimization options for the actor and the critic using rlOptimizerOptions. These options control the learning of the network parameters. For both networks, set the gradient threshold to 1. For this example, set the learning rate to 0.01. For the actor network, set the learning rate to 0.05.

criticOpts = rlOptimizerOptions( ...
    LearnRate=1e-2,...
    GradientThreshold=1);

actorOpts = rlOptimizerOptions( ...
    LearnRate=5e-2,...
    GradientThreshold=1);

Specify agent options, including the objects previously created for both actor and critic.

agentOpts = rlACAgentOptions(...
    NumStepsToLookAhead=32,...
    DiscountFactor=0.99,...
    CriticOptimizerOptions=criticOpts,...
    ActorOptimizerOptions=actorOpts);

Create an AC agent using the actor, the critic and the agent options object.

agent = rlACAgent(actor,critic,agentOpts)

agent = 
  rlACAgent with properties:

            AgentOptions: [1x1 rl.option.rlACAgentOptions]
    UseExplorationPolicy: 1
         ObservationInfo: [1x1 rl.util.rlNumericSpec]
              ActionInfo: [1x1 rl.util.rlFiniteSetSpec]
              SampleTime: 1

To check your agent, use getAction to return a random action from a given observation, using the current actor and critic network weights.

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

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

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

For additional examples showing how to create actors and critics for different agent types, see Train DDPG Agent to Control Double Integrator System and Train DQN Agent to Balance Cart-Pole System.

Create Value Function Critic from Table

Create a finite set observation specification object (or alternatively use getObservationInfo to extract the specification object from an environment with a discrete observation space). For this example, define the observation space as a finite set consisting of four possible values 1, 3, 5 and 7.

obsInfo = rlFiniteSetSpec([1 3 5 7]);

A value-function critic takes the current observation as input and returns a single scalar value as output (the estimated discounted cumulative long-term reward for following the policy from the state corresponding to the current observation).

Since both observation and action spaces are discrete and low-dimensional, use a table to model the value function within the critic. rlTable creates a value table object from the observation and action specifications objects.

vTable = rlTable(obsInfo);

The table is a column vector in which each entry stores the value of the corresponding observation, under the given policy. You can access the table using the Table property of the vTable object. The initial value of each element is zero.

vTable.Table

ans = 4×1

     0
     0
     0
     0

You can also initialize the table to any value, in this case, an array containing all the integers from 1 to 4.

vTable.Table = reshape(1:4,4,1)

vTable = 
  rlTable with properties:

    Table: [4x1 double]

Create the critic using the table and the observation specification object.

critic = rlValueFunction(vTable,obsInfo)

critic = 
  rlValueFunction with properties:

    ObservationInfo: [1x1 rl.util.rlFiniteSetSpec]
          UseDevice: "cpu"

To check your critic, use the getValue function to return the value of a given observation, using the current table entries.

v = getValue(critic,{7})

v = 4

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

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

Create Value Function Critic 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 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]);

A value-function critic takes the current observation as input and returns a single scalar as output (the estimated discounted cumulative long-term reward for following the policy from the state corresponding to the current observation).

To model the parametrized value function within the critic, use a custom basis function. Create a custom function that returns a vector of three elements, given an observation as input.

myBasisFcn = @(myobs) [
    myobs(2)^2; 
    myobs(3)+exp(myobs(1)); 
    abs(myobs(4)) ]

myBasisFcn = function_handle with value:
    @(myobs)[myobs(2)^2;myobs(3)+exp(myobs(1));abs(myobs(4))]

The output of the critic is the scalar W'*myBasisFcn(myobs), which represents the estimated value of the observation under the given policy. Here W is a weight column vector which must have the same size as the custom basis function output. The elements of W are the learnable parameters.

Define an initial parameter vector.

W0 = [3;5;2];

Create the critic. The first argument is a two-element cell containing both the handle to the custom function and the initial weight vector. The second argument is the observation specification object.

critic = rlValueFunction({myBasisFcn,W0},obsInfo)

critic = 
  rlValueFunction with properties:

    ObservationInfo: [1x1 rl.util.rlNumericSpec]
          UseDevice: "cpu"

To check your critic, use the getValue function to return the value of a given observation, using the current parameter vector.

v = getValue(critic,{[2 4 6 8]'})

v = 130.9453

You can now use the critic (along with an actor) to create an agent for the environment described by the given observation specification object. Examples of agents that can work with continuous observation spaces, and use a value function critic, are rlACAgent, rlPGAgent, 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 Value Function Critic from Recurrent Neural Network

Create an environment and obtain observation and action information.

env = rlPredefinedEnv("CartPole-Discrete");
obsInfo = getObservationInfo(env);

A value-function critic takes the current observation as input and returns a single scalar value as output (the estimated discounted cumulative long-term reward for following the policy from the state corresponding to the current observation).

To model the parametrized value function within the critic, use a recurrent neural network with one input layer (receiving the content of the observation channel, as specified by obsInfo) and one output layer (returning the scalar value).

Define the network as an array of layer objects. To create a recurrent network, use a sequenceInputLayer as the input layer (with size equal to the number of dimensions of the observation channel) and include at least one lstmLayer.

myNet = [
    sequenceInputLayer(obsInfo.Dimension(1))
    fullyConnectedLayer(8)
    reluLayer
    lstmLayer(8)
    fullyConnectedLayer(1) ];

Convert the network to a dlnetwork object.

dlNet = dlnetwork(myNet);

Display a summary of network characteristics.

summary(dlNet)

   Initialized: true

   Number of learnables: 593

   Inputs:
      1   'sequenceinput'   Sequence input with 4 dimensions

Create a value function representation object for the critic.

critic = rlValueFunction(dlNet,obsInfo)

critic = 
  rlValueFunction with properties:

    ObservationInfo: [1x1 rl.util.rlNumericSpec]
          UseDevice: "cpu"

To check your critic, use the getValue function to return the value of a random observation, using the current network weights.

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

v = single
    0.0017

You can use getState and setState to extract and set the current state of the recurrent neural network in the critic.

getState(critic)

ans=2×1 cell array
    {8x1 single}
    {8x1 single}

critic = setState(critic, ...
    {-0.01*single(rand(8,1)), ...
      0.01*single(rand(8,1))});

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

[value,state] = getValue(critic, ...
    {rand([obsInfo.Dimension 5 9])});

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

value(1,4,7)

ans = single
    0.0766

Display the updated state of the recurrent neural network.

state

state=2×1 cell array
    {8x5 single}
    {8x5 single}

You can now use the critic (along with an actor) to create an agent for the environment described by the given observation specification object. Examples of agents that can work with continuous observation spaces, and use a value function critic, are rlACAgent, rlPGAgent, rlPPOAgent. rlTRPOAgent does not support actors or critics that use recurrent 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 critics and critics, see Create Policies and Value Functions.

Create Mixed Observation Space Value Function Critic from Custom Basis Function

Create a finite-set observation specification object (or alternatively use getObservationInfo to extract the specification object from an environment). For this example, define the observation space as two channels where the first one is a single observation labeled 7, 5, 3, or 1, and the second one is a vector over a continuous three-dimensional space.

obsInfo = [rlFiniteSetSpec([7 5 3 1]) rlNumericSpec([3 1])];

A value-function critic takes the current observation as input and returns a single scalar as output (the estimated discounted cumulative long-term reward for following the policy from the state corresponding to the current observation).

To model the parametrized value function within the critic, use a custom basis function. Create a custom function that returns a vector of four elements, given the content of the two observation channels as input.

myBasisFcn = @(obsA,obsB) [ obsA(1) + norm(obsB);
                            obsA(1) - norm(obsB);
                            obsA(1)^2 + obsB(3);
                            obsA(1)^2 - obsB(3)];

The output of the critic is the scalar W'*myBasisFcn(myobs), which represents the estimated value of the observation under the given policy. Here W is a weight column vector which must have the same size as the custom basis function output. The elements of W are the learnable parameters.

Define an initial parameter vector.

W0 = ones(4,1);

Create the critic. The first argument is a two-element cell containing both the handle to the custom function and the initial weight vector. The second argument is the observation specification object.

critic = rlValueFunction({myBasisFcn,W0},obsInfo)

critic = 
  rlValueFunction with properties:

    ObservationInfo: [2x1 rl.util.RLDataSpec]
          UseDevice: "cpu"

To check your critic, use the getValue function to return the value of a given observation, using the current parameter vector.

v = getValue(critic,{5,[0.1 0.1 0.1]'})

v = 60

Note that the critic does not enforce the set constraint for the discrete set element.

v = getValue(critic,{-3,[0.1 0.1 0.1]'})

v = 12

You can now use the critic (along with an actor) to create an agent for the environment described by the given observation specification object. Examples of agents that can work with mixed observation spaces, and use a value function critic, are rlACAgent, rlPGAgent, 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.

Version History

Introduced in R2022a