# rlValueFunction

## Description

This object implements a value function approximator object that you can use as a
critic for a reinforcement learning agent. A value function (also known as state-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
actors and critics, see Create Policies and Value Functions.

## Creation

### Syntax

### Description

creates the value-function object `critic`

= rlValueFunction(`net`

,`observationInfo`

)`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`

.

creates the value function object `critic`

= rlValueFunction(`tab`

,`observationInfo`

)`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.

creates the value function object `critic`

= rlValueFunction({`basisFcn`

,`W0`

},`observationInfo`

)`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.

specifies names of the observation input layers (for network-based approximators) or
sets the `critic`

= rlValueFunction(___,`Name=Value`

)`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 `critic`

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 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.

`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 Hybrid 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.

**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])]
```

`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.`"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. Because of these errors, you can get different results on a GPU and on a CPU for the same operation.

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 approximator object

cell array of `dlarray`

objects

Learnable parameters of the approximator 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 approximator object

cell array of `dlarray`

objects

State of the approximator 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 |

`getValue` | Obtain estimated value from a critic given environment observations and actions |

`evaluate` | Evaluate function approximator object given observation (or observation-action) input data |

`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 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 obs`Info`

) 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] Normalization: "none" UseDevice: "cpu" Learnables: {4x1 cell} State: {0x1 cell}

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 Discrete 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] Normalization: "none" UseDevice: "cpu" Learnables: {6x1 cell} State: {0x1 cell}

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: ObservationInfo: [1x1 rl.util.rlNumericSpec] ActionInfo: [1x1 rl.util.rlFiniteSetSpec] Normalization: "none" UseDevice: "cpu" Learnables: {6x1 cell} State: {0x1 cell}

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 Compare DDPG Agent to LQR Controller and Train DQN Agent to Balance Discrete 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] Normalization: "none" UseDevice: "cpu" Learnables: {[4x1 dlarray]} State: {}

To check your critic, use `getValue`

to return the value of a given observation, using the current table entries.

v = getValue(critic,{7})

v = 4

Obtain values for a random batch of 8 observations.

v = getValue(critic,{[1 3 5 7 7 5 3 1]})

`v = `*1×8*
1 2 3 4 4 3 2 1

Get the seventh value in the batch.

v(7)

ans = 2

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 a batch of observations as input and returns a corresponding batch of scalars as output (each element in the batch is the estimated discounted cumulative long-term reward for following the policy from the state corresponding to the 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. Here, the third dimension is the batch dimension. For each element of the batch dimension, the output of the basis function is a vector of three elements.

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

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

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] Normalization: "none" UseDevice: "cpu" Learnables: {[1x3 dlarray]} State: {}

To check your critic, use `getValue`

to return the value of a given observation, using the current parameter vector.

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

`v = `*single*
104

Obtain values for a random batch of 10 observations.

v = getValue(critic,{rand(4,1,10)});

Get the seventh value in the batch.

v(7)

`ans = `*single*
6.9592

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.

### 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 obs`Info`

) 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] Normalization: "none" UseDevice: "cpu" Learnables: {7x1 cell} State: {2x1 cell}

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*
0.0017

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

critic.State

`ans=`*2×1 cell array*
{8x1 dlarray}
{8x1 dlarray}

critic.State = { -0.1*dlarray(rand(8,1)) 0.1*dlarray(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*
0.0769

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 Hybrid 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 an hybrid (that is mixed discrete-continuous) space with the discrete channel carrying a single observation labeled 7, 5, 3, or 1, and the second one being a vector over a continuous three-dimensional space.

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

A value-function critic takes a batch of observations as input and returns as output a corresponding batch of scalars, each representing the estimated discounted cumulative long-term reward (the value) obtained by following the policy from the state corresponding to the given 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. Note that the first channel carries a scalar (one row and one column) but the respective `myBasisFcn`

input has also the batch dimension. Similarly, the second channel carries a vector with three elements, but it has the same batch dimension as the first channel. The sequence dimension is not supported for stateless approximators.

myBasisFcn = @(obsDisc,obsCont) [ obsDisc(1,1,:) + obsCont(1,1,:); obsDisc(1,1,:) - obsCont(2,1,:); obsDisc(1,1,:).^2 + obsCont(3,1,:); obsDisc(1,1,:).^2 - obsCont(3,1,:) ];

The output of the critic is the scalar `W'*myBasisFcn(observation)`

, 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] Normalization: ["none" "none"] UseDevice: "cpu" Learnables: {[1x4 dlarray]} State: {}

To check your critic, use `getValue`

to return the value of a given observation, using the current parameter vector.

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

`v = `*single*
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 = `*single*
12

Obtain values for a random batch of 5 observations.

getValue(critic,{ ... rand([obsInfo(1).Dimension 5]), ... rand([obsInfo(2).Dimension 5]) ... })

`ans = `*1x5 single row vector*
2.8718 0.6859 0.4322 1.5246 2.9352

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.

## Version History

**Introduced in R2022a**

## See Also

### Functions

### Objects

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