accelerate

(Not recommended) Option to accelerate computation of gradient for approximator object based on neural network

Since R2022a

accelerate is not recommended. Use dlaccelerate on your loss function instead. For more information, see accelerate is not recommended.

Syntax

newAppx = accelerate(oldAppx,useAcceleration)

Description

newAppx = accelerate(oldAppx,useAcceleration) returns the new neural-network-based function approximator object newAppx, which has the same configuration as the original object, oldAppx, and the option to accelerate the gradient computation set to the logical value useAcceleration.

Examples

Accelerate Gradient Computation for a Q-Value Function

Create observation and action specification objects (or alternatively use getObservationInfo and getActionInfo to extract the specification objects from an environment). For this example, define an observation space with two channels. The first channel carries an observation from a continuous four-dimensional space. The second carries a discrete scalar observation that can be either zero or one. Finally, the action space is a three-dimensional vector in a continuous action space.

obsInfo = [rlNumericSpec([4 1]) 
           rlFiniteSetSpec([0 1])];

actInfo =  rlNumericSpec([3 1]);

To approximate the Q-value function within the critic, create a recurrent deep neural network. The output layer must be a scalar expressing the value of executing the action given the observation.

Define each network path as an array of layer objects. Get the dimensions of the observation and action spaces from the environment specification objects, and specify a name for the input layers, so you can later explicitly associate them with the appropriate environment channel. Since the network is recurrent, use sequenceInputLayer as the input layer and include an lstmLayer as one of the other network layers.

% Define paths
inPath1 = [ 
    sequenceInputLayer( ...
        prod(obsInfo(1).Dimension), ...
        Name="netObsIn1")
    fullyConnectedLayer(5,Name="infc1")
    ];

inPath2 = [ 
    sequenceInputLayer( ...
        prod(obsInfo(2).Dimension), ...
        Name="netObsIn2")
    fullyConnectedLayer(5,Name="infc2")
    ];

inPath3 = [
    sequenceInputLayer( ...
        prod(actInfo(1).Dimension), ...
        Name="netActIn")
     fullyConnectedLayer(5,Name="infc3") 
     ];

% Concatenate 3 previous layer outputs along dim 1
jointPath = [ 
    concatenationLayer(1,3,Name="cct")
    tanhLayer
    lstmLayer(8,"OutputMode","sequence")
    fullyConnectedLayer(1,Name="jntfc") 
    ];

Assemble dlnetwork object.

net = dlnetwork;
net = addLayers(net,inPath1);
net = addLayers(net,inPath2);
net = addLayers(net,inPath3);
net = addLayers(net,jointPath);

Connect layers.

net = connectLayers(net,"infc1","cct/in1");
net = connectLayers(net,"infc2","cct/in2");
net = connectLayers(net,"infc3","cct/in3");

Plot network.

plot(net)

Initialize network and display the number of weights.

net = initialize(net);
summary(net)

   Initialized: true

   Number of learnables: 832

   Inputs:
      1   'netObsIn1'   Sequence input with 4 dimensions
      2   'netObsIn2'   Sequence input with 1 dimensions
      3   'netActIn'    Sequence input with 3 dimensions

Create the critic with rlQValueFunction, using the network, and the observation and action specification objects.

critic = rlQValueFunction(net, ...
            obsInfo, ...
            actInfo, ...
            ObservationInputNames=["netObsIn1","netObsIn2"], ...
            ActionInputNames="netActIn");

To return the value of the actions as a function of the current observation, use getValue or evaluate.

val = evaluate(critic, ...
                { rand(obsInfo(1).Dimension), ...
                  rand(obsInfo(2).Dimension), ...
                  rand(actInfo(1).Dimension) })

val = 1×1 cell array
    {[0.0089]}

When you use evaluate, the result is a single-element cell array containing the value of the action in the input, given the observation.

val{1}

ans = single
    0.0089

Calculate the gradients of the sum of the three outputs with respect to the inputs, given a random observation.

gro = gradient(critic,"output-input", ...
                { rand(obsInfo(1).Dimension) , ...
                  rand(obsInfo(2).Dimension) , ...
                  rand(actInfo(1).Dimension) } )

gro=3×1 cell array
    {4×1 single}
    {[ -0.0945]}
    {3×1 single}

The result is a cell array with as many elements as the number of input channels. Each element contains the derivatives of the sum of the outputs with respect to each component of the input channel. Display the gradient with respect to the element of the second channel.

gro{2}

ans = single
    -0.0945

Obtain the gradient with respect of five independent sequences, each one made of nine sequential observations.

gro_batch = gradient(critic,"output-input", ...
                { rand([obsInfo(1).Dimension 5 9]) , ...
                  rand([obsInfo(2).Dimension 5 9]) , ...
                  rand([actInfo(1).Dimension 5 9]) } )

gro_batch=3×1 cell array
    {4×1×5×9 single}
    {1×1×5×9 single}
    {3×1×5×9 single}

Display the derivative of the sum of the outputs with respect to the third observation element of the first input channel, after the seventh sequential observation in the fourth independent batch.

gro_batch{1}(3,1,4,7)

ans = single
    0.0693

Set the option to accelerate the gradient computations.

critic = accelerate(critic,true);

Calculate the gradients of the sum of the outputs with respect to the parameters, given a random observation.

grp = gradient(critic,"output-parameters", ...
                { rand(obsInfo(1).Dimension) , ...
                  rand(obsInfo(2).Dimension) , ...
                  rand(actInfo(1).Dimension) } )

grp=11×1 cell array
    { 5×4  single                                                   }
    { 5×1  single                                                   }
    { 5×1  single                                                   }
    { 5×1  single                                                   }
    { 5×3  single                                                   }
    { 5×1  single                                                   }
    {32×15 single                                                   }
    {32×8  single                                                   }
    {32×1  single                                                   }
    {[-0.0140 -0.0424 -0.0676 -0.0266 -0.0166 -0.0915 0.0405 0.0315]}
    {[                                                            1]}

Each array within a cell contains the gradient of the sum of the outputs with respect to a group of parameters.

grp_batch = gradient(critic,"output-parameters", ...
                { rand([obsInfo(1).Dimension 5 9]) , ...
                  rand([obsInfo(2).Dimension 5 9]) , ...
                  rand([actInfo(1).Dimension 5 9]) } )

grp_batch=11×1 cell array
    { 5×4  single                                                     }
    { 5×1  single                                                     }
    { 5×1  single                                                     }
    { 5×1  single                                                     }
    { 5×3  single                                                     }
    { 5×1  single                                                     }
    {32×15 single                                                     }
    {32×8  single                                                     }
    {32×1  single                                                     }
    {[-2.0333 -10.3220 -10.6084 -1.2850 -4.4681 -8.0848 9.0716 3.0989]}
    {[                                                             45]}

If you use a batch of inputs, gradient uses the whole input sequence (in this case nine steps), and all the gradients with respect to the independent batch dimensions (in this case five) are added together. Therefore, the returned gradient always has the same size as the output from getLearnableParameters.

Accelerate Gradient Computation for a Discrete Categorical Actor

Create observation and action specification objects (or alternatively use getObservationInfo and getActionInfo to extract the specification objects from an environment). For this example, define an observation space with two channels. The first channel carries an observation from a continuous four-dimensional space. The second carries a discrete scalar observation that can be either zero or one. Finally, the action space consist of a scalar that can be -1, 0, or 1.

obsInfo = [rlNumericSpec([4 1]) 
           rlFiniteSetSpec([0 1])];

actInfo =  rlFiniteSetSpec([-1 0 1]);

Create a deep neural network to be used as approximation model within the actor. The output layer must have three elements, each one expressing the value of executing the corresponding action, given the observation. To create a recurrent neural network, use sequenceInputLayer as the input layer and include an lstmLayer as one of the other network layers.

% Define paths
inPath1 = [ 
    sequenceInputLayer(prod(obsInfo(1).Dimension))
    fullyConnectedLayer(prod(actInfo.Dimension),Name="fc1") 
    ];

inPath2 = [ 
    sequenceInputLayer(prod(obsInfo(2).Dimension))
    fullyConnectedLayer(prod(actInfo.Dimension),Name="fc2") 
    ];

% Concatenate previous paths outputs along first dimension
jointPath = [ 
    concatenationLayer(1,2,Name="cct")
    tanhLayer
    lstmLayer(8,OutputMode="sequence")
    fullyConnectedLayer( ...
        prod(numel(actInfo.Elements)), ...
        Name="jntfc")
        ];

% Assemble dlnetwork object
net = dlnetwork;
net = addLayers(net,inPath1);
net = addLayers(net,inPath2);
net = addLayers(net,jointPath);

% Connect layers
net = connectLayers(net,"fc1","cct/in1");
net = connectLayers(net,"fc2","cct/in2");

% Plot network
plot(net)

% initialize network and display the number of weights.
net = initialize(net);
summary(net)

   Initialized: true

   Number of learnables: 386

   Inputs:
      1   'sequenceinput'     Sequence input with 4 dimensions
      2   'sequenceinput_1'   Sequence input with 1 dimensions

Since each element of the output layer must represent the probability of executing one of the possible actions the software automatically adds a softmaxLayer as a final output layer if you do not specify it explicitly.

Create the actor with rlDiscreteCategoricalActor, using the network and 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 return a vector of probabilities for each possible action, use evaluate.

[prob,state] = evaluate(actor, ...
                { rand(obsInfo(1).Dimension) , ...
                  rand(obsInfo(2).Dimension) });
prob{1}

ans = 3x1 single column vector

    0.3403
    0.3114
    0.3483

To return an action sampled from the distribution, use getAction.

act = getAction(actor, ...
                { rand(obsInfo(1).Dimension) , ...
                  rand(obsInfo(2).Dimension) });
act{1}

ans = 1

Set the option to accelerate the gradient computations.

actor = accelerate(actor,true);

Each array within a cell contains the gradient of the sum of the outputs with respect to a group of parameters.

grp_batch = gradient(actor,"output-parameters", ...
                        { rand([obsInfo(1).Dimension 5 9]) , ...
                          rand([obsInfo(2).Dimension 5 9])} )

grp_batch=9×1 cell array
    {[-3.1996e-09 -4.5687e-09 -4.4820e-09 -4.6439e-09]}
    {[                                    -1.1544e-08]}
    {[                                    -1.1321e-08]}
    {[                                    -2.8436e-08]}
    {32x2 single                                      }
    {32x8 single                                      }
    {32x1 single                                      }
    { 3x8 single                                      }
    { 3x1 single                                      }

If you use a batch of inputs, the gradient uses the whole input sequence (in this case nine steps), and all the gradients with respect to the independent batch dimensions (in this case five) are added together. Therefore, the returned gradient always has the same size as the output from getLearnableParameters.

Input Arguments

oldAppx — Function approximator object

function approximator object

Function approximator object, specified as one of the following:

• rlValueFunction object — Value function critic

• rlQValueFunction object — Q-value function critic

• rlVectorQValueFunction object — Multi-output Q-value function critic with a discrete action space

• rlContinuousDeterministicActor object — Deterministic policy actor with a continuous action space

• rlDiscreteCategoricalActor — Stochastic policy actor with a discrete action space

• rlContinuousGaussianActor object — Stochastic policy actor with a continuous action space

• rlContinuousDeterministicTransitionFunction object — Continuous deterministic transition function for a model based agent

• rlContinuousGaussianTransitionFunction object — Continuous Gaussian transition function for a model based agent

• rlContinuousDeterministicRewardFunction object — Continuous deterministic reward function for a model based agent

• rlContinuousGaussianRewardFunction object — Continuous Gaussian reward function for a model based agent.

• rlIsDoneFunction object — Is-done function for a model based agent.

useAcceleration — Option to use acceleration for gradient computations

false (default) | true

Option to use acceleration for gradient computations, specified as a logical value. When useAcceleration is true, the gradient computations are accelerated by optimizing and caching some inputs needed by the automatic-differentiation computation graph. For more information, see Deep Learning Function Acceleration for Custom Training Loops.

Output Arguments

newAppx — Actor or critic

approximator object

New actor or critic, returned as an approximator object with the same type as oldAppx but with the gradient acceleration option set to useAcceleration.

Version History

Introduced in R2022a

R2024a: accelerate is not recommended

accelerate is no longer recommended.

Instead of using accelerate to accelerate the gradient computation of a function approximator object, use dlaccelerate on your loss function. Then use dlfeval on the AcceleratedFunction object returned by dlaccelerate.

This workflow is shown in the following table.

accelerate: Not Recommended	dlaccelerate: Recommended
actor = accelerate(actor,true); g = gradient(actor,@customLoss,u); g{1} where: function loss = customLoss(y,varargin) loss = sum(y{1}.^2);	f = dlaccelerate(@customLoss); g = dlfeval(@customLoss,actor,dlarray(u)); g{1} where: function g = customLoss(actor,u) y = evaluate(actor,u); loss = sum(y{1}.^2); g = dlgradient(loss,actor.Learnables);

For more information, see also gradient is not recommended.

For more information on using dlarray objects for custom deep learning training loops, see dlfeval, AcceleratedFunction, dlaccelerate.

For an example, see Train Reinforcement Learning Policy Using Custom Training Loop and Custom Training Loop with Simulink Action Noise.